Organized by: Stephanie Dodson (University of California, Davis, United States), Scott McCalla (Montana State University, United States)

• Stephanie Dodson (University of California, Davis, United States)
  "One-dimensional spiral waves and reflection-induced cardiac arrhythmia"
When propagated action potentials in cardiac tissue interact with local heterogeneities, counter propagating or reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation is not well understood, their existence is linked to that of one-dimensional (1D) spiral waves. Thus, understanding the existence and stability of 1D spirals plays a crucial role in determining the likelihood of the unwanted reflected pulses. Mathematically, we probe these issues by viewing the 1D spiral as a time-periodic antisymmetric source defect. Through a combination of direct numerical simulation and continuation methods, we investigate its existence and stability in a qualitative ionic model to determine how the systems propensity for reflections are influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral is an unstable periodic orbit that emerges through a global rearrangement of heteroclinic orbits and we identify key parameters and physiological processes that promote and deter reflection behavior.
• Matt Holzer (George Mason University, United States)
  "Locked fronts in a discrete time discrete space population model"
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking where rational speed invasion fronts are observed to persist as parameters are varied. In this article, we construct locked fronts for a particular piecewise linear reproduction function. These fronts are shown to be linear combinations of exponentially decaying solutions to the linear system near the unstable state. Based upon these front solutions we then derive expressions for the boundary of locking regions in parameter space. We obtain leading order expansions for the locking regions in the limit as the migration parameter tends to zero. Strict spectral stability in exponentially weighted spaces is also established.
• Tracy Stepien (University of Florida, United States)
  "Traveling Waves of a Go-or-Grow Model of Glioma Growth"
Glioblastoma multiforme is an aggressive brain tumor that is extremely fatal. Gliomas are characterized by both high amounts of cell proliferation as well as diffusivity, which make them impossible to remove with surgery alone. To gain insight on the mechanisms most responsible for tumor growth and the difficult task of forecasting future tumor behavior, we investigate a mathematical model in which tumor cell motility and cell proliferation are considered as separate processes. We explore the existence of traveling wave solutions and determine conditions for various wave front forms.
• Scott McCalla (Montana State University, United States)
  "Nonlocal interfacial dynamics in biological systems"
Biological pattern formation has been extensively studied using reaction-diffusion and agent-based models. In this talk we will discuss nonlocal pattern forming mechanisms in the context of bacterial colony formation and surface striping on animals with an emphasis on arrested fronts. This will lead to a novel nonlocal framework to understand the interfacial motion in biological systems. We will then use this approach to model an interesting bacterial phenomenon, and to understand simple microscopic requirements for flat stripe solutions to persist in nature. We will then examine moving defect patterns in the nonlocal framework.

Organized by: Robert Planqué (Vrije Universiteit Amsterdam, Netherlands), Diego Oyarzún (University of Edinburgh, United Kingdom), Mustafa Khammash (ETH Zurich, Switzerland)

• Elisa Franco (University of California Los Angeles, United States)
  "Ultrasensitive feedback controllers for quasi-integral feedback"
Biological organisms regulate many of their properties so they fall in a prescribed range, for example temperature, osmotic pressure, and glucose levels. The capacity to preserve a desired condition is enabled by feedback loops that adjust gene expression or metabolism in response to changes or perturbations in the environment. Theory developed in automation engineering indicates that the best way to reject perturbations in a feedback system is to include components that integrate (maintain memory) of past effects of the disturbances, and are known as integrators. While models of biological networks such as osmoregulation and chemotaxis are known to include integral feedback, a different question is how to build molecular integral control systems from the bottom up. With mathematical modeling I will describe how ultrasensitive components can be helpful within feedback loops to maintain a desired gene expression level. I will also discuss a particular ultrasensitive reaction network that combines molecular sequestration and an activation/deactivation cycle, and could be used not only for maintaining a steady state but also for setting a tunable reference. I will finally provide an overview of ongoing projects in our group focused on the role of ultrasensitivity in the context of molecular computation and non-equilibrium kinetics.
• Jorge I. Poveda (University of Colorado, Boulder, United States)
  "High-Performance Online Optimization of Bioreactor Systems via Non-Smooth and Hybrid Extremizing Feedback Controllers"
It is well-known that bioreactor systems are highly nonlinear and difficult to model in a precise way by using first principles. Yet, substantial economic benefits can be achieved when the system operates at optimal points, which are difficult to calculate offline. Instead, to achieve this optimal operation in real time, different types of feedback controllers with online adaptation have been developed during the last decades. However, a persistent challenge in most existing approaches is the emergence of prohibitively slow rates of convergence and potentially small basins of attraction, which difficult the tuning of the controller in practical settings. To address these problems, in this talk we will explore a new class of extremizing control algorithms, grounded on ideas from non-smooth control and hybrid control theory, which can overcome some of the limitations of existing approaches based on smooth feedback control laws. We will illustrate our theoretical results via numerical examples in two different types of models of bioreactors.
• Mustafa Khammash (ETH Zurich, Switzerland)
  "Beyond Perfect Adaptation: Biological Antithetic Controllers for Enhanced Transient Performance"
Proportional-Integral-Derivative (PID) feedback controllers have been the most widely used controllers in the industry for almost a century due to their simplicity and intuitive operation. Motivated by their success in various engineering disciplines, PID controllers are being explored for use in molecular biology. In this talk, we consider the mathematical realization of PID controllers using biomolecular interactions based on the antithetic controller motif. We propose a simple PID architecture based on a combination of feedback and incoherent feedforward and demonstrate its capability of enhancing the transient dynamics and reducing cell-to-cell variability.
• Diego Oyarzún (University of Edinburgh, United Kingdom)
  "Multiobjective optmization of metabolic control systems"
Progress in genetic engineering now allows the construction of molecular circuits inside living cells. In this talk I will present our approach to design such systems using multiobjective optimization. We focus on feedback control circuits designed to steer cellular metabolism toward the production of high-value chemicals. Starting from two-timescale ODE model, we pose and solve cost-benefit optimisation problems for control systems built in the literature so far. The results reveal previously unknown trade-offs between optimality, performance and robustness of metabolic control systems. Our results lay the groundwork for the automated design of control circuits in synthetic biology, with applications in the food, energy and pharma sectors.

Organized by: Paul Atzberger (University of California Santa Barbara, USA), Smita Krishnaswamy (Yale University, USA), Kevin Lin (University of Arizona, USA)
Note: this minisymposia has multiple sessions. The second session is MS09-DDMB.

