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Stability analysis and optimal control of avian influenza virus A with time delays

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Abstract

In this research article we have developed a mathematical model to describe the spread of avian influenza A (H7N9) virus from the birds to human. We also consider the incubation periods of avian influenza A (H7N9) virus in this model with different time delay in the infective avian and human populations. By analyzing behaviour of the model, we calculate the basic reproduction number and investigate the local and global stability of equilibria of the system. Here we also set up an optimal control problem and used a quadratic control to reduce the spread of the disease and the cost of treatment. Computer simulations are carried out to explain the analytical findings.

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Acknowledgements

We would like to thank Department of Mathematics, IIEST, Shibpur for financial support to run the work. The second author is thankful to the University Grants Commission, India for providing SRF (RGNF). The third author acknowledges financial support from UGC, India (MRP No. - PSW-128/15-16 (ERO)). We would also like to thank two anonymous reviewers and editors for their comments and suggestions that improved this manuscript.

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Authors and Affiliations

  1. Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA

    S. Sharma

  2. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711 103, India

    A. Mondal & G. P. Samanta

  3. Department of Mathematics, S. A. Jaipuria College, Kolkata, 700005, India

    A. K. Pal

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  1. S. Sharma
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Correspondence to S. Sharma.

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Sharma, S., Mondal, A., Pal, A.K. et al. Stability analysis and optimal control of avian influenza virus A with time delays. Int. J. Dynam. Control 6, 1351–1366 (2018). https://doi.org/10.1007/s40435-017-0379-6

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  • DOI: https://doi.org/10.1007/s40435-017-0379-6

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