Optimal vaccination in a SIRS epidemic model

Federico S, Ferrari G, Torrente M-L (2022)
Economic Theory .

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Federico, Salvatore; Ferrari, GiorgioUniBi; Torrente, Maria-Laura
Abstract / Bemerkung
We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible individuals via a vaccination campaign, while minimizing the social and economic costs related to the infectious disease. As a theoretical contribution, we provide a technical non-smooth verification theorem, guaranteeing that a semiconcave viscosity solution to the Hamilton-Jacobi-Bellman equation identifies with the minimal cost function, provided that the closed-loop equation admits a solution. Conditions under which the closed-loop equation is well-posed are then derived by borrowing results from the theory of Regular Lagrangian Flows. From the applied point of view, we provide a numerical implementation of the model in a case study with quadratic instantaneous costs. Amongst other conclusions, we observe that in the long-run the optimal vaccination policy is able to keep the percentage of infected to zero, at least when the natural reproduction number and the reinfection rate are small. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Erscheinungsjahr
2022
Zeitschriftentitel
Economic Theory
eISSN
1432-0479
Page URI
https://pub.uni-bielefeld.de/record/2968012

Zitieren

Federico S, Ferrari G, Torrente M-L. Optimal vaccination in a SIRS epidemic model. Economic Theory . 2022.
Federico, S., Ferrari, G., & Torrente, M. - L. (2022). Optimal vaccination in a SIRS epidemic model. Economic Theory . https://doi.org/10.1007/s00199-022-01475-9
Federico, Salvatore, Ferrari, Giorgio, and Torrente, Maria-Laura. 2022. “Optimal vaccination in a SIRS epidemic model”. Economic Theory .
Federico, S., Ferrari, G., and Torrente, M. - L. (2022). Optimal vaccination in a SIRS epidemic model. Economic Theory .
Federico, S., Ferrari, G., & Torrente, M.-L., 2022. Optimal vaccination in a SIRS epidemic model. Economic Theory .
S. Federico, G. Ferrari, and M.-L. Torrente, “Optimal vaccination in a SIRS epidemic model”, Economic Theory , 2022.
Federico, S., Ferrari, G., Torrente, M.-L.: Optimal vaccination in a SIRS epidemic model. Economic Theory . (2022).
Federico, Salvatore, Ferrari, Giorgio, and Torrente, Maria-Laura. “Optimal vaccination in a SIRS epidemic model”. Economic Theory (2022).

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