Mathematical model of epidemics: Analytical approach to SIRW model using homotopy perturbation method

Abstract

In this content, a non-linear system of differential equations of SIRW model has been described. In several situations, individuals who have recovered from a Cholera infection do not lose their immunity at a significant rate. So the basic SIR model is extended by adding new compartment water (W). Hence the SIR model becomes a SIRW model. Using Homotopy Perturbation Method, an approximate analytical solution of the SIRW model has been obtained and then the results are verified with the numerical simulation. We found finally a good agreement between the approximate analytical solutions and the numerical results of the same.