Posters-03

IMMU

IMMU-1 (Session: PS03)
Oleg Demin InSysBio
"Comparison of different implementations of lymphocyte proliferation in QSP models of immune response"

Objectives: To summarize conventional approaches and propose a new one of lymphocyte proliferation description in mathematical models. To compare the different implementations of cell proliferation to characterize pros and cons of their use in large scale QSP models. Results: Three different approaches to describe rate law of lymphocyte proliferation were considered: (1) linear proliferation, (2) saturable proliferation, (3) generation dependent proliferation (GDP). Two types of models imitating in vitro and in vivo conditions and describing lymphocyte proliferation, death and influx (for in vivo only) were constructed. Analytical expressions of model variables at steady states and their stability were studied. Concept of lymphocyte generation was introduced and rate laws GDP were derived via convolution of infinite ODE system describing dynamics of lymphocyte of different generations. It was found that conventional proliferation rate laws (1) and (2) do not allow to describe bell-shaped dependence of cell number on time which might be observed in vitro. Implementation of rate law (1) allows to observe stable steady state only if rate constant of degradation is larger than that of proliferation. Rate law (3) enables us to describe both bell-shaped dependence in vitro and stable positive steady state in vivo at any parameter values.

IMMU

IMMU-2 (Session: PS03)
Pooja Dnyane PhD student
"Network motifs in drug - drug interaction"

Combination therapy/multiple drug treatment is useful in some cases and necessary for the successful treatment of diseases such as leprosy, HIV/AIDS, tuberculosis and various cancers. During the treatment, drugs interact with each other and alter the medication's effect on the body. The effect could be less or more potent than intended. Drugs could also have potential antagonistic effect on each other's systemic properties. When two drugs for different diseases are administered simultaneously, it is possible that one of them could decrease the concentration of other by increasing its elimination. This could lead to increased disease severity. There are models that study autoinduction where the drug upregulates enzyme that promote its own clearance. But very few models to our knowledge include drug–drug interaction wherein they modulate each other's concentration by regulating absorption and elimination rate. We present 4 network motifs that explains the positive and negative effect a drug could have on its own elimination, or on elimination of other drug administered simultaneously. We define 32 structures that represents these network motifs. Finally, we study the sensitivity of maximum drug concentration and variation in drug concentration to different parameters. This would help in optimizing the dosing protocol that involves multiple drugs.

IMMU

IMMU-3 (Session: PS03)
Aparna Ramachandran Academy of Scientific and Innovative Research, CSIR - National Chemical Laboratory
"Studying the Effects of Anti-Tuberculosis Drugs at Extrapulmonary Sites using a Physiology-based Pharmacokinetic Model"

Tuberculosis (TB) is a major cause of mortality due to an infectious agent. Standard TB treatment is multidrug therapy with 4 drugs. While TB primarily affects the lungs, it can also affect other sites, giving rise to extrapulmonary TB (EPTB). EPTB constituted about 16% of the worldwide notifications in 2019. However, it continues to be overlooked and an optimal regimen for EPTB is not defined. The recommended treatment for most forms of EPTB is the same as pulmonary TB, but the studies these recommendations are based on are few in number. Attaining sufficient concentrations of anti-TB drugs at extrapulmonary sites, at the appropriate time and for the optimum duration is essential for efficient EPTB treatment. PBPK models can be used to study the concentration profiles of drugs at different sites. Although TB treatment entails multiple drugs, PBPK studies have focused on mono-drug therapy in the body, or multidrug therapy only in the lung. Here, we use a PBPK model for multiple anti-TB drugs to simulate their concentration-time profiles at EPTB sites. We use the simulations to understand the effect of dosing regimens on number of hours the drugs stay above their MIC at these sites.

MEPI

MEPI-2 (Session: PS03)
Martin Lopez-Garcia Department of Applied Mathematics, University of Leeds
"Exact approaches for the analysis of stochastic epidemic processes on small networks"

This research work is framed within the area of modelling hospital-acquired infections. I will introduce a number of existing compartmental-based approaches for modelling the spread of (typically antibiotic resistant) bacteria in hospital settings. Mathematical models with a relatively small number of compartments can be used for representing the spread of bacteria across patients and healthcare workers (HCWs), including relevant factors such as environmental contamination. However, more complex approaches (i.e., models with a large number of compartments, or network-based representations) are needed for example when introducing spatial considerations or HCW-patient contact network structures. When looking at network-based approaches, I will show some recent work on analysing exactly these epidemic dynamics on small networks. When considering an SIR epidemic process on a network, this analytic and computational approach amounts to the analysis of the corresponding continuous-time Markov chain (CTMC) with an explosive number of states, and makes special focus on algorithmic aspects and the organisation of the corresponding space of states S. Finally, I will present some recent results on the applicability of graph-automorphism lumping techniques in these systems.

MEPI

MEPI-32 (Session: PS03)
Eva Stadler Kirby Institute, UNSW Sydney
"Who carries malaria parasites over the dry season?"