• Smita Krishnaswamy (Yale University, USA)
  "Geometric and Topological Approaches to Representation Learning in Biomedical Data"
High-throughput, high-dimensional data has become ubiquitous in the biomedical, health and social sciences as a result of breakthroughs in measurement technologies and data collection. While these large datasets containing millions of observations of cells, peoples, or brain voxels hold great potential for understanding generative state space of the data, as well as drivers of differentiation, disease and progression, they also pose new challenges in terms of noise, missing data, measurement artifacts, and the so-called “curse of dimensionality.” In this talk, I will cover data geometric and topological approaches to understanding the shape and structure of the data. First, we show how diffusion geometry and deep learning can be used to obtain useful representations of the data that enable denoising (MAGIC), dimensionality reduction (PHATE), and factor analysis (Archetypal Analysis Network) of the data. Next we will show how to learn dynamics from static snapshot data by using a manifold-regularized neural ODE-based optimal transport (TrajectoryNet). Finally, we cover a novel approach to combine diffusion geometry with topology to extract multi-granular features from the data (Diffusion Condensation and Multiscale PHATE) to assist in differential and predictive analysis. On the flip side, we also create a manifold geometry from topological descriptors, and show its applications to neuroscience. Together, we will show a complete framework for exploratory and unsupervised analysis of big biomedical data.
• Sui Tang (UCSB, United States)
  "Data-driven discovery of interacting particle system using Gaussian processes"
Interacting particle or agent systems are widely used to model complicated collective motions of animal groups in biological science, such as flocking of birds, milling of fish, and swarming of prey. A fundamental goal is to understand the link between individual interaction rules and collective behaviors. We consider second-order interacting agent systems and study an inverse problem: given observed data, can we discover the interaction rule? For the interactions that only depends on pairwise distance, we propose a learning approach based on Gaussian processes that can simultaneously infer the interaction kernel without assuming a parametric form and learn other unknown parameters in the governing equations. The numerical results on prototype systems, including Cuker-Smale dynamics and fish milling dynamics, show that our approach produced faithful estimators from scarce and noisy trajectory data and made accurate predictions of collective behaviors. This talk is based on the joint work with Jinchao Feng.
• Rose Yu (University of California San Diego, USA)
  "Physics-Guided Deep Learning for Forecasting COVID-19"
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• Alan Aspuru-Guzik (University of Toronto, USA)
  "Artificial Intelligence and Self-Driving Laboratories for Molecular Discovery"
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Organized by: Rebecca Tyson (University of British Columbia, Canada), Maria Martignoni (Memorial University of Newfoundland, Canada), Frithjof Lutscher (University of Ottawa, Canada)
Note: this minisymposia has multiple sessions. The second session is MS07-ECOP.

• Juliana Berbert (Universidade Federal do ABC, Brazil)
  "Dessication-rehydration stress revealed by sugar-metabolite-reserve model"
We focus on the evaluation of photosynthetic organisms. Some species and tissues can endure periods of the dry season because they rely on robust dynamics of metabolites. The metabolic dynamics are complex and challenging to address because the system involves several steps, usually with hundreds of metabolites. The metabolite densities vary among species and tissues and respond to external conditions, such as an environmental stimulus like water supply. Understanding these responses, particularly the dessication-rehydration processes, are important both economically and evolutionarily, especially in the presence of climate change. Therefore, we propose a new way to analyze the dynamics of metabolites with a compartmental model which explores the metabolites’ density-dependence on water explicitly. We use a mathematical formulation to model the dynamics among three essential metabolite classes: sugar (S), active metabolite (A), and reserve accumulation (R). Through stability analysis and numerical solutions, we characterize regions on the phase space, defined by the transition rates between the classes S to A and S to R, where the system diverges or approaches zero. We show that different species and tissues respond distinctly to dessication processes, being more or less resilient according to the transition rates between the compartments of the model. Furthermore, the effects of water supply fluctuation, due to the dessication-rehydration processes, show that unless the organism has a robust reservoir for metabolism, the system cannot support itself for a long time. Many results corroborate experimental observations, and others provide a new perspective on the studies of metabolic dynamics, such as the significance of the metabolism reservoir. We understand that knowing the organism’s response to abiotic changes, particularly that of the water supply, may improve our management of the use of these organisms, for example, in the crop field during climate changes.
• Chris Heggerud (University of Alberta, Canada)
  "Niche differentiation in the light spectrum promotes coexistence of phytoplankton species: a spatial modeling approach."
The paradox of the plankton highlights the contradiction between Gause's law and the observed diversity of phytoplankton. It is well known that phytoplankton dynamics depend heavily on two main resources; light and nutrients. Here we consider light as a continuum of resources rather than a single resource. We propose a spatially explicit RD model to explore under what circumstance coexistence is possible from a mathematical and biological perspective. Furthermore, we provide biological context as to when coexistence is expected based on the degree of niche differentiation within the light spectrum and overall turbidity of the water.
• Pau Capera Aragones (University of British Columbia Okanagan, Canada)
  "Differential equation model for central-place foragers with memory: Implications for bumble bee crop pollination"
Bumble bees provide valuable pollination services to crops around the world. However, their populations are declining in intensively farmed landscapes. Understanding the dispersal behaviour of these bees is a key step in determining how agricultural landscapes can best be enhanced for bumble bee survival. In our work, we develop a partial integro-differential equation model to predict the spatial distribution of foraging bumble bees in dynamic heterogeneous landscapes. In our model, the foraging population is divided into two subpopulations, one engaged in an intensive search mode (modeled by diffusion) and the other engaged in an extensive search mode (modeled by advection). Our model considers the effects of resource-dependent switching rates between movement modes, resource depletion, central-place foraging behaviour, and memory. We use our model to investigate how crop pollination services are affected by wildflower enhancements. We find that planting wildflowers adjacent to a crop can increase the pollination services to the crop, and we quantify this benefit as a function of the location, quantity, and quality of the planted wildflowers.
• Rebecca Tyson (University of British Columbia Okanagan, Canada)
  "Phase-sensitive tipping: Cyclic ecosystems subject to contemporary climate"
Global change is expected to lead to increased reddening and amplitude of climate noise. In this paper we explore how these changes in climate variability could interact with systems that are already oscillating, namely, predator-prey systems. We include an Allee effect in the prey equation so that we can determine whether or not extinction is deterministically possible. We identify the phase of the predator-prey cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. Our analysis of these examples uncovers a counter-intuitive behaviour, which we call phase-sensitive tipping (or P-tipping), where tipping to extinction occurs only from certain phases of the cycle. We find that P-tipping can occur in both the Rosenzweig-MacArthur (RM) and Leslie-Gower-May (LGM) model systems, and for realistic parameter values for the Canada lynx and snowshoe hare. Our work identifies a new mechanism for climate-induced extinction.

