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Solutions of the SIR models of epidemics using HAM

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  • Awawdeh, Fadi
  • Adawi, A.
  • Mustafa, Z.

Abstract

In this paper, we investigate the accuracy of the Homotopy Analysis Method (HAM) for solving the problem of the spread of a non-fatal disease in a population. The advantage of this method is that it provides a direct scheme for solving the problem, i.e., without the need for linearization, perturbation, massive computation and any transformation. Mathematical modeling of the problem leads to a system of nonlinear ODEs. MATLAB 7 is used to carry out the computations. Graphical results are presented and discussed quantitatively to illustrate the solution.

Suggested Citation

  • Awawdeh, Fadi & Adawi, A. & Mustafa, Z., 2009. "Solutions of the SIR models of epidemics using HAM," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3047-3052.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3047-3052
    DOI: 10.1016/j.chaos.2009.04.012
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    References listed on IDEAS

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    1. Bai, Yanping & Jin, Zhen, 2005. "Prediction of SARS epidemic by BP neural networks with online prediction strategy," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 559-569.
    2. Gao, Shujing & Teng, Zhidong & Xie, Dehui, 2009. "Analysis of a delayed SIR epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1004-1011.
    3. Satsuma, J & Willox, R & Ramani, A & Grammaticos, B & Carstea, A.S, 2004. "Extending the SIR epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 369-375.
    4. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
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    Cited by:

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    2. Carvalho, Alexsandro M. & Gonçalves, Sebastián, 2021. "An analytical solution for the Kermack–McKendrick model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    3. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Dong, Suyalatu & Deng, Yanbin & Huang, Yong-Chang, 2019. "Exact analytic solution to nonlinear dynamic system of equations for information propagation in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 319-329.
    5. Aydin Secer & Neslihan Ozdemir & Mustafa Bayram, 2018. "A Hermite Polynomial Approach for Solving the SIR Model of Epidemics," Mathematics, MDPI, vol. 6(12), pages 1-11, December.

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