Analytical Solution of the Transmission Dynamics of Diarrhea using Homotopy Perturbation Method

Abstract

Infectious diseases like measles, tuberculosis, cholera, diarrhea, COVID-19, and staphylococcal infection continue to receive a lot of attention daily due to their high rate of transmission and deadly nature. Thus, in this study, the analytical solution of the transmission dynamics of diarrhea was studied using the Homotopy perturbation approach. The human population was divided into five major compartments namely: susceptible, infective, exposed, recovered and vaccinated. The Homotopy Perturbation Method was then applied to the system of nonlinear differential equations formulated in relation to the various compartments. To derive the analytical solution to the transmission dynamics of diarrhea the nonlinear differential equations formulated were then embedded into the homotopy perturbation constructor and solved for the solution in the form of a power series. The study, therefore, recommends that simulations can be performed on the analytical solution in order to compare the dynamics using other mathematical techniques.