Transmission of Plasmodium parasites that cause malaria is often seasonal with very low transmission during the dry season and high transmission in the rainy season. Plasmodium falciparum parasites can survive the dry season within some humans. For malaria elimination efforts, it is crucial to learn more about this parasite reservoir in humans. We use a mathematical model incorporating random mosquito bites and slow acquisition of non-sterilizing general immunity to explore which factors influence whether someone carries parasites over the dry season. Based on model simulations, we hypothesize that parasite carriage over the dry season is exposure mediated. With increasing exposure, i.e., with higher age and Force Of Infection (FOI, the mean number of infectious mosquito bites per day), immunity increases. Higher levels of immunity lead to longer infections and a higher probability of carrying parasites over the dry season. We then test this hypothesis in data from a longitudinal study in Mali and find that carriers are significantly older, have a higher FOI, and develop clinical malaria later than non-carriers.

MEPI

MEPI-33 (Session: PS03)
Helena Stage The University of Manchester
"Multi-Scale Superinfection Models in Evolutionary Epidemiology"

The study of evolutionary epidemiology is vital to understand and control the spread of anti-microbial resistance, but is inherently challenging because pathogen evolution is driven by forces acting at multiple scales: for example, HIV needs to escape the immune system within a host, but also needs to maintain the ability to be transmitted efficiently between hosts. Time-since-infection models are much more flexible than ODEs if we want to allow for realistic enough aspects of both within- and between-host scales, but capturing the feedback loops between such scales is a formidable challenge.We will discuss the main technical challenges in developing a general theory for time-since-infection models that allow for superinfection (e.g. multi-strain systems with partial cross-immunity), starting from the problem of characterising the system's steady states. We will distinguish between the cases when superinfection of the host facilitates the coexistence of two (or more) infections that interact synergistically by fuelling each other's spread (syndemic), and when these infections hinder each other. We show how in the former case multiple stable steady states are possible, while in the latter case the stable steady state is unique but possibly harder to compute. We discuss the consequent implications for public health control measures.

MEPI

MEPI-34 (Session: PS03)
Augustine Okolie Technical University of Munich
"Phylogenetic Methods for Infectious Models"

Here, we adopt the maximum-likelihood framework based on a multi-type branching process (MTBP) for heterogeneous population where each host is assigned to a type (subpopulation). We extend this multi-type birth-death branching model to a tree-based SIR model which also incorporates contact tracing. On a rooted known phylogenetic tree where only the root node is infected and infectious, we investigate the probability density of a sampled tree given some epidemiological parameters. The maximum-likelihood parameter estimation of the basic model is combined with the results for contact tracing. We expect that the tracing events incorporate information about the heterogeneity in the contact structure, while the phylogenetic methods are better to estimate the timing of the infectious process. In that, we hope that the combined method will improve the estimations of the parameters of the epidemic process, as well as on the underlying contact structure.

MEPI

MEPI-36 (Session: PS03)
Bhawna Malik https://math.snu.edu.in/people/researchers/bhawna--malik
"Emergence of drug-resistant through behavioural interactions: Game theoretic approach"

Emergence of antibiotic drug resistance has raised great concerns for public health, especially in low and lower middle income country. Many studies indicate the emergence and high burden of drug residence is a complex dynamics influenced by several socioeconomic factors like poverty, health expenses, and self-medication. Self-medication through Over-the-counter (OTC) drug sales plays a major role in ever-increasing antibiotic consumption, and it is is more ubiquitous in more economically destitute society. To explore this, we developed a game-theoretic model of human choices in self-medication integrating economic growth in population, and disease transmission process. We show that combined impact of economy, infections and behaviour yield resistance as a self-reinforcing cycle in drug resistance. Our model illustrates that individuals' perceived risk plays an important role in disease dynamics. We show that increased and timely government aid can break this self-reinforcing cycle by reducing hospital treatment cost or other medical incentives, and thus, it can recover population from economic downfall due to continuous morbidity from antibiotic drug resistance.

MEPI

MEPI-37 (Session: PS03)
Laxmi Shiv Nadar University, India
"Game theoretic approach to quantify the impact of ITNs under individuals choice on malaria transmission"

Insecticide Treated bed Nets (ITN) have proven to be highly effective control measure to reduce malaria transmission. It has been discussed earlier that ITNs with high efficacy may perform better in control malaria. But, even after massive distribution of ITN, malaria persists in most of the under developing countries, compromising the long term malaria elimination goals. However, many empirical studies pointed out that usage of ITN plays an important role in its effectiveness to control malaria. Individuals ITN usage are highly driven by ITN efficacy, mosquito density due to seasonal variation, replacement period, increment in daily productivity due to ITN misuse. To explore the complex interaction of ITN usage pattern and malaria prevalence, we develop a Game-Theoretic model of ITN usage and malaria transmission. Our results show the impact of parameters like imitation rate and ITN efficacy on human behaviour are critical. The analysis indicates that higher efficacy of ITN is not always optimal to control malaria effectively, which is an important information for malaria elimination strategies.

MEPI

MEPI-38 (Session: PS03)
Mohamed Khalil Salem GSE Department (Mathematics), Faculty of Engineering, October University for modern sciences and Arts (MSA)
"Fractional order models of HIV: A Review"

HIV is one of most serious global challenges. About 38 million people are currently living with HIV. It cased AIDS which is a chronic life-threatening disease. In this work, an overview on mathematical models of human immunodeficiency virus (HIV) with memory are presented. Non integer order models (Fractional order models) are presented to study the impact of memory on the interaction between the CD4+ T and HIV.

