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Optimal Strategies to Prevent COVID-19 from Becoming a Pandemic

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Mathematical Modeling and Intelligent Control for Combating Pandemics

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 203))

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Abstract

This chapter is dedicated to what measures could have been taken to prevent COVID-19 from becoming a pandemic. Since COVID-19 shows the distribution according to the power law and exponential law in biological networks, fractional derivatives are useful to model the spread of the virus realistically. Therefore, a mathematical model, formerly originated for COVID-19, is firstly investigated with the Caputo derivative to represent the spread of the virus according to the power law. Then, a fractional optimal control problem (FOCP) is enhanced to prevent spread. Existence-proven controls representing strategies such as non-pharmaceutical and pharmaceutical interventions and plasma transfusion therapy aim to minimize the rate of infected individuals together with the cost required for treatment and prevention of the infection. After that, the necessary optimality conditions are revealed by Pontryagin’s Maximum Principle and solved numerically using Adam’s type predictor–corrector method (PCM) combined with the forward–backward sweep algorithm (FBSA). Finally, the optimal control design is studied in terms of the Atangana–Baleanu derivative in Caputo sense (ABC) to examine the spread of the virus according to the exponential law. All results are presented comparatively under various control strategies by using MATLAB.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Balıkesir University, Balıkesir, Turkey

    Beyza Billur İskender Eroğlu

Authors
  1. Beyza Billur İskender Eroğlu
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  2. Dilara Yapışkan
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Corresponding author

Correspondence to Beyza Billur İskender Eroğlu .

Editor information

Editors and Affiliations

  1. Department of Medical Research, China Medical University Hospital, Taichung, Taiwan

    Zakia Hammouch

  2. University of Hassan II Casablanca, Casablanca, Morocco

    Mohamed Lahby

  3. Department of Mathematics and Computer Science, Cankaya University, Etimesgut, Türkiye

    Dumitru Baleanu

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Eroğlu, B.B.İ., Yapışkan, D. (2023). Optimal Strategies to Prevent COVID-19 from Becoming a Pandemic. In: Hammouch, Z., Lahby, M., Baleanu, D. (eds) Mathematical Modeling and Intelligent Control for Combating Pandemics. Springer Optimization and Its Applications, vol 203. Springer, Cham. https://doi.org/10.1007/978-3-031-33183-1_3

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