Organized by: (Natasha Ellison, University of Sheffield, UK), Alexander Fletcher (University of Sheffield, UK), Nick Monk (University of Sheffield, UK)

• Joanna Wares and Marcella Torres (Department of Mathematics and Computer Science, University of Richmond, USA)
  "Making Sense of COVID-19: Mathematics and Data Science Activities Across the Curriculum"
We present mathematical modeling and data science activities created around analyzing and interpreting COVID-19 data. Some of these activities and projects address complex social issues related to COVID-19 such as inequality in testing, wealth distributions, or disparity in health outcomes. Preliminary data suggest that COVID-19 disproportionately impacts minorities and low-income households. Much of the instructional guidance provided for the activities and projects is easily adaptable to a remote learning environment, and each activity includes reflection and discussion in addition to the quantitative work. Mathematical topics covered include: modeling the spread of infectious disease, hypothesis testing, simulation, and data fitting. In addition, we share some of our experiences in teaching these activities across the curriculum, from workshops for high school students, throughout the calculus sequence, to upper-level differential equations courses.
• Padmanabhan Seshaiyer (George Mason University, Fairfax, Virginia, USA)
  "Educational frameworks for upskilling the next generation workforce in mathematical biology"
In this talk, we will introduce some novel educational frameworks that provide the opportunity to not only engage students in the tools to represent, understand, analyze and solve real world problems in mathematical biology but also engage them in using tools to make data-driven informed predictions. Such upskilling approaches can help students to become life-long learners going beyond a content-based education in mathematical biology to also include a competency-based training. In particular, mathematical biology must include a variety of learning approaches including experiential learning, inquiry-based learning, challenge based learning and interdisciplinary problem-based learning. In this talk, we will consider some authentic tasks that incorporate a shared collaborative experience with innovative pedagogical practices to advance teaching and learning of mathematical biology in the 21st century.
• Perry Hartland-Asbury (Radley college, UK)
  "Modelling Mathematics in Secondary Schools"
A whistle-stop tour looking at how modelling of mathematical modelling (and Biology in particular) is incorporated into UK secondary school teaching, from Key Stage 3, GCSE and A-level teaching.
• Thomas Woolley (Cardiff University, UK)
  "Interactive mathematical biology: how to create your first shiny app"
This will be a live coding session in which I demonstrate how to turn the discrete logistic equation into an interactive applet that students can explore. Once you generate one app you can generate many others, or even get kids learning how to write their own codes. I’ll start with the basics in a spread sheet package, so very little coding knowledge will be needed. However, it will be useful if you download R: https://www.r-project.org/ Download R studio as a developer environment (the free one is fine) https://www.rstudio.com/products/rstudio/download/ Make a shiny account. This is the service that will host the app. https://www.shinyapps.io/ Finally, having a github account as somewhere to store your code and make it accessible is also useful. https://github.com/ By providing interactive applets you allow anyone to explore the mathematics of reproduction, modelling and chaos. This experimentation can be a useful tool for clarifying ideas for secondary school students all the way to graduate students. For those who want a sneak peak, we’ll try to create something like https://thomasewoolley.shinyapps.io/Discrete_logistic_equation/, the code for which can be found here https://github.com/ThomasEWoolley/Discrete_logistic_equation

Organized by: Chiu-Yen Kao (Claremont McKenna College, United States), Bo Zhang (Oklahoma State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS09-EVOP. The third session is MS10-EVOP.

• Suzanne Lenhart (University of Tennessee, United States)
  "Optimal control for management of an invasive population model with diffusion in a river"
Invasive species in rivers may be managed by changing flow rates. Using a partial differential equation model with diffusion representing an invasive population in a river, we consider optimal control of the time-varying water discharge rate to keep the population downstream. We will present some numerical results with varying parameters to illustrate the movement of the invasive population.
• Idriss Mazari (Institute of Analysis and Scientific Computing, TU Wien, Austria)
  "Fragmenting and concentrating resources to optimise the total population size: a qualitative analysis"
In this talk, we investigate the optimal way to spread resources inside a domain in order to maximise the total population size. More specifically, we will explain why, when the individuals disperse quickly, it is much better to concentrate resources while, when they disperse slowly, it is more relevant to scatter the resources throughout the domain. The talk will mostly be descriptive, and is based on collaborations with G. Nadin, Y. Privat and D. Ruiz-Balet.
• Yun Kang (Arizona State University, United States)
  "Dynamics of a Diffusion Reaction Prey-Predator Model with Delay in Prey: Effects of Delay and Spatial Components"
We study the complex dynamics of a Monod-Haldane-type predator-prey interaction model that incorporates: (1) A constant time delay in the prey growth; and (2) diffusion in both prey and predator. We provide the rigorous results of our system including the asymptotic stability of a positive equilibrium; Hopf bifurcation; and the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. We also perform numerical simulations on the effects of diffusion or/and delay when the corresponding ODE model has either a unique interior equilibrium with two interior attractors or two interior equilibria. Our theoretical and numerical results show that diffusion can either stabilize or destabilize the system; large delay could destabilize the system; and the combination of diffusion and delay could intensify the instability of the system. Moreover, when the corresponding ODE system has two interior equilibria, diffusion or time delay in prey or both could lead to the extinction of predator. Our results may provide us useful biological insights on population managements for prey-predator interaction systems.
• Noelle Beckman (Biology Department & Ecology Center, Utah State University, United States)
  "Population persistence of plants under global change"
Climate change and habitat loss are two of the primary causes of global biodiversity loss. Habitats gradually become unsuitable as temperature, rainfall, and related climatic variables change. In addition to climate change, 75% of the land surface around the world has been converted by humans. As habitats shift, species must adapt to the new conditions, move to stay within their suitable habitat, or die. We examine the global distribution of species’ vulnerabilities to climate change and habitat loss using integrodifference equations. With information on demography and dispersal, we can quantify a population’s spreading speed -- the ability of a population to shift its range -- and its critical patch size – the size of habitat where population growth due to reproduction balances population loss through dispersal. We analyze the distributions of spreading speeds and critical patch sizes across a defined set of species within a system (e.g., community or taxonomic group). We use a range of distributions for population growth rates and dispersal. We analyzed the distributions for spreading speeds and critical patch sizes when dispersal variance and the geometric growth rates are independent and either fixed or distributed according to an exponential, gamma, modified gamma, or log-normal. We can use these distributions to estimate the proportion of species that can shift their ranges in response to climate change or persist based on a minimum critical patch size. This approach allows us to predict responses to environmental change across a broad range of species for which data may be lacking, and this is particularly important for developing indicators of biodiversity loss and planning of remedial actions.