MEPI

MEPI-39 (Session: PS03)
Dylan Dronnier Ecole des Ponts
"Targeted Vaccination Strategies for Infinite-Dimensional Compartmental Models"

In classical homogeneous compartmental models, the critical proportion of the population needed to be immune to eradicate the disease is given by the formula: 1 - 1/R0, where R0 is the basic reproduction number. This so-called herd immunity threshold can be lower in heterogeneous models by targeting specific sub-groups of the population.In this talk, we formalize and study the problem of optimal allocation strategies for a (perfect) vaccine in infinite-dimensional compartmental models. The question may be viewed as a bi-objective minimization problem, where one tries to minimize simultaneously the cost of the vaccination, and a loss that may be either the effective reproduction number. We prove the existence of Pareto optimal strategies, describe the corresponding Pareto frontier, and study its convexity and stability properties. We also show that vaccinating according to the profile of the endemic state is a critical allocation, in the sense that, if the initial reproduction number is larger than 1, then this vaccination strategy yields an effective reproduction number equal to 1.In the second part of of the talk, we illustrate the theoretical framework developed previously with many examples.

MEPI

MEPI-40 (Session: PS03)
Chaeyoung Lee Korea university
"Mathematical modeling for estimating the unidentified infected population of COVID-19"

The COVID-19 pandemic continues and causes major damage worldwide for more than a year. To prevent the spread of the infectious disease, it is significantly important to estimate the number of people who are infected but have not yet been confirmed because they can rapidly infect other people. Therefore, a mathematical model is proposed for predicting the unidentified infected population of COVID-19. This is the Susceptible-Unidentified infected-Confirmed (SUC) model, which is simple. Moreover, the proposed model is potentially useful in estimating the unidentified infected population to secure enough supplies for infection prevention, to prepare for testing and treatment of confirmed COVID-19 patients, and to monitor the impact of the new policies such as social distancing and school closures. Therefore, it is critical to estimate the unidentified infected population to control the spread of COVID-19.

MEPI

MEPI-41 (Session: PS03)
Nicole Cusimano Basque Center for Applied Mathematics
"COVID-19 dynamics in the Basque Country: towards spatially dependent models"

More than one year after the discovery of the SARS-CoV-2 virus, the ongoing pandemic continues to affect the lives of people around the globe. Better understanding of the challenges posed by this virus are key to face the future with the right amount of caution, to guide current and future public health policies, and to inform the public to avoid the spreading of misinformation and fear. Mathematical models of infectious disease transmission have played (and will continue to play) an important role in this direction. In this talk, I will outline the development of the pandemic in the Basque Country, a compartmental modelling framework to describe the local reality (accounting for the basque government response in different stages of the pandemic), and discuss possible approaches to account for spatially refined information providing further insights into the local transmission dynamics.

MEPI

MEPI-42 (Session: PS03)
Damián Knopoff Basque Center for Applied Mathematics
"A multiscale active particle model of epidemic spreading with heterogeneous interactions"

During this talk I will present a mathematical model of contagion and spread of a viral disease. The model is based on the kinetic theory for active particles and was developed using a multiscale framework accounting for the interaction of different spatial scales: from the small scale of viral particles and immune cells, to the larger scale of individuals and further up to the collective behavior of populations.The overall population is divided into compartments (susceptible, infectious, recovered and dead). Interactions between individual entities (hosts, viral particles, immune cells) are described at the micro-scale. A model of contagion through interactions is then proposed, depending on the interaction rate and a parameter describing the so-called social distance. Within infected hosts, viral particles and the immune system develop competitive interactions with transitions that may end up in a recovery or death. The dynamics of the system is then described by distribution functions at the meso-scale. The knowledge of these distribution functions allows to compute macroscopic variables (i.e. positive cases or deaths). Some case-studies are proposed in order to perform parameter sensitivity analyses and to understand responses of the system to different control measures aimed to reduce the impact of the disease.

MEPI

MEPI-43 (Session: PS03)
Rey Audie S. Escosio Resilience Institute, University of the Philippines
"Modelling COVID-19 Dynamics with Different Community Quarantine Protocols in National Capital Region, Philippines"

The state of the pandemic in the Philippines surpasses 740,000 cumulative cases with very limited healthcare capacity as of March 30, 2021. Nearly half of this number comes from the National Capital Region of the Philippines. The response of the government is the implementation of the region-restricted Community Quarantines (CQ) labeled as Enhanced, Modified Enhanced, General, and Modified General. An SEIR mathematical model is developed to describe the transmission dynamics of the COVID-19 infection in the Philippines' capital region. The different tiers of CQs and non-pharmaceutical interventions are incorporated using population factors and a function affecting the susceptible and exposed compartments. The available data on cases and deaths are utilized for parameter estimation and uncertainty analyses of the model. Key model parameters that indicate the dynamics of the model are identified for different CQ periods. A more relaxed CQ level leads to more infections which can be attributed to the correspondent increase in the interacting population. The model could be developed for reliable use in short-term forecasting that may aid decision-making, such as in crafting and implementing CQs.

