Modeling the Complex Dynamics of Epidemic Spread Under Allee Effect

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 266)


An attempt has been made to investigate the dynamics of a diffusive epidemic model with strong Allee effect in the susceptible population and with an asymptotic transmission rate. We show the asymptotic stability of the endemic equilibria. Turing patterns selected by the reaction-diffusion system under zero flux boundary conditions have been explored. We have also studied the criteria for diffusion-driven instability caused by local random movements of both susceptible and infective subpopulations. Based on these results, we perform a series of numerical simulations and find that the model exhibits complex pattern replication: spots and spot–stripe mixture patterns. It was found that diffusion has appreciable influence on spatial spread of epidemics. Wave of chaos appears to be a dominant mode of disease dispersal.


Epidemic spread Turing instability Wave of chaos 


  1. 1.
    Allee, W.C.: Animal Aggregations: A Study in General Sociology. AMS Press, New York (1978)Google Scholar
  2. 2.
    Dennis, B.: Allee effects: population growth, critical density, and the chance of extinction. Nat. Res. Model. 3(4), 481–538 (1989)MATHMathSciNetGoogle Scholar
  3. 3.
    Wang, W., Cai, Y., Wu, M., Wang, K., Li, Z.: Complex dynamics of a reaction–diffusion epidemic model. Nonlinear Anal.: Real World Appl. 13(5), 2240–2258 (2012)Google Scholar
  4. 4.
    Jorgensen, SE.: Handbook of Environmental Data and Ecological parameters. Pergamon Press, Oxford (1979)Google Scholar
  5. 5.
    Petrovskii, S.V., Malchow, H.: Wave of chaos: new mechanism of pattern formation in spatiotemporal population dynamics. Theor. Popul. Biol. 59, 157–174 (2001)CrossRefMATHGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian School of MinesDhanbadIndia

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