On the Modeling and Simulation of a New SIR Epidemic Model with Saturated Incidence

This paper presents and studies a new epidemic SIR (Susceptible-Infectious-Recovered) model with susceptible recruitment and eventual joint vaccination efforts on newborn and susceptible individuals. Saturation effects in the incidence terms are eventually assumed for both the Infectious and the Susceptible. The vaccination action on newborn individuals is assumed to be applied to a fraction of them while that on the susceptible general population is of linear feedback type, based on information on the current levels of the Susceptible. The basic reproduction numbers (i.e. the numbers of average contagions on the Susceptible from each Infectious) are shown to decrease with the application vaccination control efforts, which implies that the allowed disease transmission rates compatible with the local stability of the disease-free equilibrium point increase under such controls.