Organized by: Jennifer Mueller (Colorado State University, United States)

• Bradford Smith (Department of Bioengineering, University of Colorado Denver | Anschutz Medical Campus, United States)
  "Ventilator waveform analysis to diagnose and prevent ventilator-induced lung injury"
Acute respiratory distress syndrome (ARDS) is caused by diverse factors including sepsis, trauma, and COVID-19. The derangements of lung function associated with ARDS necessitate mechanical ventilation to sustain life. However, the mechanical ventilator can also cause additional ventilator-induced lung injury that leads to worse ARDS outcomes. Adjusting the mechanical ventilator to minimize VILI is a challenging task because the injurious forces are functions of the applied ventilation and the mechanical properties of the lung which, in turn, depend on injury severity and type. As such, the optimal ventilation settings for each patient are likely different, change with time, and are not readily discernable from clinical data. To address this challenge, our long-term goal is to develop a system to numerically identify and apply the optimally lung-protective ventilation for any particular patient. The first step is to develop and validate simulations that can accurately predict the response of the injured lung to changes in ventilator settings. We have developed a compartment model of the respiratory system that accounts for nonlinear tissue elastance, lung resistance, and the nonlinear dynamics of alveolar recruitment. The model parameters are identified by fitting to pressures and volumes measured in mechanically ventilated mice (the training data). The model predictions are compared to evaluation data collected in the same animal to show that this approach provides accurate predictions of the response of the injured lung to ventilator adjustments. The model outputs also provide an accurate assessment of lung injury severity when compared to gold-standard lung function assessments performed using flexiVent research ventilators.
• Emily Heavner (Colorado State University, United States)
  "Estimation of airway resistance throughout the bronchial tree from mechanical ventilation output data"
We introduce a multi-compartment lung model based on resistance-capacitor circuits using an analogy between electric circuits and the human lungs. Multiple literature sources reveal a wide range of clinically used values for airway resistance, motivating an investigation to determine the role of airway resistance in the alveolar tree. The inverse problem of computing the vector of airway resistance values in the alveolar tree is studied using a linear least squares optimization approach. We compare the outputs of the model to real-world parameters collected from mechanical ventilation data of COVID-19 positive and negative patients.
• Bela Suki (Dept. Biomedical Engineering, Boston University, United States)
  "Inflation instability in the lung: An analytical model of a thick-walled alveolus with wavy fibers under large deformations"
Inflation of hollow elastic structures can become unstable and exhibit a runaway phenomenon if the tension in their walls does not rise rapidly enough with increasing volume. Biological systems avoid such inflation instability for reasons that remain poorly understood. This is best exemplified by the lung, which inflates over its functional volume range without instability. The goal of this study was to determine how the constituents of lung parenchyma determine tissue stresses that protect alveoli from instability-related over-distension during inflation. We present an analytical model of a thick-walled alveolus composed of wavy elastic fibers, and investigate its pressure-volume behavior under large deformations. Using second harmonic generation imaging, we found that collagen waviness follows a beta distribution. Using this distribution to describe human pressure-volume curves, we estimated collagen and elastin effective stiffnesses to be 1247 and 18.3 kPa, respectively. Furthermore, we demonstrate that linearly elastic but wavy collagen fibers are sufficient to achieve inflation stability within the physiological pressure range if the alveolar thickness-to-radius ratio > 0.05. Our model thus identifies the constraints on alveolar geometry and collagen waviness required for inflation stability and provides a multiscale link between alveolar pressure and stresses on fibers in healthy and diseased lungs.
• Vitor Mori (University of Vermont, United States)
  "Modelling the progression of Ventilation-Induced Lung Injury in Mice"
Mechanical ventilation is a crucial tool in the management of acute respiratory distress syndrome, yet it may itself also further damage the lung in a phenomenon known as ventilator-induced lung injury (VILI). We have previously shown in mice that volutrauma and atelectrauma act synergistically to cause VILI. We have also postulated that this synergy arises because of a rich-get-richer mechanism in which repetitive lung recruitment generates initial small holes in the blood-gas barrier which are then expanded by over-distension in a manner that favors large holes over small ones. In order to understand the causal link between this process and the derangements in lung mechanics associated with VILI, we developed a mathematical model that incorporates both atelectrauma and volutrauma to predict how the propensity of the lung to derecruit depends on the accumulation of plasma-derived fluid and proteins in the airspaces. We found that the model accurately predicts derecruitment in mice with experimentally induced VILI.

Organized by: Lihong Zhao (University of California Merced, United States), Ling Xue (Harbin Engineering University, China), Suzanne Sindi (University of California Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS09-MEPI.

