Abstract

This paper proposes a deterministic mathematical model for the transmission dynamics of malaria and typhoid co-infection incorporating loss of immunity. The sub models and the malaria and typhoid co-infection model were analyzed. The next generation matrix method was used to obtain the basic reproduction number; we also obtained the disease-free equilibrium for malaria sub model, typhoid sub model and co-infection model. Local and global stability of the system were obtained using Ruth Hurwitz criterion and Castillo-Chavez method, respectively. The results of our study shows that the disease-free point is locally asymptotically stable when The model is also globally asymptotically stable, indicating that the disease eradication is independent on the initial population size. Numerical experiments were conducted using MATLAB R2015a, we observed that infected human population increases for both malaria and typhoid with an increased value of mosquito biting rate and the result also indicate that the best way of minimizing or eradicating malaria and typhoid in a population is to keep the transmission probabilities of malaria by mosquitoes and typhoid transmission rate to a barest minimal which will in turn keep reproduction number below one (a condition for disease eradication)