Mathematical tools for understanding viral infections within-host and between-host

Monday, June 14 at 11:30am (PDT)
Monday, June 14 at 07:30pm (BST)
Tuesday, June 15 03:30am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS02" time block.
Note: this minisymposia has multiple sessions. The second session is MS01-IMMU (click here).

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Hana Dobrovolny (Texas Christian University, United States), Gilberto Gonzalez-Parra (New Mexico Tech, United States)


The SARS-CoV-2 pandemic has made it clear that mathematical modeling plays an important role in rapidly advancing scientific knowledge in emergency situations. Population scale models have provided valuable information for public health authorities at the local and national levels, allowing them to assess the effect of different non-pharmaceutical interventions. At the within-host level, models of viral dynamics have helped to assess the possibility of re-purposing antivirals to treat the emerging epidemic. In order to be prepared for the next pandemic, we need to continue to refine mathematical tools for analyzing viral dynamics. This mini-symposium includes presentations on the development of mathematical modeling techniques for viral infections, covering both the within-host dynamics and population-level dynamics.

Benito Chen-Charpentier

(University of Texas at Arlington, United States)
"Deterministic and stochastic modeling of plant virus propagation with delay"
Plant diseases caused by a virus are mostly transmitted by a vector that bites an infected plant and bites a susceptible one. There is a delay between the time a plant gets bitten by an infected vector and the time it is infected. In this paper we consider two simple models of plant virus propagation and study different ways in which delays can be incorporated including the addition of an exposed class for the plants. Simulations are done and comparisons with the results for the models without delays are presented.

Kenichi Okamoto

(University of St. Thomas, United States)
"Opposing within-host and between-host selection pressures for virulence: Implications for disease surveillance"
For many infectious diseases, including SARS-Coronavirus-2 (SARS-CoV-2), disease surveillance followed by isolating, contact-tracing and quarantining infectious individuals is critical for controlling outbreaks. These interventions often begin by identifying symptomatic individuals. However, by actively removing pathogen strains likely to be symptomatic, such interventions may inadvertently select for strains less likely to result in symptomatic infections. Additionally, the pathogen’s fitness landscape is structured around a heterogeneous host pool. In particular, uneven surveillance efforts and distinct transmission risks across host classes can drastically alter selection pressures. Here we explore this interplay between evolution caused by disease control efforts, on the one hand, and host heterogeneity in the efficacy of public health interventions on the other, on whether less symptomatic, but widespread, pathogens evolving. Using an evolutionary epidemiology model parameterized for coronaviruses, we show that symptoms-driven disease control ultimately shifts the pathogen’s fitness landscape to select for asymptomatic strains. We find such outcomes result when isolation and quarantine efforts are intense, but insufficient for suppression. Moreover, when host removal depends on the prevalence of symptomatic infections, intense isolation efforts can select for the emergence and extensive spread of more asymptomatic strains. The severity of selection pressure on pathogens caused by these interventions likely lies somewhere between the extremes of no intervention and thoroughly successful eradication. Identifying the levels of public health responses that facilitate selection for asymptomatic pathogen strains is therefore critical for calibrating disease suppression and surveillance efforts and for sustainably managing emerging infectious diseases.

Baylor Fain

(Texas Christian University, United States)
"Validation of a GPU-based ABM for rapid simulation of viral infections"
We developed a new ABM/PDEM hybrid model for simulating virus spreading in a monolayer of a million cells. In this work, aspects of the simulations, such as the time step, are checked to verify the model is producing accurate data. Physical characteristics of the viral spread, such as the growth rate, decay rate, peak amount of virus, and time of peak virus, are compared with real data ranges for Influenza virus. Values for the parameters: viral production rate, rate of infection, amount of time in the eclipse phase, and the amount of time in the infectious phase, are found for H1N1pdm09-WT from fitting the model to experimental data by minimizing the SSR (Sum of Square Residuals).

Hayriye Gulbudak

(University of Louisiana at Lafayette, United States)
"A Delay Model for Persistent Viral Infections in Replicating Cells"
Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay modelling the length of time in the eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system. Moreover, we characterize bifurcations in our model, including transcritical (backward and forward), saddle-node, homoclinic, and Hopf bifurcations, and provide evidence of a Bogdanov-Takens bifurcation. We investigate the possibility of long-term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of robust uniform persistence. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether the virus survives.

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Virtual conference of the Society for Mathematical Biology, 2021.