MEPI

MEPI-44 (Session: PS03)
Iulia Martina Bulai University of Basilicata
"Influence of asymptomatic people on malaria transmission: a mathematical model for a low-transmission area case"

Malaria remains a primary parasitic disease in the tropical world, generating high morbidity and mortality in human populations. Recently, community surveys showed a high proportion of asymptomatic cases, which are characterized by a low parasitemia and a lack of malaria symptoms. Until now, the asymptomatic population is not treated for malaria and thus remains infective for a long time. In this paper, we introduce a four-dimensional mathematical model to study the influence of asymptomatic people on malaria transmission in low-transmission areas, specifically using data from Brazil. The equilibrium points of the system are calculated, and their stability is analyzed. Via numerical simulations, more in-depth analyzes of the space of some crucial parameters on the asymptomatic population are done, such as the per capita recovery rates of symptomatic and asymptomatic people, the ratio of the density of mosquitoes to that of humans, the mortality rate of mosquitoes and the probability of undergoing asymptomatic infection upon an infectious mosquito bite. Our results indicate that the disease-free equilibrium is inside the stability region if asymptomatic people are treated and/or the ratio of the density of mosquitoes to that of humans is decreased and/or the mortality rate of mosquitoes is increased.

MEPI

MEPI-45 (Session: PS03)
Hyunwoo Cho Yonsei university
"Age-structured Pulmonary TB dynamics and cost-effectiveness analysis in Korea"

Objective: Tuberculosis(TB) is an infectious disease, causing more than 2000 deaths per year in Korea. Despite the effort of government, Korea still suffers from high mortality rate due to TB, ranking first among OECD countries. This study was aimed to evaluate the effect of close contact control strategies in different age groups and analyze cost-effectiveness of each control strategies.Method: An age-structured deterministic model was developed for the TB transmission in Korea. A SEIT (susceptible - exposed - infectious - treating) model was used with some additional compartments including 'high risk latent', 'low risk latent', and 'LTBI treated'. 15 different age groups were used to analyze different control strategies to different age group. Cost-effectiveness was analyzed using ICER through comparing incremental cost and incremental QALY by reducing number of TB patients.Result: The model suggested that close-contact control has the most effect in young age group(0-35). Expanding close-contact control will have mild effect on decreasing number of TB incidence every year, but decreasing the number of TB incidence by expanding close contact control does not guarantee cost-effectiveness in long term.

MEPI

MEPI-46 (Session: PS03)
Andrew Bate University of York
"Biosecurity coalitions in small heterogenous networks"

Preventing disease outbreaks can have widespread benefits that are dependent on the actions of many farmers but can be undermined by the inaction of others. Consequently, understanding conditions where or how well farmers will work together is important to designing policies in preventing outbreaks. We use a coalition game theoretic approach, where farmers who have two decisions, whether to cooperate in a coalition and how much effort they put into preventing outbreaks. Additionally, each farmer considers three costs; a cost from an outbreak on their farm, a cost from an outbreak on a “neighbouring” farm (e.g. within range of movement restrictions), and the costs of outbreak prevention. For two heterogeneous farms, two similar farms are likely to cooperate, whereas farms with significantly different costs are unlikely to cooperate. For three identical farms, we consider two networks: all farms are “neighbours” (triangle network) or two farms are “neighbours” to be a third middle farm (line network). For triangle networks, full cooperation requires small on-farm costs, whereas for line networks, full cooperation can happen in situations where on-farm costs are larger than those from neighbouring farms. This all suggests that location and structure is important to whether farmers cooperate.

NEUR

NEUR-3 (Session: PS03)
Hammed Olawale Fatoyinbo Massey University, New Zealand
"Stability of Travelling Waves in Electrically Coupled Smooth Muscle Cells"

Travelling waves play a vital role in understanding electrical activities in a population of excitable cells, for example, the propagation of signals in neurons. We aim to study the spatiotemporal patterns arising from a reaction-diffusion model of smooth muscle cells. Modulating model parameters, different forms of patterns including propagating pulses and fronts are observed. I will discuss the existence and stability analysis of the travelling waves. The shooting method is considered to approximate the wave speeds of the travelling waves, it turns out that the results are very similar to the wave speeds of the pulse and front solutions estimated from direct simulations of the model. Additionally, the spectral stability of the travelling wave solutions is investigated.

NEUR

NEUR-4 (Session: PS03)
Zakaria Shams Siam North South University
"Estimation of Motor Nerve Conduction Velocity Distribution: A Frequency Domain Approach"

Estimation of motor nerve conduction velocity distribution (NCVD) from the compound muscle action potential (CMAP) is a challenging problem for a long period, which would be a useful tool for evaluating the peripheral neuropathies by assessing the electrophysiological characteristics of the peripheral nerves. In the present study, we have analyzed the CMAP of ulnar nerves from the human subjects in the frequency domain. In this regard, we have expressed the collected CMAP as a circular convolution of the motor unit action potential (MUAP) and their associated delay sequence. The frequency domain analysis of the collected two CMAP's having different stimulating-recording distances helped us separate the delay sequence without even using any prior MUAP model. Finally, we have exploited the derived delay sequence to estimate the motor NCVD of ulnar nerve. Furthermore, we have estimated the derived MUAP using the frequency domain analysis. Our derived results conformed well to the previous NCVD studies and the histology results as well. The applied technique would be a helpful tool as it is non-invasive and offers a direct way to estimate the motor NCVD from the CMAP's.