• Folashade Agusto (Ecology and Evolutionary Biology, University of Kansas, United States)
  "Playing with fire: Modeling the effects of prescribed fire on Lyme disease"
Tick-borne illnesses are trending upward and are an increasing source of risks to people’s health in the United States; furthermore, the range of tick habitats is expanding due to climate change. Thus, it is imperative to find a practical and cost-efficient way of managing tick populations. Prescribed burns are a common form of land management, it can be cost efficient if properly managed. In this seminar, I will present a compartmental model for ticks carrying Lyme disease using an impulsive system, and then investigate the effect of prescribed fire intensity and the duration between burns. Our study found that fire intensity has a larger impact in reducing tick population than frequency between burns. Furthermore, burning at high intensity is preferable to burning at low intensity whenever possible, although high intensity burns may be unrealistic due to environmental factors. Annual burns resulted in the most significant reduction of infectious nymphs, which are the primary carriers of Lyme disease.
• Fabian Santiago (Department of Applied Mathematics, University of California Merced, United States)
  "Mathematical Assessment of Intervention Strategies for Mitigating COVID-19 Transmission in a University Setting "
In March 2020, the University of California, Merced (UC Merced), along with other universities throughout the United States moved to an on-line only mode of course delivery to decrease the spread of SARS-CoV-2, the virus responsible for the COVID-19 disease. During that time, the UC Merced leadership focused on how to safely bring students back to the campus in the Fall. At UC Merced this involved using mathematical models to evaluate the effectiveness of proposed mitigation strategies for containing the spread of COVID-19 within the university setting. In this talk I will discuss the mathematical model we used to evaluate Fall 2021 re-opening strategies and present a global sensitivity analysis of the contact and infection model parameters that govern the transmission dynamics of COVID-19 within the university setting.
• Zhuolin Qu (Department of Mathematics, The University of Texas at San Antonio, United States)
  "Modeling the invasion wave of Wolbachia in mosquitoes for controlling mosquito-borne diseases"
We develop and analyze partial differential equation (PDE) models to study the transmission and invasion dynamics of Wolbachia infection among the wild mosquitoes. Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as Zika, Chikungunya, and dengue fever, and releasing Wolbachia-infected mosquitoes is a rising biological control to mitigate these diseases. Both field trials and previous modeling studies have shown that the Wolbachia infection among the mosquitoes needs to exceed a threshold level to persist in time. To give a realistic prediction of the threshold condition, it is critical to capture the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes, which is created by the local introduction of the infection in the field release. We derive reaction-diffusion-type PDE models from the existing ordinary differential equation (ODE) models to better characterize the spatial invasion of Wolbachia infection into the native mosquitoes. The models account for both the complex vertical transmission parameters (inherited from the ODE models) and the horizontal transmission of infection (spatial diffusion). We analyze the threshold condition of establishing a successful invasion, the “critical bubble”, for the spatial models, and we compare it with the level in the spatially homogenous setting. We also show that the proposed PDE models can give rise to the traveling waves of Wolbachia infection. We then quantify how the magnitude of the diffusion coefficient can impact the threshold condition and the shape and velocity of the traveling front, and we numerically study different scenarios that may inform the design of the field release strategies.
• Christopher Remien (Department of Mathematics and Statistical Sciences, University of Idaho, United States)
  "Reservoir population dynamics and pathogen epidemiology drive pathogen genetic diversity, spillover, and emergence"
When several factors align, pathogens that normally infect wildlife can spill over into the human population. If pathogen transmission within the human population is self-sustaining, or rapidly evolves to be self-sustaining, novel human pathogens can emerge. Although many factors influence the likelihood of spillover and emergence, the rate of contact between humans and wildlife is critical. Thus, for those pathogens inhabiting wildlife reservoirs with pronounced seasonal fluctuations in population density, it is broadly recognized that spillover risk also varies with season. What remains unknown, however, is the extent to which seasonal fluctuations in reservoir populations influence the evolutionary dynamics of pathogens in ways that affect the likelihood of emergence. Here, we use mathematical models and stochastic simulations to show that seasonal fluctuations in reservoir population densities lead to seasonal increases in genetic variation within pathogen populations and thus influence the waiting time for mutations capable of sustained human-to-human transmission. These seasonal increases in genetic variation also lead to elevated risk of emergence at predictable times of year.  

Organized by: Erica Rutter (University of California, Merced, United States), Suzanne Sindi (University of California, Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS07-MFBM.

• Ali Heydari ((i) UC Merced Department of Applied Mathematics and (ii) Health Sciences Research Institute at UC Merced, USA)
  "Deep Generative Models for Realistic Single-Cell RNA-Seq Data Augmentation"
Single-cell RNA sequencing (scRNAseq) technologies allow for measurements of gene expression at a single-cell resolution. This provides researchers with a tremendous advantage for detecting heterogeneity, delineating cellular maps or identifying rare subpopulations. However, a critical challenge remains: the low number of single-cell observations due to limitations by cost or rarity of subpopulation. This absence of sufficient data may cause inaccuracy or irreproducibility of downstream analysis. In this talk, we present ACTIVA (Automated Cell-Type-informed Introspective Variational Autoencoder): a novel deep learning framework for generating realistic synthetic data using a single-stream adversarial variational autoencoder conditioned with cell-type information. We train and evaluate ACTIVA, and competing models, on multiple public scRNAseq datasets. Under the same conditions, ACTIVA trains up to 17 times faster than the GAN-based state-of-the-art model while performing better or comparably in our quantitative and qualitative evaluations. We show that augmenting rare-populations with ACTIVA significantly increases the classification accuracy of the rare population (more than 45% improvement in our rarest test case). Data generation and augmentation with ACTIVA can enhance scRNAseq pipelines and analysis, such as benchmarking new algorithms, studying the accuracy of classifiers and detecting marker genes. ACTIVA will facilitate analysis of smaller datasets, potentially reducing the number of patients and animals necessary in initial studies.
• Mohammad Jafari (Postdoctoral Scholar, Department of Applied Mathematics Jack Baskin School of Engineering University of California, Santa Cruz, USA)
  "Machine Learning-based Feedback Controller for Directing Stem Cell Membrane Potential"
Driving biological response with spatiotemporal precision can help advance biomedical applications for customized therapeutics where bioelectronic devices are suitable to directly interfacing with the biological systems using bioelectronic actuators and sensors. Implementation of feedback control by using these devices can help achieve this but has not been widely adopted, in part, due to a limited understanding of the complexities involved. Modeling, identification, prediction, and control, which are essential to this end, are challenging due to the presence of uncertainties, stochasticity, unmodeled dynamics, and complex nonlinearities. For example, in biological systems, cellular response can change in different environmental conditions such as changing flow characteristics and temperature. Thus, Machine Learning (ML)-based techniques, which can be applied to solve different modeling and control problems when system dynamics are fully or partially unknown, may prove suitable here. The best-known ML techniques rely on the availability of large datasets a priori and have not been applied to control biological systems using bioelectronic devices. We proposed that ML-based techniques that are explored as control solutions outside of biology for cases involving complex nonlinear systems are also suitable for closing the loop for biological systems [1]. To do this, an adaptive external “sense and respond” learning algorithm is derived using adaptive Lyapunov-based methods [2]. The satisfactory performance of the proposed method is experimentally validated by maintaining the pH in a microfluidic system that houses pluripotent mammalian stem cells. This pH control affects the membrane voltage (Vmem) of the cells that is measured using genetically encoded fluorescent Vmem reporters [3]. To the best of our knowledge, this is the first learning control method demonstrated for biological applications of its kind. [1]. Selberg, J., Jafari, M., Bradley, C., Gomez, M., & Rolandi, M. (2020). Expanding biological control to bioelectronics with machine learning. APL Materials, 8(12), 120904. [2]. Jafari, M., Marquez, G., Selberg, J., Jia, M., Dechiraju, H., Pansodtee, P., ... & Gomez, M. (2020). Feedback Control of Bioelectronic Devices Using Machine Learning. IEEE Control Systems Letters, 5(4), 1133-1138. [3]. Selberg, J., Jafari, M., Mathews, J., Jia, M., Pansodtee, P., Dechiraju, H., ... & Rolandi, M. (2020). Machine Learning‐Driven Bioelectronics for Closed‐Loop Control of Cells. Advanced Intelligent Systems, 2(12), 2000140.
• Thomas de Mondesir (Université Claude Bernard Lyon 1 & UC Merced, France)
  "Generating biological images to train deep-learning-based segmentation models"
Medical and biological imaging are areas where image segmentation plays a critical role when diagnosing pathologies or analysing experimental results study. While recent studies show that methods using deep learning achieve superior accuracy when neural networks are trained on pixel-level labeled data, sufficient amounts of annotated images are often difficult to gather. We introduce an image generation method to produce images containing biological objects and corresponding segmentation masks. Our approach creates realistic images by using B-splines to reproduce shapes of interest. Simulating objects is done by choosing control points and adjusting parameters that allow their geometries to be diverse. Adapted to cases with limited or no training data, our method offers the possibility to train any machine learning based segmentation method on generated images. Obtaining a good segmentation on real images relies on similarity with artificial images.
• Jordan Collignon (University of California, Merced, USA)
  "A High-throughput Pipeline for Analyzing Experimental Images of Sectored Yeast Colonies"
Prion proteins are most commonly associated with fatal neurodegenerative diseases in mammals, but are also responsible for a number of harmless heritable phenotypes in Saccharomyces cerevisiae (yeast). In normal conditions yeast colonies grow in a circular shape with a uniform white or pink color related to the fraction of normal (non-prion) protein in a typical cell. However, under mild experimental manipulations, which introduce changes in protein aggregation dynamics, colonies exhibit red sectors corresponding to cells with no prion protein. Such phenotypic organization provides a rich data set that can be used to uncover relationships between colony-level phenotypic transitions, molecular processes, and individual cell behaviors. In this project, we use deep learning tools to develop an automated image processing pipeline for extracting and quantifying the shape, size, and frequency of sectors in yeast colonies grown under experimental conditions. Our approach will allow us to draw conclusions about the formation of sectors in the experimental data and will help uncover more information about the mechanisms driving colony-level phenotypic transitions.

