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Dynamics of an epidemic model with spatial diffusion

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  • Wang, Tao

Abstract

Mathematical models are very useful in analyzing the spread and control of infectious diseases which can be used to predict the developing tendency of the infectious disease, determine the key factors and to seek the optimum strategies of disease control. As a result, we investigated the pattern dynamics of a spatial epidemic model with logistic growth. By using amplitude equation, we found that there were different types of stationary patterns including spotted, mixed, and stripe patterns, which mean that spatial motion of individuals can form high density of diseases. The obtained results can be extended in other related fields, such as vegetation patterns in ecosystems.

Suggested Citation

  • Wang, Tao, 2014. "Dynamics of an epidemic model with spatial diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 119-129.
    • Handle: RePEc:eee:phsmap:v:409:y:2014:i:c:p:119-129
    DOI: 10.1016/j.physa.2014.04.028
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    References listed on IDEAS

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    1. Sun, Gui-Quan & Jin, Zhen & Liu, Quan-Xing & Li, Li, 2008. "Dynamical complexity of a spatial predator–prey model with migration," Ecological Modelling, Elsevier, vol. 219(1), pages 248-255.
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    1. Davide La Torre & Danilo Liuzzi & Simone Marsiglio, 2022. "Geographical heterogeneities and externalities in an epidemiological‐macroeconomic framework," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1154-1181, October.
    2. Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2024. "Epidemic outbreaks and the optimal lockdown area: a spatial normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 349-411, February.
    3. Langmüller, Anna M. & Hermisson, Joachim & Murdock, Courtney C. & Messer, Philipp W., 2025. "Catching a wave: On the suitability of traveling-wave solutions in epidemiological modeling," Theoretical Population Biology, Elsevier, vol. 162(C), pages 1-12.
    4. Anita Triska & Agus Yodi Gunawan & Nuning Nuraini, 2023. "The Effects of the Susceptible and Infected Cross-Diffusion Terms on Pattern Formations in an SI Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    5. 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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