NEUR

NEUR-5 (Session: PS03)
Rubyat Tansnuva Hasan North South University
"Estimation of Motor Nerve Conduction Velocity Distribution: A Continuous Approach"

Estimation of motor nerve conduction velocity distribution (NCVD) from the compound muscle action potential (CMAP) is a challenging and long-studied problem in nerve conduction study. In the present study, we have explored a new approach to determine the motor NCVD from the corresponding CMAP in a non-invasive manner using a continuous approach. In our study, we have taken the diphasic sinusoidal function and also the Hermite polynomial function to simulate the motor unit action potential (MUAP). We have experimented the efficacy of different polynomial functions of different degrees and also the gaussian and double gaussian distributions etc. to model the motor NCVD. Then, using the forward approach of nerve conduction, we have synthetically created the CMAP function. The continuous function of motor NCVD in our modeling helps us exploit the gradient optimization technique to solve the inverse problem of nerve conduction, i.e., estimation of motor NCVD from CMAP minimizing the least-square error. Our estimated results conformed well to the synthetically created CMAP dataset. The proposed technique is non-invasive and offers a way to estimate the motor NCVD from the corresponding CMAP's in a continuous approach which would be a useful tool for detecting the peripheral neuropathies.

NEUR

NEUR-6 (Session: PS03)
Zeinab Tajik Mansoury University of Tehran
"Dynamical Analysis of Hippocampal Circuitry under Opioid Addiction Suggests the Mechanism of the Relapse"

Drug Addiction affects the limbic system by forming a memory in the hippocampus. Recently, we studied the effect of opioid addiction using a mean-field tripartite model for two pairs of pre and post-synaptic neurons and an astrocyte in the hippocampus. The results indicated an increase in the synchrony of neurons during opioid addiction, which represents memory formation. We added a network modeled by a correlation coefficient that shows the amount of convergence of the network. The neurons' output frequencies have feedback on input frequencies through this network. A first-order ODE models the network feedback on the inputs. The bifurcation diagram of average output frequency versus cues frequency during the withdrawal state indicates bistability. The dynamical analysis indicates that the high-frequency equilibrium points representing opioid addiction can cause relapse at withdrawal state.

NEUR

NEUR-7 (Session: PS03)
Seokjoo Chae Korea Advanced Institute of Science and Technology
"The data-based inference method reveals the network structure of the SCN"

The suprachiasmatic nucleus (SCN) is the central circadian pacemaker in mammals. Even though the SCN is composed of thousands of heterogeneous self-oscillating cells, the SCN can synchronize its component oscillators through the SCN neuronal network. To understand the SCN network structure, previous methods used the time series data to infer the network structure. However, because the SCN is synchronized, previous methods falsely inferred the network as if all the SCN cells were coupled with each other. To circumvent this, we develop a novel data-based method, which can successfully infer the SCN network from the time series data. In particular, our method accurately infers the SCN network with single-cell resolution bioluminescence data from 2,000 synchronized mice SCN cells. Furthermore, our method can infer the directionality of the coupling between SCN cells.

OTHE

OTHE-1 (Session: PS03)
Sophie Fischer University of Bergen
"A mechanistic model for endocrine profiles of female puberty maturation"

The hypothalamus-pituitary-gonadal axis (HPG axis) has a central role for female reproduction. During pubertal development, the reactivation of the HPG axis causes characteristic physical and psychological changes. Pubertal development is clinically monitored by breast development. However, a trend of earlier breast development in girls is reported since 1977. Hence, the necessity to establish new references to classify pubertal development. Our aim is to set up a mechanistic model that can be used to make predictions about pubertal maturation given the current hormone state and the age. The model consists of ordinary differential equations (ODE) describing the time courses of the main hormones GnRH, LH, FSH, and E2. We assume that all feedback mechanisms of the HPG axis exist from early childhood on and that the main pacemaker for pubertal maturation is the development of a regular GnRH release pattern.Deterministic simulation results are comparable to data. Simulations with sampled parameters reflect inter-individual variability. In future work, we plan to set up an “average model” as a prior using longitudinal hormone data and take individual hormone time series to estimate individual model parameters.

OTHE

OTHE-2 (Session: PS03)
Indrani Madhugiri Chemical Engineering and Process Development Division, CSIR-National Chemical Laboratory, Pune-411008, India
"Unintuitive effects of substrate competition on steady state concentration of product of reversible enzymatic transformations"

For a closed system, we analyze the steady state effect of alternate substrates and inhibitors, for reversible transformation catalyzed by the same enzyme. Inhibitors and alternate substrates are known to decrease the initial product formation rate. Here, without using any assumptions either of pseudo-steady state or of relative concentrations of enzyme and substrates, we analytically show that alternate substrates and competitive inhibitors will not decrease the steady state product concentration, and may lead to an unexpected increase in these concentrations. For such inhibitors, though the initial rate does decrease compared to inhibitor-free reactions, the final steady state concentration never decreases, and therefore no long-term inhibition of product levels is possible. In contrast, uncompetitive inhibitors decrease the steady state product concentrations as well as initial product formation rate. We further explore closed systems where two distinct enzymes catalyze the forward and reverse transformation, and identify conditions when an alternate substrate can increase the steady state product concentration. This study shows analytically and through simulations that steady state effects of competing substrates or inhibitors on product concentrations may be qualitatively different from their effect on initial rates. These results can contribute to the design and analysis of in vitro enzyme inhibition assays.

