Optimal control of a fractional order model for granular SEIR epidemic with uncertainty

摘要

In this study, we present a general formulation for the optimal control problem to a class of fuzzy fractional differential systems relating to SIR and SEIR epidemic models. In particular, we investigate these epidemic models in the uncertain environment of fuzzy numbers with the rate of change expressed by granular Caputo fuzzy fractional derivatives of order beta is an element of (0, 1]. Firstly, the existence and uniqueness of solution to the abstract fractional differential systems with fuzzy parameters and initial data are proved. Next, the optimal control problem for this fractional system is proposed and a necessary condition for the optimality is obtained. Finally, some examples of the fractional SIR and SEIR models are presented and tested with real data extracted from COVID-19 pandemic in Italy and South Korea. (C) 2020 Elsevier B.V. All rights reserved.