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Positive steady states of a SI epidemic model with cross diffusion

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  • Mohan, Nishith
  • Kumari, Nitu

Abstract

We propose a spatiotemporal SI epidemic model with cross diffusion. The cross diffusion term is proposed for the first time in literature and through our analysis we have confirmed that coexistence of the participating species is possible under its influence. We study the model using coupled upper and lower solutions for an elliptic partial differential equations with Dirichlet boundary conditions. We derive sufficient conditions for the coexistence of the susceptible and infected populations. Mathematical analysis is performed to prove that at least one coexistence state will exist for the proposed model system. We further proved that the system exhibits Turing instability in the presence of the proposed cross diffusion and carried out numerical simulation to observe the patterning behavior. This work provides a significant insight on how epidemic models can be influenced by cross diffusion effects.

Suggested Citation

  • Mohan, Nishith & Kumari, Nitu, 2021. "Positive steady states of a SI epidemic model with cross diffusion," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005129
    DOI: 10.1016/j.amc.2021.126423
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    References listed on IDEAS

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    1. 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).
    2. B. T. Grenfell & O. N. Bjørnstad & J. Kappey, 2001. "Travelling waves and spatial hierarchies in measles epidemics," Nature, Nature, vol. 414(6865), pages 716-723, December.
    3. Gambino, G. & Lombardo, M.C. & Sammartino, M., 2012. "Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1112-1132.
    4. Peng, Yahong & Ling, Heyang, 2018. "Pattern formation in a ratio-dependent predator-prey model with cross-diffusion," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 307-318.
    5. Derek A.T. Cummings & Rafael A. Irizarry & Norden E. Huang & Timothy P. Endy & Ananda Nisalak & Kumnuan Ungchusak & Donald S. Burke, 2004. "Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand," Nature, Nature, vol. 427(6972), pages 344-347, January.
    6. Liu, Chen & Li, Li & Wang, Zhen & Wang, Ruiwu, 2019. "Pattern transitions in a vegetation system with cross-diffusion," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 255-262.
    7. Li, Hong-Li & Zhang, Long & Teng, Zhidong & Jiang, Yao-Lin & Muhammadhaji, Ahmadjan, 2018. "Global stability of an SI epidemic model with feedback controls in a patchy environment," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 372-384.
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    Cited by:

    1. Ke, Yue & Zhu, Linhe & Wu, Peng & Shi, Lei, 2022. "Dynamics of a reaction-diffusion rumor propagation model with non-smooth control," Applied Mathematics and Computation, Elsevier, vol. 435(C).

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