English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we study the SIR epidemic model with vital dynamics _ S = −βSI + μðN − SÞ, _ I = βSI − ðγ + μÞI, _ R = γI − μR, from the point of view of integrability. In the case of the death/birth rate μ = 0, 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 μ ≠ 0, 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 μ ≠ 0 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 μ ≠ 0.

On the Integrability of the SIR Epidemic Model with Vital Dynamics