On the Homotopy Analysis Method for an Seir Tuberculosis Model

Ibrahim, M. O.; Egbetade, S. A.

doi:10.12691/ajams-1-4-4

Cited by 2 publications

(1 citation statement)

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“…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. Their analysis which is based on Homotopy Analysis Method (HAM) used Maple 15 Software to carry out their computations, and their result showed the validity and potential of HAM for computing the solution of nonlinear equations, [7].…”

Section: Introductionmentioning

confidence: 99%

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Chioma¹,

Ugonna²,

Michael³

et al. 2019

MMA

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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.

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Section: Introductionmentioning

confidence: 99%