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Turing patterns of an SI epidemic model with cross-diffusion on complex networks

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  • Duan, Moran
  • Chang, Lili
  • Jin, Zhen

Abstract

Epidemic models governed by reaction–diffusion equations with cross-diffusion can exhibit diversified pattern formations and can characterize important features of some diseases. Considering that populations are usually organized as networks instead of being continuously distributed in space, it is essential to study reaction–diffusion epidemic model with cross-diffusion on networks. Here we investigate Turing instability induced by cross-diffusion for a network organized SI epidemic model and explore Turing patterns on several different networks. Turing instability condition is obtained via linear analysis method and the condition is applied to study pattern formations for the model in question. With the help of numerical simulations, we investigate the influences of network topology and initial infection distribution on pattern formations and disease spreading from the aspects of arrival time of the first peak and steady density of the infected.

Suggested Citation

  • Duan, Moran & Chang, Lili & Jin, Zhen, 2019. "Turing patterns of an SI epidemic model with cross-diffusion on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    • Handle: RePEc:eee:phsmap:v:533:y:2019:i:c:s0378437119311598
    DOI: 10.1016/j.physa.2019.122023
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    Citations

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    Cited by:

    1. Mohan, Nishith & Kumari, Nitu, 2021. "Positive steady states of a SI epidemic model with cross diffusion," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Inferrera, G. & Munafò, C.F. & Oliveri, F. & Rogolino, P., 2024. "Reaction-diffusion models of crimo–taxis in a street," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    3. He, Haoming & Xiao, Min & He, Jiajin & Zheng, Weixing, 2024. "Regulating spatiotemporal dynamics for a delay Gierer–Meinhardt model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    4. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    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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