Modeling the Endemic Equilibrium of Typhoid Fever

Abstract

In this study, we have proposed and analyzed a nonlinear mathematical model for the spread of typhoid in a population with variable size structure. A threshold parameter is found that completely determines the stability dynamics and outcome of the disease. It is found that if the threshold parameter is less than one the disease free equilibrium is stable and the disease dies out. However, if the threshold parameter is more than one, there exists a unique endemic equilibrium that is locally asymptotically stable. Numerical simulation of the model is also performed by using fourth order Runge - Kutta method. Numerically, it has been found that the system exhibits steady state bifurcation for some parameter values. It is concluded from our analysis that endemic level of infective population increases with the increase in rate of transmission of infection due to infective among susceptible class. The results shall be presented in tabular and graphical form.