Mathematical analysis of a malaria model with partial immunity to reinfection
In this paper, a deterministic model with variable human population for the transmission dynamics of malaria disease, which allows transmission by the recovered humans, is first developed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where the stable disease-free equilibrium coexists with a stable endemic equilibrium. This phenomenon may arise due to the reinfection of host individuals who recovered from the disease. The model in an asymptotically constant population is also investigated. A complete global analysis of the model with mass action incidence is given, which reveals that the global dynamics of the malaria disease with reinfection is completely determined by the associated reproduction number. Moreover, it is shown that the phenomenon of backward bifurcation can be removed by replacing the standard incidence function with a mass action incidence. Graphical representations are provided to study the effect of the reinfection rate and to qualitatively support the analytical results on the transmission dynamics of the malaria.
scientific article; zbMATH DE number 6161328
scientific article