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Pré-Publication, Document De Travail Année : 2022

A Time-Space Integro-Differential Economic Model of Epidemic Control

Carmen Camacho
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  • PersonId : 921371
  • IdRef : 175893594
Rodolphe Desbordes
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  • PersonId : 1084794
Davide Torre
  • Fonction : Auteur
  • PersonId : 1136496

Résumé

In this paper we propose a time-space economic model to control the evolution and the spread of a disease. The underlying epidemiological model is formulated as a reaction-diffusion integro-differential partial differential equation. This specific model formulation, supported by empirical data, contains three different terms: a pure diffusion term, a linear growth term, and an integral term. These three terms capture different diffusion channels of a transmissible disease: a pure spatial diffusion effect, a local effect and a global effect. The decision maker aims at deciding the optimal effort to be implemented in order to control the number of infections and, at the same time, minimize the cost of treatment. We analyze both the finite and the infinite horizon cases, and provide the closed-form expression of the optimal policy to be implemented to control the epidemic while sustaining economic growth.
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Dates et versions

hal-03693086 , version 1 (10-06-2022)

Identifiants

  • HAL Id : hal-03693086 , version 1

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Carmen Camacho, Rodolphe Desbordes, Davide Torre. A Time-Space Integro-Differential Economic Model of Epidemic Control. 2022. ⟨hal-03693086⟩
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