Mathematical analysis of typhoid model with saturated incidence rate

Abstract

Typhoid fever is considered one of the communicable disease, it's infection causes diarrhea and a rash. It is most commonly due to a type of bacterium called Salmonella typhi (S. typhi). In many developing countries this disease is endemic and remains one of the public health problem. In this paper, we consider a math- ematical model of the type SEIR (Susceptible, Exposed, Infected and Recovered) to understand the dynamics of this disease. We investigate the stability results for both local and global. For the basic reproduction number R 0 < 1, the disease free equilibrium is stable both locally and globally at E 0 . When R 0 > 1, the endemic equilibrium is stable both locally and globally at E 1 . Finally, the numerical results are obtained for analytical results.