A mathematical model with numerical simulations for malaria transmission dynamics with differential susceptibility and partial immunity

Abstract

Malaria is a deadly vector-borne infectious disease with high prevalence in the world’s endemic tropical and subtropical regions. Differences in individuals’ disease susceptibility may lead to their differentiation of susceptibility to infection. We formulate a mathematical model for malaria transmission dynamics that accounts for the host’s differential susceptibility, where partial immunity is acquired after infection. As customary, the explicit formula for the basic reproduction number is derived and used to determine the local stability of the model’s equilibria. An analysis of a special case with two susceptible classes shows that the model could have two endemic equilibria when the disease threshold parameter is less than unity. Numerical simulations are provided for a differential susceptibility when individuals are re-infected seven times after the initial infection. Graphical representations show that the transient transmission dynamics of the infected components are indistinguishable when there is no inflow into the susceptible classes. When there is an inflow into the various susceptible classes, the graphs of the infected component of the model are fundamentally different, showing that individuals who have been infected multiple times tend to be less infected over time. Knowledge of the inflow rate and the infection reduction rate due to prior infection in each class could be key drivers to mitigate the burden of malaria in a community.