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.
Highlights
Mathematical models have been used in comparing, planning, implementing, evaluating and optimizing various detection, prevention, therapy and control programs.World Health Statistics (2000) shown that some vector borne diseases as Malaria, Dengue and Yellow fever, continue to threaten throughout the public health of many people
Modeling of natural phenomena in science and engineering mostly leads to nonlinear problems
A Homotopy Analysis Method was presented for SEIR tuberculosis model
Summary
Mathematical models have been used in comparing, planning, implementing, evaluating and optimizing various detection, prevention, therapy and control programs. A Homotopy Analysis Method was presented for SEIR tuberculosis model In their paper, they provided a very accurate, non-perturbative, semi-analytical solution to a system of nonlinear first-order differential equations modeling the transmission of tuberculosis (TB) in a homogeneous population. Driven by seasonality the diseases were characterized by annual oscillations with variation contact rate which is a periodic function of time in years They used HAM to obtain a semi analytic approximate solution of nonlinear simultaneous differential equations. It is observed that for some values of B the temperature distribution in the bar is an increasing function of B while for other values of B it is a decreasing function In their work, they introduced the basic idea of HAM and applied it to find an approximate analytical solution of the nonlinear one-dimensional heat conduction problem with temperature dependent thermal conductivity, [3]. Denote the numbers of individuals in the compartments S, E, I, R, and S, at time t as S(t), E(t), I(t), R(t), and S(t) respectively
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