Stability analysis and optimal control of a fractional-order model for African swine fever

Abstract

In this paper, a basic fractional-order model is proposed to describe the transmission of African swine fever. Two cases are considered: constant control and optimal control. In the former case, the existence and uniqueness of positive solution is proved firstly; then the basic reproduction number and the sufficient conditions for the stability of two equilibriums are obtained by using the next generation matrix method and Lyapunov LaSalle's invariance principle. In the latter case, optimal control is considered. By using the Hamiltonian function and Pontryagin's maximum principle, the optimal control formula is obtained. In addition, some examples and numerical simulations (based on Adama-Bashforth-Moulton predictor-corrector method) are performed to verify the theoretical results. At last, we present some brief discussion and conclusion.