Biomathematics
Department of Mathematics and Statistics
Texas Tech University
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Social hierarchies are ubiquitous in social groups such as human societies and social insect colonies, however, the factors that maintain these hierarchies are less clear. Motivated by the shared reproductive hierarchy of the ant species Harpegnathos Saltator, we have developed simple compartmental nonlinear differential equations to explore how key life-history and metabolic rate parameters may impact and determine its colony size and the length of its shared hierarchy. Our modeling approach incorporates nonlinear social interactions and metabolic theory. The results from the proposed model, which were linked with limited data, show that: (1) the proportion of reproductive individuals decreases over colony growth; (2) an increase in mortality rates can diminish colony size but may also increase the proportion of reproductive individuals; and (3) the metabolic rates have a major impact in the colony size and structure of a shared hierarchy.
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A history of genetic pest management is provided, culminating with the explosive development of gene drives in the past few decades. Gene drives are any natural or synthetic mechanism of propagating a gene into a target population, even if the gene imposes a fitness cost. This technology offers a promising solution to the burden posed by crop pests and vectors of important human diseases. However, gene drive dynamics in the wild are presently unknown, so scientists must leverage mathematical and computational models to understand how gene drives behave in a natural population. One of the most critical factors affecting gene drive performance is insect dispersal. The role of dispersal is explored in the case of the yellow fever mosquito, Aedes aegypti, using a spatially explicit patch model. Numerical results illustrate the complex relationship between gene drive function and dispersal behavior.
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Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
The transmission of mosquito-borne diseases depends on time-varying processes, such as temperature, precipitation, ecological habitat, and vector demography. The Climate Integrated Model of Mosquito-borne Infectious Diseases (CIMMID) initiative at the Los Alamos National Laboratory uses heterogeneous data fusion and mechanistic modeling to quantify future mosquito-borne disease risk under different scenarios of climate change. We first present a data-fusion framework for connecting mosquito time series data to our epidemiology models – a nonautonomous logistic model with periodically-varying parameters captures the interannual variability of mosquito population data across different species and geographical regions. We then introduce a partial differential equations model for West Nile Virus (WNV) transmission. This PDE model includes infection-age dynamics of mosquito vectors and bird hosts. Finally, we explain how projected climate data will be used to compare current and future WNV transmission risk between temperate and desert climates. As climate change continues to threaten our world, developing data-driven mathematical models becomes crucial to controlling and mitigating future vector-borne diseases.
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Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in varied clinical outcomes including asymptomatic, mild, severe, or fatal disease. While the mechanisms responsible for the pathogenesis of COVID-19 are not fully understood, studies suggest that virus-induced chronic inflammation and tissue injury are associated with severe outcomes. To determine the role of tissue damage on immune populations recruitment and function, we develop a mathematical model of innate immunity following SARS-CoV-2 infection. The model was fit to published longitudinal immune marker data from patients with mild and severe COVID-19 disease and key parameters were estimated for each clinical outcome. Analytical, bifurcation, and numerical investigations were conducted to determine the effect of parameters and initial conditions on long-term dynamics. The results were used to suggest changes needed to achieve immune resolution. Such results can guide interventions.
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Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
No abstract.
Join Zoom Meeting
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
No abstract.
Join Zoom Meeting
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
No abstract.
Join Zoom Meeting
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Gbemi will be presenting on a paper she read, by Lozano-Ochoa et. al. and titled 'Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion' (Discrete Dynamics in Nature and Society, 2017).
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Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
No abstract.
Join Zoom Meeting
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models.
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Many species have a consumer-resource relationship in which the resource species serve as food to the consumer species, causing death for the resource and growth for the consumer species. This relationship can involve a consumer and a resource, or multiple consumers and a resource. In the case of multiple consumers, competition for a resource is possible, and this can lead to death in any of the consumers. These processes can be continuous (which monitors populations of the consumer and resource at every time), or discrete (which monitors the populations yearly). Models that are only continuous or discrete may fail to take on the various workings of the species. Hence, this work combines continuous and discrete approaches to model consumer-resource interactions. For this model, it is vital to understand what leads to the death of the species, the survival of either, or the coexistence of both. However, identifying and understanding the behaviors possible require careful analysis and computations due to the model approach. In the case of competing consumers, we establish necessary conditions on model parameters for the existence of a coexistence fixed point. For the rest of our parameter space, we use a numerical approach to create a bifurcation-like image that shows the possible behaviors this model can exhibit. This is accomplished by testing the model over a wide span of parameters and varying initial conditions using Latin Hypercube Sampling. We identify parameters and initial conditions that produce the persistence of both species. In the case of a single consumer, we compare the behavior in different regions to existing bifurcation curves and obtain a better understanding of parameter regions without analytic results.
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Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.