An Approximate Solution of Fractional Order Epidemic Model of Typhoid using the Homotopy Perturbation Method

Abstract

The epidemic model of typhoid is considered to be a control strategy for the undeviating transference of infectious disease. Due to its high accuracy and efficiency in solving nonlinear differential equations, the homotopy perturbation method is coupled with the Riemann-Liouville fractional integral operator I of order n E (0,1) to obtain the approximate analytical solution of the epidemiology model presented at different level of n. The obtained results were subjected to simulation process where the effect of the causative bacterial in the medium was studied at various level of n . The entirety of the computational procedures was conducted utilizing Maple 18, and graphical representations and tabular data were exhibited to facilitate a lucid understanding of the simulation outcomes. These findings indicate that curtailing Salmonella contamination is of paramount importance for minimizing the hazard of sickness and infection. This can be achieved through the observance of meticulous hygiene, which includes consistent hand washing with soap and water, thorough cooking of food, and appropriate storage and handling of edibles.