On the Integrability of the SIR Epidemic Model with Vital Dynamics

Ding Chen

Advances in Mathematical Physics, 2020, vol. 2020, 1-10

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 .

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:5869275

DOI: 10.1155/2020/5869275

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