MS08 - ECOP-2
Brutus Buckeye Room (#3044) in The Ohio Union

Feedbacks between infectious disease and ecosystems

Friday, July 21 at 10:30am

SMB2023 SMB2023 Follow Friday during the "MS08" time block.
Room assignment: Brutus Buckeye Room (#3044) in The Ohio Union.
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Mihrab Uddin Chowdhury, Lale Asik, Benito Chen-Charpentier, Christina Cobbold'


Mathematical models are powerful tools for understanding and informing complex biological phenomena. In recent years, there has been broad interest in applying mathematics to study a variety of biological fields, such as epidemiology and ecology. The relation between these two fields is particularly important since environmental factors such as temperature, humidity, and habitat restriction, as well as harvesting, hunting, and the number of predators, affect the spread of disease. Also, the existence of disease affects some of the species vital to the environment. This mini-symposium will highlight the new developments in these areas and bring together researchers who work on various models for biological systems from the perspectives of modeling, analysis, and computation. It will serve as a platform to present recent progress, exchange research ideas, extend academic networks, and seek future collaboration.

Saikanth Ratnavale

University of Notre Dame (Department of Biological Sciences)
"Optimal controls of the mosquito-borne disease, Dengue with vaccination and control measures"
Dengue is one of the most common mosquito-borne diseases in the world, and a person can get infected by one of the four serotypes of the virus named DENV-1, DENV-2, DENV-3, and DENV-4. After infection with one of these serotypes, an individual will maintain permanent immunity to that serotype, and partial immunity to the other three serotypes. Therefore, there is a risk of getting infected by this virus a maximum of four times, and the symptoms may vary from mild fever to high fever, bleeding, enlarged liver, and severe shock, and sometimes these symptoms may lead to death. It is obvious that the increase in the number of infected individuals makes a negative impact on a country’s economy. Hence, the use of different control measures such as mosquito repellents and the introduction of a vaccine against the virus is important in controlling the spread of the virus. In this study, I am presenting a methodology on how to estimate the optimal rate of vaccinations based on the QDENGA dengue vaccine and the optimal rate of control measures to reduce the number of new and severe dengue cases while minimizing the overall cost. In addition, this vaccine claims high protection against symptomatic disease and waning protection over time for some DENV serotypes. However, the extent to which protection against disease conditional on infection is unknown. I consider different scenarios subject to the possible combinations of vaccine protection and control measures to investigate the most effective parameter values to control the transmission of the virus. Disease forecasts including the number of newly infected individuals in each serotype, the optimal rate of control measure, and vaccinations for a period of ten years are performed with the help of computer software.
Additional authors: Alex Perkins

Damie Pak

Cornell University
"Resource availability constrains the proliferation rate of malaria parasites"
The life cycle of the malaria-causing species involves multiple rounds of replication, with a fraction of infected red blood cells (RBCs) being committed to producing specialized stages for onward transmission to vectors. The proliferation rate is limited by the burst size or the average number of daughter cells to emerge from each infected RBC. To increase transmission, parasites would be expected to evolve to the maximal burst size that does not prematurely end the infection by killing its host. The variability in observed burst size, however, suggests that maximizing the burst size is not always the best strategy.Using a within-host model parameterized for the rodent malaria, Plasmodium chabaudi, we investigate how host mortality and resource limitation affect the optimal burst size. We focus on the acute phase which encompasses the first and typically largest wave of parasite abundance with most of the parasite’s transmission success gained disproportionately in this phase. By calculating the cumulative transmission potential at the end of the acute phase, we can then compare the transmissibility of strains with varying burst sizes.We find that greater proliferation leads to the production of more sexual forms, but there are diminishing returns in transmission success. Moreover, the benefits of faster proliferation come at the cost of significantly shortening the period of high infectivity. Therefore, the optimal burst size emerges from the trade-off between the length of the acute phase and the production of the sexual forms. By identifying resource availability as a key mechanism limiting the burst size, we are better able to understand how parasite traits can influence the varying virulence we see in malaria infections.
Additional authors: Tsukushi Kamiya, Megan Greischar

Gabriella Torres Nothaft

Cornell University (Department of Mathematics)
"Impact of Disease on a Lotka-Volterra Predation Model"
Quantifying the relationship between predator and prey populations under the influence of disease provides important insight into their roles and behaviors in the ecosystem. This paper uses two models as the base for the analysis: the Lotka-Volterra predation model and the SIR disease model. Developed in the 20th century, the Lotka-Volterra predation model provides a mathematical explanation of this phenomenon and is widely recognized in both the mathematical and biological communities . Epidemiology models such as the standard susceptible-infected-susceptible (SIS) model can be used to understand the dynamics of a disease in a given population or area. There are multiple variations of this predation and infection impacting the prey population, affecting the basic model, all focused on variations on the spread of some infectious agent in the desired population. To fully understand the regulatory mechanisms that the two populations go through, we need to analyze how both predation and infection impact the prey population, which in turn affects the number of predators. In this work, we first go through the dynamics of the original Lotka-Volterra model, then perform stability and further analyses on the combined model.
Additional authors:  William Clark

Karan Pattni

University of Liverpool
"Eco-evolutionary dynamics in finite network-structured populations with migration"
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We looked at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.
Additional authors: Wajid Ali, Mark Broom, Kieran J Sharkey

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Annual Meeting for the Society for Mathematical Biology, 2023.