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Dynamical analysis and perturbation solution of an SEIR epidemic model

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  • Wang, Xiaoyun
  • Wei, Lijuan
  • Zhang, Juan

Abstract

In this paper we present a kind of technique to obtain the asymptotical solution of an SEIR (where S is the susceptible population, E is the exposed population, I is the infectious population and R is the recovered population) epidemic model by employing the method of perturbation. At first, we investigate the epidemic model by analysing its dynamical behavior. Then, we use the method of perturbation to obtain the analytical solution of the model. We assign values for parameters and draw figures to observe the magnitude of error of the perturbation method in a macro view. Finally, we analyse macroscopically the two comparison chart on analytical solution and the exact solution, and know that it is feasible to analyse the solution of the epidemic model by using the perturbation method.

Suggested Citation

  • Wang, Xiaoyun & Wei, Lijuan & Zhang, Juan, 2014. "Dynamical analysis and perturbation solution of an SEIR epidemic model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 479-486.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:479-486
    DOI: 10.1016/j.amc.2014.01.090
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    References listed on IDEAS

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    1. Jia, Junguo & Wang, Miansen & Li, Meili, 2007. "Periodic solutions for impulsive delay differential equations in the control model of plankton allelopathy," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 962-968.
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    Cited by:

    1. 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.
    2. Dantas, Eber & Tosin, Michel & Cunha Jr, Americo, 2018. "Calibration of a SEIR–SEI epidemic model to describe the Zika virus outbreak in Brazil," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 249-259.
    3. Siriprapaiwan, Supatcha & Moore, Elvin J. & Koonprasert, Sanoe, 2018. "Generalized reproduction numbers, sensitivity analysis and critical immunity levels of an SEQIJR disease model with immunization and varying total population size," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 70-89.

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