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Effect of time delay on pattern dynamics in a spatial epidemic model

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  • Wang, Yi
  • Cao, Jinde
  • Sun, Gui-Quan
  • Li, Jing

Abstract

Time delay, accounting for constant incubation period or sojourn times in an infective state, widely exists in most biological systems like epidemiological models. However, the effect of time delay on spatial epidemic models is not well understood. In this paper, spatial pattern of an epidemic model with both nonlinear incidence rate and time delay is investigated. In particular, we mainly focus on the effect of time delay on the formation of spatial pattern. Through mathematical analysis, we gain the conditions for Hopf bifurcation and Turing bifurcation, and find exact Turing space in parameter space. Furthermore, numerical results show that time delay has a significant effect on pattern formation. The simulation results may enrich the finding of patterns and may well capture some key features in the epidemic models.

Suggested Citation

  • Wang, Yi & Cao, Jinde & Sun, Gui-Quan & Li, Jing, 2014. "Effect of time delay on pattern dynamics in a spatial epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 137-148.
    • Handle: RePEc:eee:phsmap:v:412:y:2014:i:c:p:137-148
    DOI: 10.1016/j.physa.2014.06.038
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    References listed on IDEAS

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    Cited by:

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    3. Mann Manyombe, M.L. & Tsanou, B. & Mbang, J. & Bowong, S., 2017. "A metapopulation model for the population dynamics of anopheles mosquito," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 71-91.
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    5. Alzahrani, Faris & Razzaq, Oyoon Abdul & Rehman, Daniyal Ur & Khan, Najeeb Alam & Alshomrani, Ali Saleh & Ullah, Malik Zaka, 2022. "Repercussions of unreported populace on disease dynamics and its optimal control through system of fractional order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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    7. Jang, Junyoung & Kwon, Hee-Dae & Lee, Jeehyun, 2020. "Optimal control problem of an SIR reaction–diffusion model with inequality constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 136-151.

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