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. 2025 Jul 17;15(1):25925.
doi: 10.1038/s41598-025-97785-8.

Discussing the epidemiology of COVID-19 model with the effective numerical scheme

Abeer Aljohani  1 , Shahbaz Mustafa  2 , Shan Ali Khan  3 , Abdullah Alhushaybari  4 , Herbert Mukalazi  5
Affiliations

Discussing the epidemiology of COVID-19 model with the effective numerical scheme

Abeer Aljohani et al. Sci Rep. .

Abstract

COVID-19 is a contagion that's container lead to lung difficulties such as pneumonia and, in the greatest severe circumstances, serious respirational disease. In response to these challenges, the present research proposes and analyses an SEIQR model with a nonlinear recovery and incidence rate. The appearance aimed at fundamental threshold quantity [Formula: see text] is established, which is critical to the stability of disease-free and endemic equilibria. A non-standard Finite difference (NSFD) Scheme is developed and for the model, and the denominator function is select so that the proposed structure maintains solution boundedness. It is demonstrated that the NSFD scheme is not dependent on the step size produces superior outcomes in totally admirations. The Jacobian approach is employed to establish the local stability of the disease free equilibrium, while Schur-Cohn conditions are used for the endemic equilibrium point in the the discrete NSFD scheme. The Enastu Criterion and the Lyapunov Function are used to demonstrate the global stability of the disease free and endemic equilibria. Numerical simulation are also presented to discuss the benefits of the NSFD scheme and to validate the theoretical conclusions. Calculated simulations show that the NSFD method preserves the important aspects of the continuous model. As a result, they generate estimates that align consistently with the model's solutions.

Keywords: Incidence rate; Local and global stability; Lyapunov function; Numerical simulations.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
A graphic depiction of the illness energetic in a compartmental model (1).
Fig. 2
Fig. 2
Numerical simulation of SEIQR model (1) by using NSFD scheme with formula image other parameters remain fixed as Table 1.
Fig. 3
Fig. 3
Numerical simulation for model (1) by using NSFD scheme with formula image(a–c) Stable DFE point with formula image (d) Unstable DFE point formula image Other parameters stay stable as Table 1.
See this image and copyright information in PMC

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