A dynamical model for HIV-typhoid co-infection with typhoid vaccine

Individuals living with HIV/AIDS are significantly at higher risk of infection with Salmonella Typhi. A deterministic nonlinear mathematical model that describes the co-infection dynamics of HIV and typhoid incorporating typhoid vaccine and treatment has been developed. The basic reproduction number for the co-infection model is computed. The co-infection model exhibits four steady states, namely, the disease-free, HIV alone endemic, typhoid alone endemic, and the co-infection endemic states. The local stability of the disease-free state has been investigated. The co-infection endemic state, if it exists, is found to be locally stable. The minimum vaccination rate that eliminates the typhoid infection is determined. Sensitivity analysis has been performed to ascertain model parameters that have a strong impact on the disease dynamics. It is demonstrated that the co-infection basic reproduction number can be reduced to below unity by simultaneous preventive measures, thereby eliminating both diseases. Numerical simulation of the co-infection model is carried out to examine the effects of parameters on disease spread. The study suggests that the two diseases need to be managed simultaneously for effective control of the co-infection.