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

Santiago Alonso-Quesada, Manuel De la Sen and Raúl Nistal
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Santiago Alonso-Quesada: Department of Electricity and Electronics, Campus of Leioa, University of the Basque Country, UPV/EHU, Barrio Sarriena s/n, 48940 Leioa, Spain
Manuel De la Sen: Department of Electricity and Electronics, Campus of Leioa, University of the Basque Country, UPV/EHU, Barrio Sarriena s/n, 48940 Leioa, Spain
Raúl Nistal: Department of Electricity and Electronics, Campus of Leioa, University of the Basque Country, UPV/EHU, Barrio Sarriena s/n, 48940 Leioa, Spain

Mathematics, 2021, vol. 10, issue 1, 1-32

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 R c 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 R ¯ c , 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 R c > R ¯ c , 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 R c and R ¯ c . 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.

Keywords: epidemic models; vaccination and treatment actions; feedback control; equilibrium points; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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