Mathematical Analysis of Typhoid Model with Saturated Incidence Rate

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Mathematical Analysis of Typhoid Model with Saturated Incidence Rate

by Sarah Lindsay January 6, 2015

Authors

Muhammad Altaf Khan, Muhammad Parvez, Saeed Islam, Ilyas Khan, Sharidan Shafie, and Taza Gul.

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 mathematical 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 R0 < 1, the disease free equilibrium is stable both locally and globally at E0. When R0 > 1, the endemic equilibrium is stable both locally and globally at E1. Finally, the numerical results are obtained for analytical results.

 

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