Dynamical behavior of a fractional-order epidemic model for investigating two fear effect functions

Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both t...

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Bibliographic Details
Published in:Results in control and optimization Vol. 16; p. 100474
Main Authors: Thirthar, Ashraf Adnan, Abboubakar, Hamadjam, Alaoui, Abdesslem Lamrani, Nisar, Kottakkaran Sooppy
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2024
Elsevier
Subjects:
Asymptotic stability
Epidemic
Fear effect
Reproduction number
Epidemic
Asymptotic stability
92D30
Fear effect
Reproduction number
26A33
ISSN:2666-7207, 2666-7207
Online Access:Get full text
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Summary:Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both the control reproduction and strength numbers and derive the stability criteria of the disease-free equilibrium. In fact, we use the comparison theorem to show that the disease-free equilibrium point is globally asymptotically stable whenever Rc<1. Next, we prove that the solutions of the fractional model exist and are unique. Finally, several numerical simulations are conducted to verify our theoretical results.
ISSN:2666-7207
2666-7207
DOI:10.1016/j.rico.2024.100474