On a safety distribution for a class of SEIRS epidemic model

Abstract

The present paper analyse conditions on a given a non-linear SEIRS epidemic model parameters, to provide a safety set for the epidemic containment. After having determined this set, we look for control actions constraining the epidemic to remain within the safety set with infection rates below an allowed threshold. This means that for any initial state in a certain safety set of the state space, there exists an appropriate control strategy maintaining the state of the system in the considered safety set. To ensure the solvability under feedback control of our problem, sufficient assumptions are derived in terms of linear inequalities on the input vectors at the vertices of a polytope.