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A two-thresholds policy for a Filippov model in combating influenza

Journal of Mathematical Biology volume 81, pages 435–461 (2020)Cite this article

Abstract

This work designs a two-thresholds policy for a Filippov model in combating influenza, so as to estimate when and whether to take control strategies, including the media coverage, antiviral treatment of infected individuals and vaccination of susceptible population. By introducing two tolerance thresholds \(S_{c}\) and \(I_{c}\) of susceptible and infected individuals, the two-thresholds policy is designed as: a vaccination program is implemented when the number of susceptible individuals is above \(S_{c}\); an antiviral treatment strategy is taken and the mass media begins to report information about influenza when the infection number is larger than \(I_{c}\); no control strategies are required in other cases. Furthermore, the global dynamics of the model are analyzed by varying these two thresholds, including the existence and dynamics of sliding mode, and the existence and global stability of equilibrium. It is shown that the model solutions ultimately converge to a pseudoequilibrium or a pseudoattractor on the switching surface, or a real equilibrium. The obtained results indicate that, by choosing susceptible and infected thresholds properly, the infection number can be remained below or at an acceptable level.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11801528 and 11801140), Foundation of Henan Educational Committee (Nos. 19A110035 and 19A110008) and Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions(No. 20zx003).

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Affiliations

  1. School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, 450046, China

    Can Chen & Litao Zhang

  2. College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450046, China

    Pengde Wang

Authors
  1. Can Chen
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  2. Pengde Wang
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  3. Litao Zhang
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Correspondence to Can Chen.

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Chen, C., Wang, P. & Zhang, L. A two-thresholds policy for a Filippov model in combating influenza. J. Math. Biol. 81, 435–461 (2020). https://doi.org/10.1007/s00285-020-01514-w

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  • DOI: https://doi.org/10.1007/s00285-020-01514-w

Keywords

  • Influenza
  • Filippov model
  • Two-thresholds policy
  • Global dynamics
  • Sliding-mode dynamics

Mathematics Subject Classification

  • 34A38
  • 92D30
  • 34D23