Stability analysis of a fractional-order two-strain epidemic model with general incidence rates

Abstract

This paper is devoted to the study of the dynamics of a fractional order two-strain SEIR epidemic model with two general incidence rates. The basic results of the fractional-order calculus are recalled. Four equilibrium points for the model are given, namely the disease free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the total endemic equilibrium with respect to both strains. Local and global stability analysis is given using the basic reproduction rate. First, the local stability of the equilibrium point is proved by the Routh Hurwitz criterion for the fractional-order system (FR-H), and then the global stability is shown by using the Barbalat’s lemma to the fractional-order system (FB). The Barbalat’s lemma is a reliable method for the asymptotic analysis of the fractional dynamic systems. Finally, numerical simulations illustrated our analytical results.