A novel control set-valued approach with application to epidemic models (Q2053139)

This paper studies an approach to characterize one or more controls to achieve the null number of infected population at a final time. The epidemic model is described as \(\dot{x}=f(x,y,u)\) and \(\dot{y}=\psi(x,y,u)\), where \(x=(x_1,\cdots,x_n)\) with each component positive indicates the numbers of individuals in a population such as susceptible and recovered and \(y\), which is positive, denotes the number of infected individuals. The control \(u\) takes values in a bounded constraints subset. Here \(f\) can be non-affine with respect to the control and the dynamics \(\psi\) rely on the control variable. Based on the viability theory, the paper finds the control \(u\) such that the solution of the system is confined in a region while the number of infected individuals dies out eventually. Control set-valued approaches have been used and the existence of continuous selections under sufficient conditions has been tackled. An application to SIRS compartmental model is also provided.