Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models

In this paper, we present a new result that allows for studying the global stability of disease-free equilibrium point when basic reproduction number is less than 1, in fractional calculus context. The method only involves linear algebra and can be easily applied to study asymptotic stability. After proving some auxiliary lemmas involving Mittag–Leffler function, main paper. Under assumptions, prove differential system globally asymptotically stable. We then exemplify procedure with epidemiological models: fractional-order SEIR model classical incidence SIRS general HIV/AIDS.