A consistent SIR model on time scales with exact solution

2025/09/15 by Lemos-Silva, Márcia, Vaz, Sandra, Torres, Delfim F. M.
#34N05 #92D30 #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE)

paper · doi:10.48550/arxiv.2509.22675

Abstract

We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free equilibria, and deduce some necessary conditions for the monotonic behavior of the infected population. The new results are illustrated with several examples in the discrete, continuous, and quantum settings.

Citations

• SIR models with vital dynamics, reinfection and randomness to investigate the spread of infectious diseases

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