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On the Integrability of the SIR Epidemic Model with Vital Dynamics

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  • Ding Chen

Abstract

In this paper, we study the SIR epidemic model with vital dynamics , from the point of view of integrability. In the case of the death/birth rate , the SIR model is integrable, and we provide its general solutions by implicit functions, two Lax formulations and infinitely many Hamilton-Poisson realizations. In the case of , we prove that the SIR model has no polynomial or proper rational first integrals by studying the invariant algebraic surfaces. Moreover, although the SIR model with is not integrable and we cannot get its exact solution, based on the existence of an invariant algebraic surface, we give the global dynamics of the SIR model with .

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlamp:5869275
    DOI: 10.1155/2020/5869275
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    Cited by:

    1. Hernández, G. & Martín del Rey, A., 2022. "Community-distributed compartmental models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    2. Chakir, Yassine, 2023. "Global approximate solution of SIR epidemic model with constant vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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