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The numerical solution of epidemic models on moving domains using combined masses

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  • Christou, Katerina

Abstract

The application of a moving mesh finite difference method, based on mass conservation, is described for epidemic models, integrating cross- and self-diffusion to represent social distancing and self-isolation. A significant feature of the models is the moving boundary which describes the spread of the disease in the domain. Numerical illustrations emphasise the influence of social interactions on transmission and infection rates. Notably, simulations show containment of disease spread within a small initial infected radius despite a high reproductive parameter. The results affirm the efficacy of the moving mesh approach for multi-population systems in epidemic models.

Suggested Citation

  • Christou, Katerina, 2026. "The numerical solution of epidemic models on moving domains using combined masses," Applied Mathematics and Computation, Elsevier, vol. 509(C).
    • Handle: RePEc:eee:apmaco:v:509:y:2026:i:c:s0096300325004175
    DOI: 10.1016/j.amc.2025.129691
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    References listed on IDEAS

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    1. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "A SIR model assumption for the spread of COVID-19 in different communities," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. David Berger & Kyle Herkenhoff & Chengdai Huang & Simon Mongey, 2022. "Testing and Reopening in an SEIR Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 1-21, January.
    3. Michael te Vrugt & Jens Bickmann & Raphael Wittkowski, 2020. "Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    4. M. J. Baines & Katerina Christou, 2022. "A Numerical Method for Multispecies Populations in a Moving Domain Using Combined Masses," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    5. Wencai Zhao & Tongqian Zhang & Zhengbo Chang & Xinzhu Meng & Yulin Liu, 2013. "Dynamical Analysis of SIR Epidemic Models with Distributed Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Michael John Baines & Katerina Christou, 2021. "A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    7. Rowell, Jonathan T., 2009. "The limitation of species range: A consequence of searching along resource gradients," Theoretical Population Biology, Elsevier, vol. 75(2), pages 216-227.
    8. Wencai Zhao & Tongqian Zhang & Zhengbo Chang & Xinzhu Meng & Yulin Liu, 2013. "Dynamical Analysis of SIR Epidemic Models with Distributed Delay," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-15, July.
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