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Complex dynamics of an epidemic model with vaccination and treatment controls

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Abstract

This paper describes the dynamical behavior of an epidemic model in the presence of vaccination and treatment controls. In the first part of our analysis we study both the local as well as global dynamics of the deterministic model. Next in the second part of our analysis we modify the model with an additional perturbation around the endemic equilibrium and study the asymptotically mean square stability of the modified system. Some numerical simulations are carried out on both the deterministic and the modified models to support our analytical results.

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Acknowledgments

The research of T. K. Kar is partially supported by the Council of Scientific and Industrial Research (CSIR) (Grant No.: 25(0224)/14/EMR II, dated December 2, 2014). Further, the authors are very much grateful to the anonymous reviewers for their constructive comments and helpful suggestions to improve the manuscript significantly.

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Authors and Affiliations

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

    Soovoojeet Jana

  2. Department of Mathematics, Sundarban Hazi Desarat College, Pathankhali, 743611, West Bengal, India

    Palash Haldar

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

    T. K. Kar

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  1. Soovoojeet Jana
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  2. Palash Haldar
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Correspondence to Soovoojeet Jana.

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Jana, S., Haldar, P. & Kar, T.K. Complex dynamics of an epidemic model with vaccination and treatment controls. Int. J. Dynam. Control 4, 318–329 (2016). https://doi.org/10.1007/s40435-015-0189-7

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  • DOI: https://doi.org/10.1007/s40435-015-0189-7

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