SIRS model for the dynamics of non-typhoidal salmonella epidemics

Abstract

A continuous mathematical model of salmonella diarrhea is introduced in this paper. According to the pathogenesis of salmonella, the model had been designed as an SIRS system comprising of a non-constant population. The disease-free state and the basic reproduction number (R0) have been computed for this system. In epidemics, there are always two cases: R0 < 1 (disease-free state) and R0 > 1 (epidemic existing state). Simulations of the system have been presented for both these cases which show the variations of the population in different situations. Data that has been used for examples and simulations is based on the demographics and disease outbreaks in Botswana.