A Mathematical Model for Malaria Disease Dynamics with Relapse Parameter

Malaria is one of the oldest diseases that has been extensively researched from multiple perspectives. Although many infectious diseases, including malaria, are preventable, they remain widespread in numerous communities due to insufficient, delayed, or ineffective control measures. Effective disease control involves rapidly reducing the infected population when a cure is available and minimizing susceptibility through vaccination when possible. Since malaria vaccines are still under development, vaccination offers a potential strategy for reducing the number of susceptible individuals. In this paper, we have analyzed and modified the SPITR mathematical model by Adamu et al. (2017) to study the transmission and control of malaria. Our modifications include the incorporation of a relapse parameter, and we have determined the basic reproduction number for the revised model. We demonstrated that the disease-free equilibrium (DFE) is locally asymptotically stable when the reproduction number is less than one and becomes unstable when it exceeds one. This finding suggests that with a combination of effective treatment, malaria relapse rate can be reduced and malaria in general can be effectively controlled in the population if the reproduction number is kept below unity.