Deterministic Mathematical Model for Dynamics of Water Borne Diseases

Abstract

In this study a mathematical model is formulated using ordinary differential equations in order to understand the population dynamics of water borne diseases. The entire population is divided into five compartments depending upon their status. These compartments are – susceptible (S), exposed (E), symptomatically infected (I), recovered but carrying the infection asymptotically (RC) and completely recovered (R). We have taken pathogen population into account as compartment (P). Here, two ways of getting infected are considered which are from person-to-person and from environment-to-person. i.e. a susceptible person can get infected either by coming directly in contact with the person having disease or by consuming contaminated food or water. A relation for the basic reproduction number is established. The analysis results show that the disease free equilibrium is locally asymptotically stable in R0<1. Sensitivity analysis tells that the most important parameters are pathogen population and rate of transmission of disease from environment-to-person. Simulation is done using MATLAB. On the basis of sensitivity analysis and numerical simulation results we concluded that we need to cure an infected individual as soon as we identify the disease so that he would not contaminate environment for long.