Kashkynbayev, ArdakRihan, Fathalla A.2021-12-232021-12-232021-08-03Kashkynbayev, A., & Rihan, F. A. (2021). Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay. In Mathematics (Vol. 9, Issue 15, p. 1829). MDPI AG. https://doi.org/10.3390/math91518292227-7390https://doi.org/10.3390/math9151829https://www.mdpi.com/2227-7390/9/15/1829http://nur.nu.edu.kz/handle/123456789/5960Abstract: In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate the local and global stability of the steady-states. We deduce the basic reproductive threshold parameter, so that if R0 < 1, the disease-free steady-state is locally and globally asymptotically stable. However, for R0 > 1, there exists a positive (endemic) steady-state which is locally and globally asymptotically stable. A Holling type III response function is considered in the numerical simulations to illustrate the effectiveness of the theoretical results. Keywords: epidemic model; fractional calculus; global stability; lyapunov functionals; time-delayenAttribution-NonCommercial-ShareAlike 3.0 United Statesepidemic modelfractional calculusglobal stabilitylyapunov functionalstime-delayType of access: Open AccessArticle