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Modeling the Complex Dynamics of Epidemic Spread Under Allee Effect

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Recent Advances in Information Technology

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

Abstract

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.

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References

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  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)

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, Jharkahnd, India

    Parimita Roy & Ranjit Kumar Upadhyay

Authors
  1. Parimita Roy
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  2. Ranjit Kumar Upadhyay
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Corresponding author

Correspondence to Ranjit Kumar Upadhyay .

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Editors and Affiliations

  1. Computer Science and Engineering, Indian School of Mines, Dhanbad, Dhanbad, Jharkhand, India

    G. P. Biswas

  2. Computer Science and Engineering, Indian School of Mines, Dhanbad, Dhanbad, Jharkhand, India

    Sushanta Mukhopadhyay

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Roy, P., Upadhyay, R.K. (2014). Modeling the Complex Dynamics of Epidemic Spread Under Allee Effect. In: Biswas, G., Mukhopadhyay, S. (eds) Recent Advances in Information Technology. Advances in Intelligent Systems and Computing, vol 266. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1856-2_13

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  • DOI: https://doi.org/10.1007/978-81-322-1856-2_13

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1855-5

  • Online ISBN: 978-81-322-1856-2

  • eBook Packages: EngineeringEngineering (R0)

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