Numerical analysis of COVID-19 model with Caputo fractional order derivative

This paper focuses on the numerical solutions of a six-compartment fractional model with Caputo derivative. In this model, we obtain non-negative and bounded solutions, equilibrium points, and the basic reproduction number and analyze the stability of disease free equilibrium point. The existence an...

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Bibliographic Details
Published in:AIP advances 2024-03, Vol.14 (3), p.035202-035202-15
Main Authors: Shahabifar, Reza, Molavi-Arabshahi, Mahboubeh, Nikan, Omid
Format: Article
Language:English
Subjects:
Differential equations
Fixed points (mathematics)
Fractional calculus
Mathematical models
Numerical analysis
Parameter sensitivity
Stability analysis
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Summary:This paper focuses on the numerical solutions of a six-compartment fractional model with Caputo derivative. In this model, we obtain non-negative and bounded solutions, equilibrium points, and the basic reproduction number and analyze the stability of disease free equilibrium point. The existence and uniqueness of the solution are proven by employing the Picard–Lindelof approach and fixed point theory. The product–integral trapezoidal rule is employed to simulate the system of FODEs (fractional ordinary differential equations). The numerical results are presented in the form of graphs for each compartment. Finally, the sensitivity of the most important parameter (β) and its impact on COVID-19 dynamics and the basic reproduction number are reported.
ISSN:2158-3226
2158-3226
DOI:10.1063/5.0189939