Abstract: Malaria is one of the deadliest infectious diseases globally, causing hundreds of thousands of deaths each year. It disproportionately affects young children, with two-thirds of fatalities occurring in under-fives. Individuals acquire protection from disease through repeated exposure, and this immunity plays a crucial role in the dynamics of malaria spread. We develop and analyze an age-structured PDE model, which couples vector-host epidemiological dynamics with immunity dynamics. Our model tracks the acquisition and loss of anti-disease immunity during transmission and its corresponding nonlinear feedback onto the transmission parameters. We derive the basic reproduction number (R0) as the threshold condition for the stability of disease-free equilibrium and interpret R0 probabilistically as a weighted sum of cases generated by infected individuals at different infectious stages and ages. Numerical bifurcation analysis demonstrates the existence of an endemic equilibrium, and we observe a forward bifurcation in R0. Our model reproduces the heterogeneity in the age distributions of immunity profiles and infection status created by frequent exposure. Motivated by the recently approved RTS,S vaccine, we also study the impact of vaccination; our results show a reduction in severe disease among young children but a small increase in severe malaria among older children due to lower acquired immunity from delayed exposure. This is joint work with Denis Patterson, Lauren Childs, Christina Edholm, Joan Ponce, Olivia Prosper, and Lihong Zhao. 

Short Bio: Zhuolin Qu obtained her Ph.D. in Applied Mathematics in 2016 from Tulane University. She was a postdoctoral fellow at Tulane from 2016 – 2020, and she is currently an Assistant Professor at the University of Texas at San Antonio. She has been working on mathematical biology with particular interests in the mathematical modeling of infectious diseases, computational epidemiology, dynamical systems, and numerical methods for PDEs. She develops both equation-based compartmental models for mosquito-borne diseases and agent-based stochastic models for sexually transmitted diseases.