@article{6f4529b9a29240869214fa80abd4f2aa,
title = "Dynamics of fractional-order epidemic models with general nonlinear incidence rate and time-delay",
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",
author = "Ardak Kashkynbayev and Rihan, {Fathalla A.}",
note = "Funding Information: Funding: This research was funded by the research grant No. AP08052345 “Mathematical models for glioblastoma proliferation” from the Ministry of Education and Science of the Republic of Kazakhstan. Funding Information: Acknowledgments: A.K. would like to thank the Department of Mathematical Sciences at UAE University for their hospitality as well as the Asian Universities Alliance (AUA) for their support of this trip. The authors thank the editor, C.Rajivganthi, and reviewers for their valuable comments which improved the quality of the paper. Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",
year = "2021",
month = aug,
day = "1",
doi = "10.3390/math9151829",
language = "English",
volume = "9",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "15",
}