DYNAMICS OF FRACTIONAL-ORDER EPIDEMIC MODELS WITH GENERAL NONLINEAR INCIDENCE RATE AND TIME-DELAY
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Date
2021-08-03
Authors
Kashkynbayev, Ardak
Rihan, Fathalla A.
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI AG
Abstract
Abstract: 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-delay
Description
Keywords
epidemic model, fractional calculus, global stability, lyapunov functionals, time-delay, Type of access: Open Access
Citation
Kashkynbayev, 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/math9151829