Optimal Vaccination in a SIRS Epidemic Model

Federico S, Ferrari G, Torrente M-L (2022) Center for Mathematical Economics Working Papers; 667.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | 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 compart-mental 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 colosed-loop equation admits a solution. Coditions 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 quadrativ 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.

MSC2010 subject classification: 93C15, 49K15, 49L25, 92D30
Stichworte
SIRS model; optimal control; viscosity soltuion; nonsmooth verification theorem: epidemic; optimal vaccination
Erscheinungsjahr
2022
Serientitel
Center for Mathematical Economics Working Papers
Band
667
Seite(n)
18
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2963714

Zitieren

Federico S, Ferrari G, Torrente M-L. Optimal Vaccination in a SIRS Epidemic Model. Center for Mathematical Economics Working Papers. Vol 667. Bielefeld: Center for Mathematical Economics; 2022.
Federico, S., Ferrari, G., & Torrente, M. - L. (2022). Optimal Vaccination in a SIRS Epidemic Model (Center for Mathematical Economics Working Papers, 667). Bielefeld: Center for Mathematical Economics.
Federico, S., Ferrari, G., and Torrente, M. - L. (2022). Optimal Vaccination in a SIRS Epidemic Model. Center for Mathematical Economics Working Papers, 667, Bielefeld: Center for Mathematical Economics.
Federico, S., Ferrari, G., & Torrente, M.-L., 2022. Optimal Vaccination in a SIRS Epidemic Model, Center for Mathematical Economics Working Papers, no.667, Bielefeld: Center for Mathematical Economics.
S. Federico, G. Ferrari, and M.-L. Torrente, Optimal Vaccination in a SIRS Epidemic Model, Center for Mathematical Economics Working Papers, vol. 667, Bielefeld: Center for Mathematical Economics, 2022.
Federico, S., Ferrari, G., Torrente, M.-L.: Optimal Vaccination in a SIRS Epidemic Model. Center for Mathematical Economics Working Papers, 667. Center for Mathematical Economics, Bielefeld (2022).
Federico, Salvatore, Ferrari, Giorgio, and Torrente, Maria-Laura. Optimal Vaccination in a SIRS Epidemic Model. Bielefeld: Center for Mathematical Economics, 2022. Center for Mathematical Economics Working Papers. 667.
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2022-06-08T09:03:43Z
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