Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Abstract

In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.

Application of the Modified Adomian Decomposition Method on a Mathematical Model of COVID-19

“…The equilibrium points are calculated by equating the left hand side of equation system (1) to zero. This leads to the following system of equations,…”

“…In [1], Homotopy Analysis Method (HAM) was used to solve the differntial equations of the Susptible, Exposed, Infective and Removed (SEIR) epidemic model. The results showed that the series solution converged very fast and the solutions were accurate.…”