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Impacts of Media Awareness on a Stage Structured Epidemic Model

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Abstract

Nowadays the nature of the emerging infectious diseases is becoming very complicated. Diseases spread among human beings through different stages and also initially proper control measures are hardly available to prevent these diseases. In this article, we propose a stage structured epidemic model incorporating the media awareness and assuming that the disease can be transmitted only among the mature populations. The model is analyzed by means of its different equilibria and their stability. The global stability of both the infection free and infected steady states are proved under some parametric conditions. The existence of the transcritical bifurcation is also examined. Further to manage the outspread of the disease, an optimal control problem is formulated considering media awareness as a control parameter. Then the control problem is solved analytically by applying the Pontryagin’s maximum principle. The influence of the media awareness on the disease dynamics and the analytical findings of this work are illustrated through several numerical simulations. Finally, this article comes to an end with a brief discussion on the whole work.

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Acknowledgements

Research of Anupam Khatua is financially supported by Department of Science and Technology-INSPIRE, Government of India (No. DST/INSPIRE Fellowship/2016/IF160667, dated: 21st September, 2016). We are grateful to the anonymous reviewers and editors for their valuable comments and useful suggestions to improve 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, 711103, West Bengal, India

    Anupam Khatua & Tapan Kumar Kar

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Khatua, A., Kar, T.K. Impacts of Media Awareness on a Stage Structured Epidemic Model. Int. J. Appl. Comput. Math 6, 152 (2020). https://doi.org/10.1007/s40819-020-00904-4

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