Subharmonic Bifurcation in Malaria Epidemic Model

Abstract

Seasonal variations in rainfall and resource availability are ubiquitous and can exert strong pressure on population dynamics. This study considered seasonal variation of mosquito on the transmission dynamics if malaria. The epidemic thresholds parameters are computed to examine variation in the basic reproduction number. Stability of disease free and endemic equilibria with respect to seasonal variation in mosquito birth and transmission of malaria when the basic reproduction number is less or greater than unity are discussed. Applying perturbation methods, stable subharmonic bifurcation solutions of periods “n” are proved to coexist simultaneously and an infinite number of stable subharmonic bifurcation solutions were established. Numerical simulations are carried out to investigate the effects of seasonal variation of mosquito birth and transmission rate on the dynamic behavior of the system. This study suggest that intervention strategies needs to be deployed especially when there is sufficient rainfall that can sustain vector development and survival. Also, every effort must be put in place by all concerned to prevent the parasite infection by reducing the basic reproduction number, until malaria eradication is achieved.