Women in Mathematical Epidemiology

Thursday, June 17 at 04:15am (PDT)
Thursday, June 17 at 12:15pm (BST)
Thursday, June 17 08:15pm (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS18" time block.
Note: this minisymposia has multiple sessions. The second session is MS19-MEPI (click here).

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Katharine Gurski (Howard University, United States), Kathleen Hoffman (University of Maryland, Baltimore County, United States)


These special sessions highlight the work of female mathematicians working in the field of epidemiology who are also in the AWM Women in Mathematical Biology (WIMB) research network. The global pandemic has put a spotlight on epidemiological research and the value of mathematical models to predict the time course of the disease dynamics in the presence of vaccines, treatments, and behavior adaptation such as social distancing. These special sessions feature female researchers in epidemiology working on a wide variety of diseases such as HIV, COVID-19, MERS, Ebola, and Malaria. The types of models considered span ODE models, PDE models, and stochastic models. population models, agent-based models as well as within host models and between host models. These special sessions provide a broad sampling of current work in mathematical epidemiology and demonstrates the growth of the Women in Mathematical Biology network.

Zhilan Feng

(Purdue University, United States)
"Applications of mathematical models in epidemiology"
Mathematical modeling of infectious diseases has affected disease control policy throughout the developed world. Policy goals vary with disease and setting, but preventing outbreaks is common. In this talk, I will present several examples to demonstrate how various models can be used to answer questions related to disease control and prevention for specific diseases in real populations. These models are systems of integral and/or differential equations. The mathematical results are motivated to address specific biological questions.

Marissa Renardy

(Applied BioMath, United States)
"Structural identifiability analysis of PDEs: A case study in continuous age-structured epidemic models"
Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.

Olivia Prosper

(University of Tennessee Knoxville, United States)
"Within-mosquito parasite heterogeneity and its impact on population-level malaria transmission"
The malaria parasite Plasmodium falciparum requires a vertebrate host and a female Anopheles mosquito to complete a full life cycle, with sexual reproduction occurring in the mosquito. This sexual stage of the parasite life cycle allows for the production of genetically novel parasites. In the meantime, a mosquito’s biology creates bottlenecks in the infecting parasites’ development. In earlier work, we developed a stochastic model of within-mosquito parasite dynamics and the generation of parasite diversity within a mosquito. We demonstrated the importance of heterogeneity in parasite dynamics across a population of mosquitoes on estimates of parasite diversity. Here, we investigate the implications of this heterogeneity on population-level transmission dynamics of malaria.

Miranda Teboh-Ewungkem

(Lehigh University, Lehigh University)
"Using Continuous-time Systems of Non-Linear Ordinary Differential Equations to study Removal of Mosquito-Breeding Site Density Under Community Action and Temperature Effects"
: A system of two first order nonlinear ordinary differential equations is used to model and theoretically investigate the dynamics of the formation of mosquito breeding sites in a uniform environment. The model captures the dynamic interplay between community action, climatic factors, and the availability of mosquito breeding sites. The developed model is analysed using standard methods in nonlinear dynamical systems' theory. Model results show that it is possible to attempt the problem of the dynamics of formation of breeding sites by considering the level of human consciousness as measured through human response to community action. Different feedback response functions are used to excite the breeding site removal and community action. For the case where the response functionals are both constants, we identify an indicator function whose size can indicate whether in the long run, community action can lead to the removal and elimination of breeding sites near human habitats. Using a predictor-corrector procedure that fits real climatic data to a continuous periodic function, we demonstrate how climatic variables can be included in the model and how models for the time variation of temperature and precipitation in a given area can be constructed just by appropriately choosing the parameters of a sinusoidal function and then correcting the output using nonlinear least squares analysis. Numerical simulation results are used to complement our analytical results.

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Virtual conference of the Society for Mathematical Biology, 2021.