Solution of the epidemic model by homotopy perturbation method

Rafei, M.; Ganji, D.D.; Daniali, Hamid Reza Mohammadi

doi:10.1016/j.amc.2006.09.019

Cited by 112 publications

(83 citation statements)

References 16 publications

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“…Second, (HAM) was shown to be a simple, yet powerful analytic numeric scheme for handling systems of fractional order. The results obtained by (HAM) are the same results obtained in [1] using (ADM), in [7] using (VIM), and in [8] using (HPM) at In other words (ADM), (VIM), (HPM) are special cases of (HAM). A comparison in fig.2 was presented between the HAM 3 rd order results, ADM 5 th order results obtained in [1], and RK4 method.…”

Section: Resultssupporting

confidence: 70%

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Approximate analytical solution of the fractional epidemic model

Rida¹,

Rady²,

Arafa³

et al. 2012

International Journal of Applied Mathematical Research

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Section: Resultssupporting

confidence: 70%

“…represents the HAM 3rd order series solution of system (18) in case of and . At we obtain three terms approximations which are the same solutions obtained in [1] using (ADM), in [7] using (VIM), and in [8] using (HPM) as follows …”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Approximate analytical solution of the fractional epidemic model

Rida¹,

Rady²,

Arafa³

et al. 2012

International Journal of Applied Mathematical Research

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“…In recent years, the mathematical epidemic models given by Eqs. (1)- (3) and (4)- (6) were investigated numerically in a number of papers, with the use of a wide variety of methods and techniques, namely, the Adomian decomposition method [13], the variational iteration method [14], the homotopy perturbation method [15], and the differential transformation method [16], respectively. Very recently, a stochastic epidemic-type model with enhanced connectivity was analyzed in [17], and an exact solution of the model was obtained.…”

Section: Introductionmentioning

confidence: 99%

Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates

Harkó

Lobo

Mak

2014

Applied Mathematics and Computation

430

376

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In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the parameters, and show that the numerical solution reproduces exactly the analytical solution. We also show that the generalization of the SIR model, including births and deaths, described by a nonlinear system of differential equations, can be reduced to an Abel type equation. The reduction of the complex SIR model with vital dynamics to an Abel type equation can greatly simplify the analysis of its properties. The general solution of the Abel equation is obtained by using a perturbative approach, in a power series form, and it is shown that the general solution of the SIR model with vital dynamics can be represented in an exact parametric form.

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“…This paper also suggests an alternative approach for construction of the homotopy equation with an auxiliary term. The HPM has been successfully applied to solve variety of linear and nonlinear problems in [31][32][33][34][35][36]. Recently, the application of HPM was extended to chaotic Genesio system [37], heat transfer analysis on the Hiemenz flow of a nonNewtonian fluid [38], long porous slider problem [39], and nonlinear boundary value problems of fractional order [40].…”

Section: Introductionmentioning

confidence: 99%

The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System

Chowdhury

Razali

Asrar

et al. 2015

Abstract and Applied Analysis

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The multistage homotopy-perturbation method (MHPM) is applied to the nonlinear chaotic and hyperchaotic Lü systems. MHPM is a technique adapted from the standard homotopy-perturbation method (HPM) where the HPM is treated as an algorithm in a sequence of time intervals. To ensure the precision of the technique applied in this work, the results are compared with a fourthorder Runge-Kutta method and the standard HPM. The results show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems.

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Solution of the epidemic model by homotopy perturbation method

Cited by 112 publications

References 16 publications

Approximate analytical solution of the fractional epidemic model

Approximate analytical solution of the fractional epidemic model

Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates

The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System

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