A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses

Mathematical analysis of epidemics is crucial for long-term disease prediction and helps to guide decision-makers in terms of public health policy. In this study, we develop a within-host mathematical model of the malaria parasite dynamics with the effect of an adaptive immune response. The model includes six compartments, namely, the uninfected red blood cells, infected red blood cells, merozoites, gametocytes, cytotoxic T cells immune response, and antibodies immune response, which are activated in the host to attack the parasite. We establish the well-posedness and biological feasibility of the model in terms of proving the non-negativity and boundedness of solutions. The most important threshold value in the epidemiological model known as the basic reproduction number, R0, which is used to determine the stability of the steady state, is investigated. Furthermore, the parasite-free equilibrium is locally and globally stable if the basic reproduction number, R0 1, then there exist four parasite-persistence equilibria. The stability conditions of these parasite-persistence equilibria are presented. Sensitivity analysis of the basic reproduction number shows that parameters representing the recruitment rate of uninfected red blood cells, infection rate of red blood cells by merozoites, and the average number of merozoites per ruptured infected red blood cells are the most influential ones in affecting the dynamics. Finally, several numerical simulations of the model are presented to supplement the theoretical and analytical findings. It has been observed that numerical simulations and theoretical results are coherent. The response of cytotoxic T cells and antibodies has a significant impact on suppressing infected cells and malaria parasites in the host’s body.