OTHE

OTHE-3 (Session: PS03)
Kaniz Fatima Lima Lecturer, University of Science and Technology Chittagong
"Impact of Mutation on the Invasion Potential of Chikungunya Outbreak"

Chikungunya is an arthritogenic alphavirus responsible for chikungunya fever that is transmitted by Aedes aegypty and Aedes albopictus. As an RNA virus, a single mutation is introduced with a new variant ECSA-V, which has a shorter extrinsic incubation period (EIP). The SEIR model of chikungunya transmission is delineated, that explained the reduction of basic reproduction number (R_0) due to the mutation. The purpose of this work is to investigate the impact of mutation on the disease outbreak. Numerical simulation of the mathematical model has illustrated the realizations of the stochastic simulation of the estimation of invasion potential and revealed the distribution of mutant and non-mutant individual applying the Direct Method of Gillespie Algorithm. For R_0 near 1, the impact of the mutation on the invasion potential is examined. Also, the aptness of the mosquitoes for invasion potential is established mathematically.

OTHE

OTHE-4 (Session: PS03)
Manisri Centre for Computational Natural Sciences and Bioinformatics, IIIT Hyderabad
"Mathematical modelling of transcriptional network of liver regeneration"

Tissue homeostasis and regeneration depend on the reversible transitions between quiescence (G0) and proliferation. The liver has a remarkable capacity to regenerate after injury or resection by cell growth and proliferation. During regeneration, the liver needs to maintain the essential metabolic tasks and meet the metabolic requirement for hepatocyte growth and division. In this work, we studied the crosstalk between cell cycle and metabolism during the liver generation after two-thirds partial hepatectomy (PH). First, we modeled the temporal gene expression data of liver regeneration using the Hidden Markov Model, which revealed the dynamic balance of metabolic and cell cycle genes in hepatocytes. We further developed a mathematical model of the transcriptional network of liver regeneration, which explained the coordination of different events of liver regeneration. We demonstrate that mutual antagonism between the cell cycle and liver metabolic function makes the system bistable, which controls the initiation and termination of liver regeneration and different stable population-level expressions. This framework was also used to explain the transition to an uncontrolled proliferation state in Hepatocellular Carcinoma (HCC).

OTHE

OTHE-5 (Session: PS03)
Souvadra Hati BSSE, Indian Institute of Science
"Operating Principles of Circular Toggle Polygons"

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating 'master regulators' A and B, also called toggle switch. Typically, it can allow for three stable states. A toggle triad – three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly can allow for six stable states: three 'single positive' and three 'double positive' ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was even or odd numbered. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The odd- numbered networks enable usually twice the number of components with the states that follow 'circular permutation' patterns. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.

OTHE

OTHE-6 (Session: PS03)
Shama Javeed Pusan National university
"Numerical study of blood flow through catheterized artery"

AbstractThe evolution of coronary balloon angioplasty has increased the use of various sizes catheters in the arteries during the recent years. In the present study, pulsatile blood flow through catheterized artery is analyzed by the flow modelling of two immiscible fluids. The fluid flow in the primary region is treated as non-Newtonian power law fluid while, the fluid flow in peripheral region is categorized as Newtonian fluid. The catheter inside the vessel is treated as rigid body of small radius. The resulting system of differential equations that represents the velocity profiles of the respective fluids are solved numerically by finite difference method. Additionally, the results of velocity profiles with different physical quantities are analyzed for the purposes of a comprehensive summary of blood flow through catheterized artery.

OTHE

OTHE-7 (Session: PS03)
Ashley Sreejan Chemical Engineering and Process Development Division, CSIR-National Chemical Laboratory
"Mathematical model of the multi-amino acid multi-transporter system in CHO cells"

Mammalian cells express a large number of amino acid transporters of multiple types that can transfer multiple amino acids with varying efficacies. This combinatorial transfer makes it challenging to predict the effect of perturbations in the external amino acid pool or transporter expression levels on individual amino acid flux. Building on existing models, we develop a general model for such a complex transport system. Steady state analysis is carried out for single-carrier systems, and an analytical solution is derived for the transport rate under constant cellular and external concentrations. We apply the model to Chinese hamster ovary (CHO) cells in chemically defined media and estimate the short-term effects of perturbations in transporter expression and medium concentration on amino acid fluxes. Conditions for synergistic and repressive effects are identified, and the model can successfully predict known amino acid interactions and dependencies that were not used in constructing the model. This model can act as a tool to formulate testable hypotheses on the effect of process and genetic changes on amino acid initial uptake. Coupled with amino acid metabolism models, it can serve as the transporter dynamics component of a comprehensive model for intra- and extra-cellular amino acid dynamics.

POPD

POPD-26 (Session: PS03)
Vitor De Oliveira Sudbrack DEE - UniL
"Population dynamics in highly fragmented landscapes"

It's important to study how populations respond to changes in habitat distribution in landscapes. In this project, we use numerical methods to simulate reaction-diffusion equations in artificial binary landscapes with different structural distributions of the same habitat amount. We discuss the net effects of fragmentation into the steady total population in those landscapes. These effects are dependent on matrix hostility and we analyse 3 different scenarios: soft, intermediate and hostile matrices. In soft matrices, highly fragmented landscapes support greater total populations compared to slightly fragmented landscapes - and the opposite is true for hostile matrices. Regarding conservation, highly fragmented landscapes eventually led to the extinction of species for a sufficiently hostile matrix in low HA. We compared statistical models to conclude those where the effects of fragmentation and HA are interdependent presented the best statistical descriptions of average abundance in landscapes. Our synthetic data supported that fragmentation effects are not negligible compared to habitat loss, and effects of fragmentation considering linear interdependence with HA and effects of fragmentation per se are similar in direction across the HA gradient. The model we present can generate synthetic data to elucidate patterns of the effects of fragmentation on the ecological value of landscapes.

