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A new analysis of infection dynamics: multi-regions discrete epidemic model with an extended optimal control approach

Abstract

We propose in this paper an extended optimal control approach applied to multi-regions discrete model for the study of infection dynamics and control of an epidemic when it emerges in many regions which are supposed to be accessible for health authorities. We apply optimal control theory for investigating the effectiveness of an optimal control approach for the prevention of disease outbreaks, and which is based on both vaccination and travel-blocking strategies. First, the vaccination method taken into account in this work, aims to highlight the importance of mass vaccination campaigns that health policy-makers could lead in all regions affected by an epidemic, and important to control, for reducing the number of their infected people and increasing the number of their removed people. Second, the travel-blocking optimal control approach introduced here, is presented as a defensive strategy to limit the number of people traveling from regions with high-risk of infection towards regions with a risk relatively smaller. These regions are also controlled by vaccinations, and movements of their people intending to reach other regions, are restricted, in order to help contain the spread of the epidemic by following convenient vaccination for each region.

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Correspondence to Ilias Elmouki.

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This work is supported by the Systems Theory Network (Réseau Théorie des Systèmes), and Hassan II Academy of Sciences and Technologies-Morocco.

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Zakary, O., Rachik, M. & Elmouki, I. A new analysis of infection dynamics: multi-regions discrete epidemic model with an extended optimal control approach. Int. J. Dynam. Control 5, 1010–1019 (2017). https://doi.org/10.1007/s40435-016-0264-8

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Keywords

  • Multi-regions
  • Discrete SIR model
  • Optimal control
  • Multi-points boundary value problems