Mathematical modeling of co-infections of hepatitis A viral disease and typhoid fever with optimal control strategies

In this study, a mathematical model with optimal control measures was used to investigate the transmission dynamics of co-infection of hepatitis A virus and typhoid fever. A deterministic compartmental model was used and an analysis of the effect of various control measures was compared. The pathogen fitness that represents the epidemic indicator is obtained by using the next-generation matrix. We have shown the existence of two equilibrium states: the disease-free steady state in which there are no populations that are infected by the co-infection of hepatitis A virus and typhoid fever, the endemic state in which a co-infected population exists and is capable of transmitting the disease. The local and global stability conditions of the endemic equilibrium points were also proved. Further, it was proved that the co-infection of the model exhibited a backward bifurcation. Finally, a numerical simulation of the model was made and it reveals that prevention has a significant impact in reducing the transmission of the co-infection and applying all the control measures can successfully eliminate co-infection of hepatitis virus and typhoid fever from the community.