| The thesis is based on using mathematical approaches to gain insights into the transmission dynamics of malaria, a disease of major public health significance. Since mosquito vector is critically important to malaria dynamics, a model for the population dynamics of the malaria vector is considered first of all. The model takes the form of a system of delay differential equations. The asymptotic stability of the associated equilibria as well as the existence of Hopf bifurcation are established using various mathematical techniques and theories (such as the fluctuation method, Fatou's lemma and Hopf bifurcation theory).;Finally, the thesis addresses the problem of the role of repeated malaria exposure on the transmission dynamics of the disease in a population. It is shown that such repeated exposure induces the phenomenon of backward bifurcation, the epidemiological consequence of which is that the classical requirement of having the associated reproduction number less than unity becomes only necessary, but not sufficient, for the effective control of malaria in a population. Numerical simulations of the model show that the size of the backward bifurcation region increases with increasing rate of re-infection of first-time infected individuals.;A model assessing the impact of immune response and a potential anti-malaria vaccine on controlling malaria dynamics in an infected host is developed and rigorously analysed. The model, which is derived based on progressive refinements of some existing models, has a globally-asymptotically stable disease-free equilibrium (for a special case) when the associated reproduction threshold is less than unity. The model allows for the assessment of various assumed vaccine characteristics. |
