Mathematical Model for Hepatocytic-Erythrocytic Dynamics of Malaria

Abstract

Human malaria remains a major killer disease worldwide, with nearly half (3.2 billion) of the world’s population at risk of malaria infection. The infectious protozoan disease is endemic in tropical and subtropical regions, with an estimated 212 million new cases and 429,000 malaria-related deaths in 2015. An in-host mathematical model of Plasmodium falciparum malaria that describes the dynamics and interactions of malaria parasites with the host’s liver cells (hepatocytic stage), the red blood cells (erythrocytic stage), and macrophages is reformulated. By a theoretical analysis, an in-host basic reproduction number R0 is derived. The disease-free equilibrium is shown to be locally and globally asymptotically stable. Sensitivity analysis reveals that the erythrocyte invasion rate βr, the average number of merozoites released per bursting infected erythrocyte K, and the proportion of merozoites that cause secondary invasions at the blood phase ζ are the most influential parameters in determining the malaria infection outcomes. Numerical results show that macrophages have a considerable impact in clearing infected red blood cells through phagocytosis. Moreover, the density of infected erythrocytes and hence the severity of malaria are shown to increase with increasing density of merozoites in the blood. Concurrent use of antimalarial drugs and a potential erythrocyte invasion-avoidance vaccine would minimize the density of infected erythrocytes and hence malaria disease severity.