An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns

Abstract

This paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is considered. The control reproduction number Rc of the controlled epidemic model is calculated, and its influence in the existence and stability of equilibrium points is studied. If such a number is smaller than a threshold value Rc, then the model has a unique equilibrium point: the so-called disease-free equilibrium point at which there are not infectious individuals. Furthermore, such an equilibrium point is locally and globally asymptotically stable. On the contrary, if Rc>Rc, then the model has two equilibrium points: the referred disease-free one, which is unstable, and an endemic one at which there are infectious individuals. The proposed control strategy provides several free-design parameters that influence both values Rc and Rc. Then, such parameters can be appropriately adjusted for guaranteeing the non-existence of the endemic equilibrium point and, in this way, eradicating the persistence of the infectious disease.

On the Properties of a Newly Susceptible, Non-Seriously Infected, Hospitalized, and Recovered Subpopulation Epidemic Model

“…During the first stage of the COVID-19 epidemic evolution, as no vaccine was available, reducing social contact was a widely adopted measurement all over the world, and the impact of this prevention method is researched in [34,35]. Other works included vaccination strategies such as newborn vaccination [36], vaccinating a proportion of the susceptible subpopulation [37,38], and implementing dynamic vaccination and treatment with an SIR-like model [39]. All of these analyze the local and global stability of their respective systems' equilibrium points, among other things.…”

Estimation of the Instantaneous Reproduction Number and Its Confidence Interval for Modeling the COVID-19 Pandemic

“…To study the reproduction of this virus, health experts designed a series of strategies [1]. Consequently, recent investigations have been developed to model the COVID-19 pandemic [2][3][4].…”

Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”

“…Alonso-Quesada et al [10] investigate an SIRS epidemic model involving the immunization of susceptible individuals and the treatment of contagious individuals, which are both governed by a designed control system for which its inputs are the subpopulations of the epidemic model. Additionally, newborn vaccinations are also taken into account and control strategies are proposed to eradicate the infectious disease.…”