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Controlled Compartmental Models with Time-Varying Population: Normalization, Viability and Comparison

Author

Listed:
  • Florin Avram

    (Université de Pau)

  • Lorenzo Freddi

    (Dipartimento di Scienze Matematiche, Informatiche e Fisiche)

  • Dan Goreac

    (Shandong University, Weihai
    LAMA, Univ Gustave Eiffel, UPEM, Univ Paris Est Creteil, CNRS)

  • Juan Li

    (Shandong University, Weihai
    Shandong University)

  • Junsong Li

    (Shandong University, Weihai)

Abstract

This paper focuses on the characterization of viability zones in compartmental models with varying population size, due both to deaths caused by epidemics and to natural demography. This is achieved with the use of viscosity characterizations of viability and extensively illustrated on several models. An example taking into consideration real data is provided. The paper is completed with a viscosity approach to the optimality of minimal (“greedy”) non-pharmaceutical interventions.

Suggested Citation

  • Florin Avram & Lorenzo Freddi & Dan Goreac & Juan Li & Junsong Li, 2023. "Controlled Compartmental Models with Time-Varying Population: Normalization, Viability and Comparison," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1019-1048, September.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02274-5
    DOI: 10.1007/s10957-023-02274-5
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    References listed on IDEAS

    as
    1. Fernando E. Alvarez & David Argente & Francesco Lippi, 2020. "A Simple Planning Problem for COVID-19 Lockdown," NBER Working Papers 26981, National Bureau of Economic Research, Inc.
    2. Avram, Florin & Freddi, Lorenzo & Goreac, Dan, 2022. "Optimal control of a SIR epidemic with ICU constraints and target objectives," Applied Mathematics and Computation, Elsevier, vol. 418(C).
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