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Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment

Acta Biotheoretica volume 64, pages 65–84 (2016)Cite this article

Abstract

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried out to validate our analytical results.

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Acknowledgments

Research of T. K. Kar is financially supported by the Council of Scientific and Industrial Research (CSIR) (File No. 25(0224)/14/EMR-II, dated 2/12/14). Further the authors are very much grateful to the anonymous reviewers and Associate editor Lia Hemerik, for their careful reading, useful comments and constructive suggestions for the improvement of the manuscript of the present research work.

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Affiliations

  1. Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia, Birbhum, West Bengal, 731234, India

    Soovoojeet Jana

  2. Department of Mathematics, Nayabasat P. M. Sikshaniketan, Paschim Medinipur, West Bengal, 721253, India

    Swapan Kumar Nandi

  3. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    T. K. Kar

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  1. Soovoojeet Jana
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  2. Swapan Kumar Nandi
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  3. T. K. Kar
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Correspondence to Soovoojeet Jana.

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Jana, S., Nandi, S.K. & Kar, T.K. Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment. Acta Biotheor 64, 65–84 (2016). https://doi.org/10.1007/s10441-015-9273-9

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  • DOI: https://doi.org/10.1007/s10441-015-9273-9

Keywords

  • Epidemiology
  • Basic reproduction number
  • Global stability
  • Backward bifurcation
  • Optimal treatment control