MATHEMATICAL MODELLING OF THE IMPACT OF WANING IMMUNITY AND IMMUNE SYSTEM BOOSTING ON MALARIA TRANSMISSION

Abstract

A deterministic model is formulated to describe the dynamics of malaria transmission using mosquito population and human population structured by immune status. The variation in mortality of humans and mosquitoes due to causes other than malaria, the infectiousness of recovered humans, the decay of acquired immunity and the immune system boosting are taken into account. The existence of biological meaningful solutions has been analyzed and a single disease-free equilibrium has been identified. The basic reproduction number is expressed in terms of the parameters of the model. The stability of the disease-free equilibrium has been analyzed. We have provided some basic conditions in which the disease dies out or persists. The numerical results showed the impact of immunity decay and immune system boosting on malaria transmission. Received: July 31, 2023Accepted: September 26, 2023