Fractional-order mathematical modeling of COVID-19 dynamics with different types of transmission

Mohamed Amouch; Noureddine Karim

doi:10.3934/naco.2023019

Article Contents

2025, Volume 15, Issue 2: 386-415. Doi: 10.3934/naco.2023019

This issue Previous Article A brief discussion about a predator-prey model including disease in predators with the delay effect Next Article On equilibrium multivalued problems in the general model with the Boolean-valued bifunction

Fractional-order mathematical modeling of COVID-19 dynamics with different types of transmission

Mohamed Amouch^1, and
Noureddine Karim^1, ,

1.
Chouaib Doukkali University, Department of Mathematics, Faculty of Science El Jadida, Morocco

^*Corresponding author: Noureddine Karim
^*Corresponding author: Noureddine Karim

Received: January 2023

Revised: August 2023

Early access: September 2023

Published: June 2025

This work was carried out as part of the project "Gestion de la COVID-19: approach système dynamique" financed by the research program related to COVID-19 2020 and supported by MENFPESRS, Morocco grant and CNRST, Morocco grant.

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Abstract

This paper investigates the novel coronavirus (COVID-19) infection system with a mathematical model presented with the Caputo derivative. We calculate equilibrium points and discuss their stability. We also go through the existence and uniqueness of a nonnegative solution for the system under study. We obtain numerical simulations for different order derivatives using the Fractional Natural Decomposition Method (FNDM) to understand better the dynamical structures of the physical behavior of COVID-19. The novel fractional model outperforms the existing integer-order model with ordinary temporal derivatives according to results from real-world clinical data. This behavior is based on the COVID-19 mathematical model's available features. The mathematical model is composed of real data reported from Morocco.

Keywords:

Equilibrium point,
mathematical model,
fractional differential system,
fractional natural decomposition method,
numerical simulation.

Mathematics Subject Classification: 26A33, 92D30.

Citation:

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Figure 1. Flowchart of model 4

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Figure 2. Daily evolution of the number of COVID-19 cases, recovered and deaths in Morocco from March 1, 2021 to August 1, 2021

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Plots of Susceptible for different values of $\alpha$

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Plots of infected people with severe symptoms for different values of $\alpha$ ( $I_{\max} = 60000$ )

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Plots of Recovered people for different values of $\alpha$ ( $R_{\max} = 60000$ )

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Table 1. The absolute and relative errors for $I(t)$

Model	$\alpha$	Absolute error	Relative error
Fractional	0.98	8.9252	0.0324
Integer	1	10.4541	0.0511

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Table 2. The absolute and relative errors for $R(t)$

Model	$\alpha$	Absolute error	Relative error
Fractional	0.98	8.9243	0.0364
Integer	1	10.7544	0.0401

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Table 3. Values of the model parameters corresponding to the situation of Morocco

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