Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis
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Published:2021-01-04
Issue:1
Volume:2021
Page:
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ISSN:1687-1847
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Container-title:Advances in Difference Equations
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language:en
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Short-container-title:Adv Differ Equ
Author:
Alqahtani Rubayyi T.
Abstract
AbstractIn this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number $R_{0}$R0is less than unity and unstable when$R_{0} > 1$R0>1. The analysis shows that the phenomenon of backward bifurcation occurs when$R_{0}<1$R0<1. Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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