Optimal control of an SIQRS epidemic model with three measures on networks

At present, the main measures for disease control are vaccination, quarantine and treatment. Taking the three measures into consideration, time-varying optimal control problems of an SIQS epidemic model of the network are proposed, and the aim of this paper is to reduce control costs. The existence and solutions of the problems are solved by the optimal control theory. At last, the theoretical results are illustrated by numerical simulations. The results of numerical simulations show the advantages of different control strategies. It may be helpful for the development of disease control strategies. Our results are suitable for diseases in which a recovered individual may have lost immunity and can be infected again.