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Global approximate solution of SIR epidemic model with constant vaccination strategy

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  • Chakir, Yassine

Abstract

Providing a global semi-analytical method has the advantage of offering a global and accurate solution to the epidemic model, which can help in studying and controlling the spread of the disease. Unlike numerical methods such as the Runge–Kutta–Fehlberg method, global semi-analytical methods can provide an explicit expression of the solution over the entire time period, including obtaining the peak time, which is crucial information for understanding disease spread. In this paper, a global semi-analytical method based on the two-point Padé approximants for solving the SIR epidemic model of childhood diseases is presented. The objective of this study is to examine the temporal dynamics of a childhood disease when a preventive vaccine is present. For this purpose, we have first derived the solution of the SIR model of childhood diseases in terms of series expansions for small and large values. Then, the theory of two-point Padé approximations is used to provide the global approximate solution. The peak time related to this model is also obtained via these global approximants. Furthermore, in order to show the efficiency of our study, some graphs have been given to compare our results with those obtained using the classical Padé approximations and the numerical Runge–Kutta–Fehlberg method.

Suggested Citation

  • Chakir, Yassine, 2023. "Global approximate solution of SIR epidemic model with constant vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923002242
    DOI: 10.1016/j.chaos.2023.113323
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    References listed on IDEAS

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    1. Ding Chen, 2020. "On the Integrability of the SIR Epidemic Model with Vital Dynamics," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-10, July.
    2. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2021. "SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 514-534.
    4. Turkyilmazoglu, Mustafa, 2022. "An extended epidemic model with vaccination: Weak-immune SIRVI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
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