Synchronous and asynchronous oscillations in a model for antigenically varying malaria, including the effects of constant and state-dependent delay.

摘要

My dissertation is comprised of three chapters. The first two pertain to modeling a malarial infection within an infected individual. More specifically, the model consists of a system of delay-differential equations with state variables as distinct parasitic variants or strains and corresponding specific and cross-reactive immune-response effectors. Some of my conclusions include conditions for recurrent clinical episodes of the disease, competition between types of oscillatory states, and critical delay times above which immunity is not attained. The third chapter investigates how a state-dependent delay influences the nonlinear behavior of a commonly-used weakly-damped nonlinear oscillator. In short, I derive conditions on the functional form of the delay which can cause the delay-induced Hopf bifurcation to be sub- or supercritical as well as predict the amplitude of the bifurcating branch of periodic solutions.