Open AccessON A SAFETY SET FOR AN EPIDEMIC MODEL WITH A BOUNDED POPULATION
Author(s) -
Carmen Coll,
Sergio RomeroVivó,
Elena Sánchez
Publication year - 2022
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2022.14586
Subject(s) - bounded function , set (abstract data type) , polytope , mathematics , state (computer science) , containment (computer programming) , population , class (philosophy) , state space , epidemic model , combinatorics , computer science , algorithm , statistics , mathematical analysis , demography , artificial intelligence , sociology , programming language
Given a class of non-linear SIRS epidemic model, we analyse some useful conditions on the model parameters to determine a safety set for the containment of an epidemic. In addition, once that set is determined, we find control actions so that the epidemic remains within the security set with infection rates below an allowed amount. More specifically, for every initial state in a certain safety set of the state space there exists an adequate control policy maintaining the state of the system in such safety set. Sufficient conditions for the existence of a solution under a feedback are derived in terms of linear inequalities on the input vectors at the vertices of a polytope.