Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative

摘要

An epidemic system of HIV/AIDS transmission is examined in this paper. The classical time derivative is modelled with the Atangana-Baleanu nonlocal and nonsingular fractional operator in the Caputo sense. Mathematical analysis which shows that both the disease free equilibrium state and endemic equilibrium are locally asymptotically stable. A viable numerical approximation technique of Atangana-Baleanu operator is also given. Some numerical simulation results obtained for different instances of fractional order gamma are reported to justify the theoretical results. (C) 2019 Elsevier Ltd. All rights reserved.