Mathematical modelling of malaria transmission and pathogenesis

In this thesis we will consider two mathematical models on malaria transmission and patho- genesis. The transmission model is a human-mosquito interaction model that describes the development of malaria in a human population. It accounts for the various phases of the disease in humans and mosquitoes, together with treatment of both sick and partially im- mune humans. The partially immune humans (termed asymptomatic) have recovered from the worst of the symptoms, but can still transmit the disease. We will present a mathematical model consisting of a system of ordinary differential equations that describes the evolution of humans and mosquitoes in a range of malarial states. A new feature, in what turns out to be a key class, is the consideration of reinfected asymptomatic humans. The analysis will include establishment of the basic reproduction number, R0, and asymptotic analysis to draw out the major timescale of events in the process of malaria becoming non-endemic to endemic in a region following introduction of a few infected mosquitoes. We will study the model to ascertain possible time scale in which intervention programmes may yield better results. We will also show through our analysis of the model some evidence of disease control and possible eradication. The model on malaria pathogenesis describes the evolution of the disease in the human host. We model the effect of immune response on the interaction between malaria parasites and erythrocytes with a system of delay differential equations in which there is time lag between the advent of malaria merozoites in the blood and the training of adaptive immune cells. We will study the model to ascertain whether or not a single successful bite of an infected mosquito would result in death in the absence of innate and adaptive immune response. Stability analysis will be carried out on the parasite free state in both the immune and non immune cases. We will also do numerical simulations on the model to track the development of adaptive immunity and use asymptotic methods, assuming a small delay to study the evolution of the disease in a naive individual following the injection of small amount of merozoites into the blood stream. The effect of different levels of innate immune response to the pathogenesis of the disease will be considered in the simulations to elicit a possible immune level that can serve as a guide to producing a vaccine with high efficacy level.