Mathematical analysis of an extended SIRS-SI malaria model incorporating seasonal vector recruitment with standard incidence

In this study an extended deterministic SIRS-SI malaria model incorporating seasonality on vector recruitment with standard incidence and vaccination is developed and analyzed. Positivity and boundedness of model solutions are shown. The vaccine reproductive number Rv is obtained using next generation matrix approach. The Routh Hurwitz criterion is applied to analyze the local stability of Malaria-Free Equilibrium (MFE) point which is found to be locally asymptotically stable whenever Rv < 1. Gershgorin discs is applied to analyze the local stability of Malaria Persistence Equilibrium (MP E) point which is locally asymptotically stable when Rv > 1, implying that the disease would persist in the population. The Castillo-Chavez technique is applied to analyze the global stability of MF E. The analysis shows that the MF E point is globally asymptotically stable provided that Rv < 1. The numerical simulation show that an increase in vaccination rate (α) while using a vaccine of higher efficacy (ϵ) leads to reduction of malaria infection. It is shown that during rainy seasons, there is high mosquito recruitment hence there are expectation of malaria infectious periods. Therefore, the policy makers should educate on the use of mosquito treated bed nets, clearing of bushes around homestead, and spraying the insecticides during rainy seasons.