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A robust study of dual variants of SARS-CoV-2 using a reaction-diffusion mathematical model with real data from the USA

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Abstract

This study proposes a mathematical model to analyze the transmission mechanism of SARS-CoV-2 using a reaction-diffusion framework. The importance of incorporating diffusion in mathematical models of SARS-CoV-2 is emphasized, as it can lead to a more accurate understanding of disease spread and inform effective public health interventions. The impact of diffusion effects on the SARS-CoV-2 epidemic model has been significant, as the virus has rapidly spread across the globe since it was first identified in late 2019. The speed and efficiency of transmission have been a key factor in the severity of the pandemic, as many individuals may be asymptomatic or experience mild symptoms, making it difficult to identify and control the spread of the virus. The model includes six classes, namely Susceptible, Exposed to strain 1 SARS-CoV-2 and strain 2 SARS-CoV-2, infected by strain 1 SARS-CoV-2 and strain 2 SARS-CoV-2, and Recovered or Removed (\(\mathbb {S}\) \(\mathbb {E}_1\) \(\mathbb {E}_2\) \(\mathbb {I}_1\) \(\mathbb {I}_2\) \(\mathbb {R}\)), which are dependent on both time and space. This study uses the next-generation matrix approach to calculate the threshold number \(R_0\) and estimates parameter values through the use of least squares curve fitting tools. A combination of the operator splitting approach, finite difference method, and Crank–Nicolson method is used to simulate the model. The study looks at how stable the disease-free and endemic equilibrium points are, and it performs sensitivity analysis to look at the effects of different parameters. The simulation results of the model are compared in detail with and without diffusion and are verified through mutual comparison and theoretical analysis to ensure the accuracy of the solution. This study provides valuable insights into the transmission mechanism of SARS-CoV-2 and has important implications for public health policy.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data generated or analyzed during this study are included in this article].

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Acknowledgements

The first author appreciates the support provided by Petchra Pra Jom Klao Ph.D. Research Scholarship through grant no (50/2565), by King Mongkut’s University of Technology Thonburi, Thailand.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Rahat Zarin & Usa Wannasingha Humphries

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  1. Rahat Zarin
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  2. Usa Wannasingha Humphries
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Correspondence to Usa Wannasingha Humphries.

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Zarin, R., Humphries, U.W. A robust study of dual variants of SARS-CoV-2 using a reaction-diffusion mathematical model with real data from the USA. Eur. Phys. J. Plus 138, 1057 (2023). https://doi.org/10.1140/epjp/s13360-023-04631-9

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