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Dynamical behavior of an epidemic model with fuzzy transmission and fuzzy treatment control

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Abstract

In this paper, we have considered an SIS epidemic model with arbitrary disease transmission function and arbitrary treatment control function. We have analyzed the model considering the disease transmission function as an increasing and decreasing function separately. To introduce heterogeneity in the system we have taken both the disease transmission function and treatment function as fuzzy numbers. Fuzzy expected value of the infected individual is defined and determined. Then fuzzy basic reproduction number is computed. At last, a threshold value is determined in both the cases where the system undergoes a transcritical and backward bifurcation.

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Acknowledgements

The work of Soovoojeet Jana is financially supported by Dept of Science & Technology and Biotechnology, Govt. of West Bengal (vide memo no. 201 (Sanc.)/ST/P/S&T/16G-12/2018 dt 19-02-2019). Moreover, the authors are very much thankful to the anonymous reviewers and Chin-Hong Park, the editor in chief of the journal, for their constructive comments and helpful suggestions to improve both the quality and presentation of the manuscript significantly.

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

    Sayani Adak

  2. Department of Mathematics, Ramsaday College, Amta, Howrah, West Bengal, 711401, India

    Soovoojeet Jana

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  1. Sayani Adak
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  2. Soovoojeet Jana
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Correspondence to Soovoojeet Jana.

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Adak, S., Jana, S. Dynamical behavior of an epidemic model with fuzzy transmission and fuzzy treatment control. J. Appl. Math. Comput. 68, 1929–1948 (2022). https://doi.org/10.1007/s12190-021-01597-8

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