POPD

POPD-27 (Session: PS03)
Simon Syga TU Dresden
"Studying the interplay of spatio-temporal interactions and evolutionary dynamics during cancer cell invasion"

Genome instability and mutations as well as the activation of invasion are defining characteristics of cancer. However, in most mathematical models only one of the two aspects is studied at a time, neglecting the complex interplay between the spatio-temporal interactions and evolutionary dynamics. To fill this gap, we here propose a mathematical model of individual cells that migrate, proliferate, die, and pass on their properties to their offspring with small variations.In particular, we assume that the set of individual properties results in a phenomenological fitness of each cell influencing its proliferation rate.In computer simulations, we show that the interplay of evolution and spatio-temporal dynamics leads to a propagating wave of invading cells, where the wave speed increases over time and clones of higher fitness appear preferably at the wave front.We use a mean-field approach to show that the system can be approximated by a PDE that is similar to the KPP-Fisher equation.We also show that the increase in average fitness over time is proportional to the variance in fitness in the population, in agreement with Fisher's fundamental theorem of natural selection.

POPD

POPD-28 (Session: PS03)
Peter Nabutanyi Bielefeld University, Germany
"Modelling Interaction of Genetic Problems in Small Populations and Minimum Viable Population Size"

An important goal for conservation is to define minimum viable population sizes (MVPs) for long-term persistence in the face of ecological and genetic problems. Such genetic problems include mutation accumulation (MA), inbreeding depression (ID) and loss of genetic variation at loci under balancing selection, but most studies on MVPs only include ID. Verbal arguments suggest that extinction risk is exacerbated when genetic problems interact, but a comprehensive quantitative theory is missing. Using deterministic and stochastic eco-evolutionary models, we estimated MVP size as the lowest population size that avoids an eco-evolutionary extinction vortex after sufficient time for mutation-selection-drift equilibrium to establish. As mutation rates increase, MVP size decreases rapidly under balancing selection but increases rapidly under ID and MA. MVP sizes also increase rapidly with increasing number of loci with the same or different selection mechanism until a point is reached at which even arbitrarily large populations cannot survive. However, when keeping the number of loci constant, the observed MVP size is dominated by the mechanism which when in isolation yields the smallest MVP estimate. For better estimates, there is need for more empirical studies to reveal how different genetic problems interact in the genome.

POPD

POPD-29 (Session: PS03)
Martin Pontz Tel Aviv University
"Aneuploidy as a transient evolutionary step to adaptation"

Aneuploidy, i.e. the change to a different number of chromosomes in single cells, occurrs quite frequently in nature. Prominent examples are human cancer cells and yeast populations under stress. We investigate if and under which conditions aneuploidy can facilitate local adaptation. We analyze both mathematical models and numerical simulations in which aneuploidy acts as a transient step towards a better adapted population. The main methods are based on the Wright-Fisher model and the theory of branching processes. One example for an important quantity that is derived, is the expected time until the population is successfully adapted. It depends heavily on the mutation rate, which is the rarest event that has to occur in order to achieve adaptation. This work can be seen as a first step towards establishing basic evolutionary theory for the process of aneuploidy as it seems currently to be lacking.

POPD

POPD-30 (Session: PS03)
Ayan Das Center for Ecological Sciences, Indian Institute of Science, Bengaluru
"Demographic noise can promote abrupt transitions in ecological systems"

Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise - arising from the probabilistic and discrete nature of birth and death processes in finite systems - makes the transitions gradual or continuous. In this paper, we show that demographic noise may, in fact, promote abrupt transitions in systems that would otherwise show continuous transitions. We begin with a simple spatially-explicit individual-based model with local births and deaths influenced by positive feedback processes. We then derive a stochastic differential equation that describes how local probabilistic rules scale to stochastic population dynamics. The infinite-size well-mixed limit of this SDE for our model is consistent with mean-field models of abrupt regime-shifts. Finally, we analytically show that as a consequence of demographic noise, finite-size systems can undergo abrupt shifts even with weak positive interactions. Numerical simulations of our spatially-explicit model confirm this prediction. Thus, we predict that small-sized populations and ecosystems may undergo abrupt collapse even when larger systems - with the same microscopic interactions - show a smooth response to environmental stress.

POPD

POPD-31 (Session: PS03)
Wissam Barhdadi Ghent University
"Analyzing eco-evolutionary dynamics under environmental change in a physiologically-structured individual-based model"

Recent rapid changes in the environment increasingly affect populations around the globe. Theoretical and empirical studies show that both individual life-history traits as well as evolutionary responses could mediate a population's response to these changes. Population models that integrate both ecological processes arising from individual life-history traits and the evolutionary forces acting on these traits can provide better predictions and a general approach for analyzing eco-evolutionary dynamics of populations facing rapid environmental change.We propose an individual-based modelling (IBM) framework adopting standardized submodels representing the life-history of individuals as well as inheritance mechanisms of adaptive traits. IBMs provide an intuitive approach to integrate ecological and evolutionary processes. Adopting an energy-budget based submodel to represent an individual's life-history allows for the emergence of individual fitness within the local environment. Further integration of a quantitative genetic approach to inheritance of adaptive life-history traits (resulting from energy-budget parameters), allows for the modelling of eco-evolutionary feedbacks as a function of the population's environment. In this simulation-based work, we explore the modelling framework to analyze the emerging eco-evolutionary dynamics in a Daphnia magna laboratory population. This analysis underpins the further coupling of evolutionary and ecological theory in populations models.