Organized by: Matea Santiago (University of California, Merced, United States), Shilpa Khatri (University of California, Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS09-MMPB.

• Christiana Mavroyiakoumou (University of Michigan, United States)
  "Large amplitude flutter of membranes"
We study the dynamics of thin membranes---extensible sheets with negligible bending stiffness---initially aligned with a uniform inviscid background flow. This is a benchmark fluid-structure interaction that has previously been studied mainly in the small-deflection limit, where the flat state may be unstable. Related work includes the shape-morphing of airfoils and bat wings. We study the initial instability and large-amplitude dynamics with respect to three key parameters: membrane mass density, stretching rigidity, and pretension. When both membrane ends are fixed, the membranes become unstable by a divergence instability and converge to steady deflected shapes. With the leading edge fixed and trailing edge free, divergence and/or flutter occurs, and a variety of periodic and aperiodic oscillations are found. With both edges free, the membrane may also translate transverse to the flow, with steady, periodic, or aperiodic trajectories.
• Alyssa Taylor (North Carolina State University, United States)
  "Fluid dynamics in hypoplastic left heart syndrome patients in supine and upright positions"
Patients with hypoplastic left heart syndrome (HLHS) have an underdeveloped left heart, leaving them with a single functioning ventricle. Their treatment involves a series of surgeries that create a univentricular (Fontan) circulation and includes a reconstructed aorta. While patients typically survive into adulthood, most experienced cardiovascular problems, including reduced cardiac output. Current clinical assessments are derived from 4D MRI images that quantify 3D flow patterns in the aorta. However, this data does not provide information about energy loss, wave intensity, or cerebral perfusion. This study uses a 1D arterial network model for the Fontan circulation to compute quantities of clinical interest in patients with HLHS. To investigate the effects of vascular reconstruction on perfusion, model predictions will be compared to a single ventricle control patient with a double outlet right ventricle (DORV) and native aorta. Outputs include pressure and flow predictions in vessels of the systemic system for patients at supine rest and upright exercise.
• Christina Hamlet (Bucknell University, Department of Mathematics, United States)
  "Modeling the small-scale ballistics and fluid dynamics of nematocyst firing"
We model the fluid dynamics of nematocyst (stinging cell) firing to shed light on the importance of Reynolds number transitions due to ultrafast accelerations and boundary layer interactions in successful ballistic strategies on the microscale. Nematocyst firing is the fastest-known accelerating mechanism in the natural world and occurs on microscales. In this study, we combine mathematical modeling and computational fluid dynamics to simulate the fluid-structure interactions of an accelerating nematocyst stylus and its target prey coupled to viscous, incompressible fluid. 2D models of a fast-accelerating projectile and a passive target were modeled in an immersed boundary framework. In this presentation, results and insights into the effects of boundary layer interactions on predator-prey dynamics are analyzed and discussed.
• Ebrahim Kolahdouz (University of North Carolina at Chapel Hill, United States)
  "Migration and trapping of deformable blood clots using a sharp interface Lagrangian"
Understanding the transport dynamics and fluid-structure interaction (FSI) of flexible blood clots in the venous vasculature is critical to predicting the performance of embolic protection devices like inferior vena cava (IVC) blood clot filters. IVC filters are metallic medical devices that are implanted in the IVC, a large vein in the abdomen through which blood returns to the heart from the lower extremities, to capture clots before they can migrate to the lungs and cause a potentially fatal pulmonary embolism. In this work, I introduce a FSI framework to simulate the migration and trapping of blood clots in the IVC, which is especially challenging due to the relatively large size of the clots that affects the local fluid dynamics, the large nonlinear deformations that are generated, and the occurrence of contact between the clots, the vein wall, and the implanted device. The proposed sharp interface immersed Lagrangian-Eulerian (ILE) method combines a partitioned approach to FSI with an immersed coupling strategy. Like other partitioned formulations, the ILE approach uses distinct momentum equations for the fluid and solid regions. Unlike body-fitted arbitrary Lagrangian-Eulerian methods, our approach uses a non-conforming discretization of the dynamic fluid-structure interface that is “immersed” in the surrounding fluid and does not require any grid regeneration or mesh morphing to treat large structural deformations. Blood is modeled as a Newtonian fluid and the blood clot is modeled with a non-linear finite element model and nearly incompressible hyperelastic material behavior. Fluid-structure interaction is mediated by a coupling approach that uses the immersed interface method that accounts for both dynamic and kinematic coupling conditions between the fluid and structure. A penalty approach is used to relax the kinematic constraint. Specifically, the penalty formulation uses two representations of the fluid structure interface, including a thin surface mesh and a bulk volumetric mesh, that are connected by forces that impose kinematic and dynamic interface conditions. The dynamics of the volumetric mesh are driven by the accurate exterior fluid traction obtained from the sharp interface approach. Simulation of clot transport and IVC filter trapping are presented. Verification and validation of the simulations is underway and will be performed by comparing with in vitro experimental measurements.

