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

Ardak Kashkynbayev and Fathalla A. Rihan
Additional contact information
Ardak Kashkynbayev: Department of Mathematics, Nazarbayev University, Nur-Sultan 010000, Kazakhstan
Fathalla A. Rihan: Department of Mathematical Sciences, College of Sciences, UAE University, Al Ain 15551, United Arab Emirates

Mathematics, 2021, vol. 9, issue 15, 1-16

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 R 0 < 1 , the disease-free steady-state is locally and globally asymptotically stable. However, for R 0 > 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/15/1829/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/15/1829/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:15:p:1829-:d:607276

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().