POPD

POPD-32 (Session: PS03)
Connah Johnson University of Warwick
"ChemChaste: Modelling chemical dynamics in spatially distributed bio-films"

Biofilms are ubiquitous in medical settings. Biofilms can contain multiple distinct bacterial strains which complicate the task of tackling infections. Mathematical modelling can help us improve our understanding of, and design better-informed experiments to probe, the dynamics of such systems. We seek to understand the biofilm wide dynamics through developing a hybrid continuum-discrete software library, ChemChaste. Building upon the multi-scale simulation package Chaste, ChemChaste introduces the means to simulate general reaction-diffusion PDEs coupled to individual based cell cycle models. Each cell within the simulation contains its own metabolic pathways, cell cycle model, and membranous transport to enable the simulation of complex chemical interactions between heterogeneous communities. The emergence of structure within the communities is simulated through the segregation of cell types driven by the chemical signaling and external reaction systems. This combination of cell based and external domain reactions enables ChemChaste to simulate chemical dynamics occurring within biofilms. From this we probe the role of microenvironment-metabolism feedback on the community structure and infer how the distribution of cell types may protect the community from external stress. Our results provide insights which may further our understanding of bacterial infections in clinical practice.

POPD

POPD-33 (Session: PS03)
Sou Tomimoto Mathematical Biology Laboratory, Department of Biology, Faculty of Sciences, Kyushu University
"Modeling mutation accumulation and expansion in long-lived trees with complex branching structure"

Somatic mutations accumulated in trees have now become quantitatively detectable with recent progresses in next-generation sequencing (NGS) technology. This is the first step to understand the impacts of somatic mutations on longevity of trees. However, NGS can only detect mutations that are shared by majority of stem cells. Minor somatic mutations may be hidden in many branches in the same individual. Because the processes of mutation accumulation and expansion remain poorly understood, we constructed a mathematical model at the stem cell population level to simulate these processes in silico. In our model, the growth of tree is described as a combination of elongation and branching processes. At these processes, stem cells in each meristem can be selected randomly or cell lineage persists for each stem cell without random selection. Depending on the randomness in stem cell selections, we developed three different models and compared the number and pattern of accumulated mutations among models in a branching structure measured in a Popular tree. We found that randomness in the selection process contributes to a decreased accumulation of somatic mutations. Comparison of our predictions with the data highlighted the possibility that more somatic mutations are accumulated in long-lived trees than previously expected.

POPD

POPD-34 (Session: PS03)
Baeckkyoung Sung KIST Europe / UST Korea
"Endocrine dynamics modelling on the hypothalamic-pituitary-gonadal axis of the aquatic lower vertebrates"

The endocrine signalling pathways of the lower vertebrates in the aquatic environments (e.g., fish and amphibians) comprise multiscale biochemical networks ranging from the subcellular transcriptomes, cell and tissue-specific metabolisms, and hormone-mediated inter-organ communications. The entire signalling circuitry thus typically demonstrates a dynamic complexity controlled by the physiological mechanisms such as cardiovascular circulation and neurosecretory regulations. The primary cross-talk paths involved in this circuitry can be effectively reduced to the serial multi-organ system linking the brain, ovary or testis, and liver, which is often called the hypothalamic-pituitary-gonadal (HPG) axis.In this presentation, we develop a general theoretical framework as a model for the signalling pathway network that regulates the HPG axis of the aquatic lower vertebrates. A linear system of ordinary differential equations was constructed to represent the metabolic networking structure where the uni- and bi-directional signalling flows and homeostatic feedback loops were coupled together. The model was designed to predict the dynamic behaviours of hormone syntheses in the HPG axis by simulating the environmentally relevant steroidogenic perturbations. Using this mechanistic model, it was shown that some potential scenarios of ecological risks could be quantitatively predicted in terms of the reproductive toxicology.

POPD

POPD-35 (Session: PS03)
Samuel Dijoux Dept. of Ecosystem Biology, Faculty of Science, University of South Bohemia, České Budejovice, Czech Republic
"'Symmetry in asymmetries' of body sizes and productivities drives consumer coexistence in multi-channel food webs"

Multi-channel food webs are shaped by the ability of apex predators to link asymmetric energy flows in mesohabitats differing in productivity and community traits. While body size is a fundamental trait underlying life histories and demography, its implications for structuring multi-channel food webs are unexplored. To fill this gap, we develop a model that links population responses to predation and resource availability to community-level patterns using a tri-trophic food web model with two populations of intermediate consumers and a size-selective top predator. We show that asymmetries in mesohabitat productivities and consumer body sizes drive food web structure, merging previously separate theory on apparent competition and emergent Allee effects (i.e., abrupt collapses of top predator populations). Our results yield theoretical support for empirically observed stability of asymmetric multi-channel food webs and discover three novel types of emergent Allee effects involving intermediate consumers, multiple populations or multiple alternative stable states.