Doctoral Dissertations

Date of Award

12-2025

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Olivia Feldman

Committee Members

Olivia Feldman, Suzanne Lenhart, Ioannis Sgouralis, Mark Wilber

Abstract

Mathematical modeling can serve as a tool for understanding complex biological systems and elucidating host-pathogen interactions. We illustrate the utility of mathematical modeling applied to host-pathogen systems by presenting three mathematical modeling frameworks. The first two frameworks are applied to within-human-host Plasmodium falciparum malaria and the third framework is applied to the fungal pathogen Batrachochytrium salamandrivorans (Bsal).

Human malaria is a vector-borne disease caused by Plasmodium parasites transmitted through the bite of an infected Anopheles mosquito. Within-human-host malaria dynamics are complex, involving several parasite life-stages, including asexual replication (the parasite stage associated with symptom onset), and sexual development into gametocytes (the parasite stage responsible for human-to-mosquito transmission). When considering new antimalarial treatments, approaches that balance reduction of asexual parasite forms (and thus morbidity and mortality) with the selection of drug resistant parasites are needed. We present a within-host differential equations model that includes time-dependent drug dynamics to assess the impact of a triple artemisinin-based combination therapy (TACT) on the probability of human-to-mosquito transmission. For our second malaria model we develop a more biologically realistic and flexible model framework of within-host dynamics that allows for arbitrary distributions for the waiting times for each red blood cell and parasite life cycle stage. Using the model, we assess how varying the distribution assumptions impacts the probability of human-to-mosquito transmission.

Integral projection models (IPMs) provide a framework for using individual-level demographic data to make population-level predictions. However, if not properly accounted for, measurement error in individual-level experimental data can have effects that propagate through the model and bias predictions. To address this limitation, we develop an Integrated Survival Model Framework (Integrated IPM) that combines individual-level demographic data with host death time observation data to parameterize an IPM, from which we can predict emergent survival curves. We illustrate the ability of the Integrated IPM to account for measurement error by testing the model on simulated host-pathogen load data that contains measurement error. We then apply the Integrated IPM to experimental data from adult and juvenile eastern newts, salamander hosts susceptible to the fungal pathogen Bsal.

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