Organized by: Seth Weinberg (The Ohio State University, United States) & Eleonora Grandi (UC Davis, United States)

• Eric Sobie (Icahn School of Medicine at Mount Sinai, United States)
  "Creating cell-specific models to infer changes to pig myocyte physiology after myocardial infarction"
Following myocardial infarction (MI), the region surrounding the infarct scar, known as the border zone (BZ), undergoes heterogeneous remodeling. These changes impact the cardiomyocytes’ electrophysiological behavior resulting in variable changes between myocytes depending on whether cells are near or remote from the BZ. In this study we sought to understand these heterogeneous electrophysiological changes by constraining model parameters, in a cell-by-cell manner, to fit data obtained in individual cells. In experiments, action potentials and intracellular calcium were recorded in cells with and without MI, in the border zone and remote from the MI. A genetic algorithm was run to estimate the ionic conductances in each cell studied (> 40), and repeated runs were performed to estimate the extent to which each conductance was identifiable. Results indicate which conductances exhibit more or less variability than others, and how conductances are altered by MI, in both regions. Overall, the study suggests a methodology for understanding complex disease states in which several variables have been altered.
• Haibo Ni (University of California Davis, United States)
  "Quantifying cAMP- and Ca(2+)-dependent proarrhythmic mechanisms using populations of atrial myocyte and tissue models"
The β-adrenergic receptor (βAR)/cAMP/PKA and multifunctional Ca(2+)-calmodulin-dependent protein kinase II (CaMKII) signaling pathways are key regulators of cardiac excitation-contraction coupling (ECC) by modulating multiple common downstream targets. Hyperactivation of both signaling pathways contributes to the initiation and maintenance of atrial fibrillation (AF), the world’s most common arrhythmia. Here, we developed a novel computational model of human atrial myocytes to couple electrophysiology and Ca(2+) handling with detailed descriptions of βAR/cAMP/PKA and CaMKII pathways. Populations of atrial myocytes revealed a synergy between the PKA and CaMKII effects on the atrial ECC proteins by promoting a vicious cycle of Ca(2+) and membrane potential instabilities. Logistic regression analyses uncovered the relative roles of the ECC proteins and the signaling components in generating cellular arrhythmogenic events. Further, we constructed 2D heterogeneous atrial tissue models and demonstrated that βAR stimulation and CaMKII hyperactivation promote arrhythmogenicity by invoking spontaneous Ca(2+)-overload-mediated action potentials, whereas CaMKII inhibition substantially reduced the vulnerability. Our simulations highlight a novel role of CaMKII-dependent cell-to-cell uncoupling in exacerbating the arrhythmia. Collectively, our simulations reveal synergy in PKA and CaMKII effects on cellular- and tissue-level arrhythmogenic outcomes, and depict a novel paradigm for Ca(2+)-CaMKII-dependent involvement in both enhanced triggered activity and conduction disturbances in AF. These findings suggest that interrupting the vicious cycle of Ca(2+)-CaMKII-Ca(2+) (e.g., via CaMKII inhibition) may be a valuable pharmacotherapy approach to counteract both triggers and functional substrate in AF.
• Nicolae Moise (The Ohio State University, United States)
  "Intercalated Disk Nanoscale Structure Regulates Cardiac Conduction"
The intercalated disk (ID) is a specialized subcellular region that provides electrical and mechanical connections between myocytes in the heart. The ID has a clearly defined passive role in cardiac tissue, transmitting mechanical forces and electrical currents between cells. Recent studies have shown that Na+ channels, the primary current responsible for cardiac excitation, are preferentially localized at the ID, particularly within nanodomains around mechanical and gap junctions, and that perturbations of ID structure alter cardiac conduction. This suggests that the ID may play an important, active role in regulating conduction. However, the structure of the ID and intercellular cleft are not well characterized, and to date, no models have incorporated the influence of ID structure on conduction in cardiac tissue. In this study, we developed an approach to generate realistic finite element model (FEM) meshes replicating ID nanoscale structure, based on experimental measurements from transmission electron microscopy (TEM) images. We then integrated measurements of the intercellular cleft electrical conductivity, derived from the FEM meshes, into a novel cardiac tissue model formulation. FEM-based calculations predict that the distribution of cleft conductances is sensitive to regional changes in ID structure, specifically the intermembrane separation and gap junction distribution. Tissue-scale simulations demonstrated that ID structural heterogeneity leads to significant spatial variation in electrical polarization within the intercellular cleft. Importantly, we find that this heterogeneous cleft polarization regulates conduction by desynchronizing the activation of post-junctional Na+ currents. Additionally, these heterogeneities lead to a weaker dependence of conduction velocity on gap junctional coupling, compared with prior modeling formulations that neglect or simplify ID structure. Further, we find that disruption of local ID nanodomains can lead to either conduction slowing or enhancing, depending on gap junctional coupling strength. Overall, our study demonstrates that ID nanoscale structure can play a significant role in regulating cardiac conduction.
• Jonathan Silva (Washington University in St. Louis, United States)
  "Using molecular detail and genetic background to predict patient response to anti-arrhythmic therapy"
Small molecule anti-arrhythmic therapies are generally considered to be moderately effective in suppressing arrhythmia, and patient outcomes are highly variable. This situation persists even when the genetic background that predisposes patients with congenital arrhythmias is known. We investigated the variability in patient response to the class I anti-arrhythmic molecule, mexiletine, in patients who were diagnosed with Long QT Syndrome Type 3. These patients harbor disease-linked variants in the gene that encodes the cardiac Na+ channel. Our results showed that variant effects on the voltage sensing domain of repeat III (VSD-III) of the Na+ channel could be used to predict whether patients were well-treated with mexiletine therapy with a partial least squares regression approach. A follow-on kinetic model that described the molecular details of the channel and block by mexiletine suggests a novel therapeutic approach by targeting VSD-III. Ongoing work is focused on developing new methods to create optimized kinetic channel models and testing whether the correlation between variant effects on VSD-III and mexiletine therapeutic outcomes holds for the general population.

