Sensitivity analysis was performed on the mathematical model of Cholera to determine the influence and importance of each parameter on the basic reproduction number (R0) in the dynamical spread of Cholera. Basic Reproduction Number (R0) was obtained using next generation matrix method (NGM). The disease free equilibrium was analyzed for stability and the analysis shows that the disease free equilibrium point is globally asymptotically stable whenever the basic reproduction number is less than unity i.e (R0<1). Also, there exist endemic equilibrium points of the model whenever R0>1. The relative sensitivity indices of the model with respect to each parameter in the basic reproduction number is calculated in order to find the most sensitive parameter which the medical practitioners and policy health makers should work on in order to reduce the spread of cholera in the society. The result shows that effective contact rate and fraction of individuals with low immunity are the most sensitive parameters in the reproduction number. Numerical simulation was carried out by MAPLE 17 software using Runge-kutta method of order four to show the effects of contact rate and fraction of individuals with low immunity in the dynamical spread of Cholera. This work will allow the health policy makers to know the best control measure to be adopted in order to have disease free environment.

In this paper, Sumudu Transform Series Decomposition Method (STSDM) for solving Integro-Differential Equation is presented. The method is an elegant combination of Sumudu Transform method, series expansion and Adomian polynomial. Three numerical problems were solved and compared with the exact solutions and the results by other approximate methods in order to check the effectiveness, reliability, accuracy, and the convergence of the method. The results obtained by STSDM showed that it is a powerful mathematical technique for solving wide range of physical problems arising in science and engineering fields.