Mathematical analysis of the dynamics of malaria disease transmission model

Abstract

We formulate a deterministic model for the transmission dynamics of malaria parasite in mosquito and human. The model, which allows for the transmission of the parasite, has a global asymptotic stable disease-free if a certain epidemiological threshold called the reproductive number is less than unity. We realized that the model has a unique academic equilibrium whenever this threshold exceeds unit. We proved that, using a Lyapunov function, that this endemic equilibrium is globally asymptotically stable whenever the basic reproduction number is greater than unity. We also carried out numerical simulations to support our analytical results.