Organized by: Lisette dePillis (Department of Mathematics, Harvey Mudd College, United States), Amina Eladdadi (Department of Mathematics, The College of St. Rose, United States)

• Raluca Eftime (University of Franche-Comté, France)
  "Modelling oncolytic virotherapies for cancer: the complex roles of innate immune responses"
Oncolytic viruses are emerging as important approaches in cancer treatment. However, the effectiveness of these therapies depends significantly on the interactions between the oncolytic viruses and the host immune response. Macrophages are one of the most important cell types in the anti-viral immune responses, as well as in the anti-cancer immune responses. Nevertheless, the heterogeneity of macrophage population (with the two extreme phenotypes represented by the M1 and M2 cells) makes it difficult to understand the anti-cancer as well as anti-viral roles of these cells. We start by focusing on a single-scale model for oncolytic virus--cancer cell interactions in the presence of immune responses represented by macrophages. We show that cell polarization towards either an M1 or M2 phenotype can enhance oncolytic virus therapy through either (i) anti-tumour immune activation, or (ii) enhanced oncolysis. Then, we discuss the impact of the spatial spread of macrophages inside solid tumours on the heterogeneous spatial distributions of oncolytic viruses.
• Justin Le Sauteur (University of Montreal, Canada)
  "Optimizing combined oncolytic vaccinia and PAC-1 treatment of ovarian cancer using in silico clinical trials"
Ovarian cancer poses a unique challenge due to its late diagnosis and high rate of relapse. In response, oncolytic vaccinia virus (VACV), which selectively kills tumour cells through infection and viral replication, and procaspase-activating compound 1 (PAC-1), a small tumour cell apoptosis-inducing molecule, have been recently proposed as a combination therapy that may better control ovarian cancer growth. The combination of VACV and PAC-1 has already been shown to be a promising treatment, however a delicate therapeutic balance must be stuck, as PAC-1 induces apoptosis in cells that VACV needs for continued replication. To provide a quantitative basis behind the use of VACV with PAC-1 in ovarian cancer, we developed a mathematical and computational biology model that accounts for tumour growth and treatment-induced death. Our model was calibrated to experimental measurements of the individual and combined effects of each molecule. To determine the optimal dose size and therapeutic schedule for combined VACV and PAC-1, we expanded an in silico clinical trial of 200 patients to bolster the preclinical translation of this investigational therapy. Our results contribute to the evaluation of the validity of this proposed treatment, and establish maximal PAC-1 concentrations that maintain VACV efficacy. Overall, this work demonstrates the ability to use simple mathematical modelling techniques to inform treatment design in real time.
• Pantea Pooladvand (The University of Sydney, Australia)
  "The dynamics of oncolytic virotherapy in dense tumours"
The growth of a tumour can be characterised by a complex network of cells, fibers and molecules. Images of tumour histology show that cell-stroma landscapes can vastly differ from one tumour to another. These variations in structure, density and cell placement inevitably change the outcome of treatment. Mathematical studies often focus on modelling the degradation and reconstruction of extracellular matrix (ECM) by tumour cells to capture tumour progression. However, the extracellular matrix can also significantly hinder anti-cancer therapy. In this project we explore the role of ECM differently. Here, we focus on how changes in stroma affect oncolytic virotherapy. We want to understand how different configurations of tumour-ECM landscape change the spread and efficacy of viral treatment. By building a system of partial differential equations that includes a novel diffusion term for virus spread in ECM, we look for patterns in tumour-cell ratios, collagen density and collagen configurations to predict treatment outcome. We find that collagen density, cell-collagen ratio and gaps in the collagen surface can significantly affect tumour treatment. Therefore, to accurately describe treatment outcome in oncolytic virotherapy, models need to consider the influence of cell-collagen interactions on therapy.
• Khaphetsi J. Mahasa (National University of Lesotho, Lesotho)
  "Natural killer cells recruitment in oncolytic virotherapy: a mathematical model"
In this talk, we investigate how natural killer (NK) cell recruitment to the tumor microenvironment (TME) affects oncolytic virotherapy. NK cells play a major role against viral infections. They are, however, known to induce early viral clearance of oncolytic viruses, which hinders the overall efficacy of oncolytic virotherapy. Here, we formulate and analyze a simple mathematical model of the dynamics of the tumor, OV and NK cells using currently available preclinical information. The aim of this study is to characterize conditions under which the synergistic balance between OV-induced NK responses and required viral cytopathicity may or may not result in a successful treatment. In this study, we found that NK cell recruitment to the TME must take place neither too early nor too late in the course of OV infection so that treatment will be successful. NK cell responses are most influential at either early (partly because of rapid response of NK cells to viral infections or antigens) or later (partly because of antitumoral ability of NK cells) stages of oncolytic virotherapy. The model also predicts that: (a) an NK cell response augments oncolytic virotherapy only if viral cytopathicity is weak; (b) the recruitment of NK cells modulates tumor growth; and (c) the depletion of activated NK cells within the TME enhances the probability of tumor escape in oncolytic virotherapy. Taken together, our model results demonstrate that OV infection is crucial, not just to cytoreduce tumor burden, but also to induce the stronger NK cell response necessary to achieve complete or at least partial tumor remission. Furthermore, our modeling framework supports combination therapies involving NK cells and OV which are currently used in oncolytic immunovirotherapy to treat several cancer types.