A consistent SIR model on time scales with exact solution

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.