Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay

Ardak Kashkynbayev, Fathalla Ali Rihan

2021

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DOI 10.3390/math9151829
Data confidence 70 medium
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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.