Dynamic analysis and optimal control of a fractional order model for hand-foot-mouth Disease

Abstract

In this paper, a fractional order mathematical model is constructed to describe the transmission of hand-foot-mouth disease. Two cases are considered: constant control and optimal control. In the former case, the existence and uniqueness of positive solutions are proved; then the sufficient conditions for the existence and stability of two equilibriums are obtained. In the latter case, the existence of an optimal control solution is obtained; next, the optimality control conditions are derived by using Pontryagin’s Maximum Principle. After that, some numerical simulations are performed to verify the theoretical prediction.