Population Dynamics Across Interacting Networks or Scales

Thursday, June 17 at 11:30am (PDT)
Thursday, June 17 at 07:30pm (BST)
Friday, June 18 03:30am (KST)

SMB2021 SMB2021 Follow Thursday (Friday) during the "MS20" time block.
Note: this minisymposia has multiple sessions. The second session is MS19-ECOP (click here).

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Necibe Tuncer (Florida Atlantic University, USA), Hayriye Gulbudak ( University of Louisiana at Lafayette, USA), Cameron Browne (University of Louisiana at Lafayette, USA)


Modeling the complexity of populations and ecosystems requires innovative applications of dynamical systems and differential equations. Of particular interest are multi-scale or multi-species models where components, in themselves representing commonly studied systems in mathematical biology, are coupled together to form complex systems. For example, ecosystems may be viewed as high-dimensional networks of interacting species. Rapidly evolving and diverse interacting populations, such as a viral ``quasi-species'' and host immune response, quickly build a dynamic network of multiple variants whose structure can possibly be predicted through analytical or computational tools. Another layer of complexity to consider can be connecting the interdependent scales of within-host (immunology) and between-host (epidemiology) for infectious diseases. Modeling populations across networks or scales can bring genetic, biological or spatial structure into the equation, and motivates novel application of partial or high-dimensional ordinary differential equations. In this special session, we collect a variety of speakers who model population dynamics across interacting networks or scales.

Maia Martcheva

(University of Florida, USA)
"A Network Immuno-epidemiological Model of HIV and Opioid Epidemics"
We introduce a network immuno-epidemiological model of HIV and opoid epidemics where the jointly affected class is structured by the within-host dynamics. We fit the within-host model to data, collected in monkeys. We compute the reproduction numbers of the HIV and opiod epidemics. We show that the disease-free equilibrium is locally stable if both reproduction numbers are below one, and unstable if at least one of the reproduction numbers is above one. The HIV-only equilibrium exists if the reproduction number of HIV is larger than one. The opioid-use only equilibrium exists if the reproduction number of opioid use is larger than one. The HIV-only equilibrium is locally asymptotically stable if the invasion number of the opioid epidemic is below one and unstable if the invasion number of opoioid epidemic is above one. The opoioid-only equilibrium is locally asymptotically stable if the invasion number of the HIV epidemic is below one and unstable if the invasion number of HIV epidemic is above one. Simulation suggest that larger networks lead to higher reproduction numbers.

Stanca M. Ciupe

(Virginia Tech, USA)
"Neutrophil dynamics and their role in disease: a multi-scale investigation"
The highly controlled migration of neutrophils toward the site of an infection can be altered when they are challenged with competing external signals, leading to their dysregulation and oscillatory movement. In this talk, I will use mathematical models to evaluate the mechanistic interactions responsible for neutrophil migratory decision-making and to determine molecular and cellular contributions to disease pathogenesis. The results are applicable to sepsis and SARS-CoV-2 infections.

Michael Cortez

(Florida State University, USA)
"Using sensitivity analysis to explore the context dependent relationships between host species richness and disease prevalence"
In multi-host communities, the dilution effect is the phenomenon wherein focal host infection prevalence (i.e., the fraction of infected individuals in a focal host species) decreases with increases in host species richness. The opposite phenomenon is called an amplification effect. Empirical and theoretical studies show that relationships between host species richness and prevalence are likely to be context dependent, depending on the identity of the host species present in and added to a given community. However, current theory is limited in its ability to identify the context-dependent rules governing host species richness-prevalence relationships. This is due, in part, to modeling studies making different assumptions about the pathogen transmission mechanism, the presence/absence of interspecific interactions between host species, and the characteristics of the host species (e.g., competence and competitive ability). In this talk, I show how sensitivity analysis applied multihost-pathogen models can yield insight into how host characteristics, host density, and the pathogen transmission mechanism affect infection prevalence in a focal host. Specifically, I present an n-host model of an environmentally transmitted pathogen and show that it can unify common epidemiological ODE models for direct and environmental transmission under a single framework via fast-slow dynamical systems theory. I then use local sensitivity analysis applied to endemic equilibrium of the model to analytically derive the relationships between focal host infection prevalence and host densities and model parameters. This identifies how host competence, density, and the pathogen transmission mechanism jointly shape host richness-disease relationships. For example, the strength of interspecific host competition determines whether responses in focal host infection prevalence to increased density of a non-focal host are driven by the characteristics of the non-focal host or other host species in the community. I interpret these results in terms of factors promoting amplification and dilution of disease.

Juan B. Gutiérrez

(University of Texas at San Antonio, USA)
"Data, reality, and cognitive dissonance. On modeling what we don’t see with data we don’t have."
During the ongoing COVID-19 pandemic, the discrepancy between daily reports of cases and the trajectory of the disease has posed a substantial challenge to modeling efforts. In this talk, we will present the contrast between patient data and daily counts for the City of San Antonio, TX. We will demonstrate that a non-autonomous adjustment to data deficiencies can substantially improve forecasts. We present the extension of this method to multi-strain outbreaks. An exact data correction is possible with detailed patient data and genomic sequencing of the pathogen, which might not be available in all localities. To alleviate this problem, we propose a framework that incorporates information at multiple spatial and temporal scales to estimate the non-autonomous data correction. A derivation of classic quantities (R_o, R_e) is presented for a SEYAR model (Susceptible, Exposed, Symptomatic, Asymptomatic, Recovered) under this framework.

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Virtual conference of the Society for Mathematical Biology, 2021.