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S-I-R Model with Directed Spatial Diffusion

Author

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  • FABIO MILNER
  • RUIJUN ZHAO

Abstract

A S-I-R epidemic model is described in which susceptible individuals move away from foci of infection, and all individuals move away from overcrowded regions. It consists of hyperbolic partial differential equations, the sum of these equations being parabolic. Positivity and regularity of solutions are discussed and finite time blow-up of some solutions is illustrated through numerical simulations. A numerical test of the finite time blow-up of solutions is proposed.

Suggested Citation

  • Fabio Milner & Ruijun Zhao, 2008. "S-I-R Model with Directed Spatial Diffusion," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(3), pages 160-181.
    • Handle: RePEc:taf:mpopst:v:15:y:2008:i:3:p:160-181
    DOI: 10.1080/08898480802221889
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    Cited by:

    1. Rauf Ahmed Shams Malick & Syed Kashir Hasan & Fahad Samad & Nadeem Kafi Khan & Hassan Jamil Syed, 2023. "Smart Methods to Deal with COVID-19 at University-Level Institutions Using Social Network Analysis Techniques," Sustainability, MDPI, vol. 15(6), pages 1-17, March.
    2. Lazebnik, Teddy, 2023. "Computational applications of extended SIR models: A review focused on airborne pandemics," Ecological Modelling, Elsevier, vol. 483(C).
    3. Norberto Aníbal Maidana & Hyun Mo Yang, 2013. "How Do Bird Migrations Propagate the West Nile virus," Mathematical Population Studies, Taylor & Francis Journals, vol. 20(4), pages 192-207, October.
    4. Chang, Lili & Jin, Zhen, 2018. "Efficient numerical methods for spatially extended population and epidemic models with time delay," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 138-154.
    5. Victoria Chebotaeva & Paula A. Vasquez, 2023. "Erlang-Distributed SEIR Epidemic Models with Cross-Diffusion," Mathematics, MDPI, vol. 11(9), pages 1-18, May.
    6. Mi-Young Kim & Tsendayush Selenge, 2016. "Discontinuous-continuous Galerkin methods for population diffusion with finite life span," Mathematical Population Studies, Taylor & Francis Journals, vol. 23(1), pages 17-36, January.
    7. d’Onofrio, Alberto & Banerjee, Malay & Manfredi, Piero, 2020. "Spatial behavioural responses to the spread of an infectious disease can suppress Turing and Turing–Hopf patterning of the disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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