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Modelling and optimal control of multi strain epidemics, with application to COVID-19

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  • Edilson F Arruda
  • Shyam S Das
  • Claudia M Dias
  • Dayse H Pastore

Abstract

Reinfection and multiple viral strains are among the latest challenges in the current COVID-19 pandemic. In contrast, epidemic models often consider a single strain and perennial immunity. To bridge this gap, we present a new epidemic model that simultaneously considers multiple viral strains and reinfection due to waning immunity. The model is general, applies to any viral disease and includes an optimal control formulation to seek a trade-off between the societal and economic costs of mitigation. We validate the model, with and without mitigation, in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil. The model can derive optimal mitigation strategies for any number of viral strains, whilst also evaluating the effect of distinct mitigation costs on the infection levels. The results show that relaxations in the mitigation measures cause a rapid increase in the number of cases, and therefore demand more restrictive measures in the future.

Suggested Citation

  • Edilson F Arruda & Shyam S Das & Claudia M Dias & Dayse H Pastore, 2021. "Modelling and optimal control of multi strain epidemics, with application to COVID-19," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-18, September.
    • Handle: RePEc:plo:pone00:0257512
    DOI: 10.1371/journal.pone.0257512
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    References listed on IDEAS

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    1. Ewen Callaway, 2020. "The coronavirus is mutating — does it matter?," Nature, Nature, vol. 585(7824), pages 174-177, September.
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    Cited by:

    1. Giorgio Bagarella & Mauro Maistrello & Maddalena Minoja & Olivia Leoni & Francesco Bortolan & Danilo Cereda & Giovanni Corrao, 2022. "Early Detection of SARS-CoV-2 Epidemic Waves: Lessons from the Syndromic Surveillance in Lombardy, Italy," IJERPH, MDPI, vol. 19(19), pages 1-10, September.
    2. de León, Ugo Avila-Ponce & Avila-Vales, Eric & Huang, Kuan-lin, 2022. "Modeling COVID-19 dynamic using a two-strain model with vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Liu, Kanglin & Liu, Changchun & Xiang, Xi & Tian, Zhili, 2023. "Testing facility location and dynamic capacity planning for pandemics with demand uncertainty," European Journal of Operational Research, Elsevier, vol. 304(1), pages 150-168.
    4. Omame, Andrew & Abbas, Mujahid & Din, Anwarud, 2023. "Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 302-336.
    5. Jiraporn Lamwong & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2022. "Vaccination’s Role in Combating the Omicron Variant Outbreak in Thailand: An Optimal Control Approach," Mathematics, MDPI, vol. 10(20), pages 1-29, October.
    6. Alberto Olivares & Ernesto Staffetti, 2021. "Optimal Control Applied to Vaccination and Testing Policies for COVID-19," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    7. Thomas Harweg & Mathias Wagner & Frank Weichert, 2022. "Agent-Based Simulation for Infectious Disease Modelling over a Period of Multiple Days, with Application to an Airport Scenario," IJERPH, MDPI, vol. 20(1), pages 1-20, December.
    8. Grass, D. & Wrzaczek, S. & Caulkins, J.P. & Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Kuhn, M. & Prskawetz, A. & Sanchez-Romero, M. & Seidl, A., 2024. "Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses," Theoretical Population Biology, Elsevier, vol. 156(C), pages 46-65.
    9. Vashishth, Anil K. & Basaiti, Komal, 2024. "Modeling the effect of non-pharmaceutical measures and vaccination on the spread of two variants of COVID-19 in India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 139-168.

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