Optimal vaccination in a SIRS epedemic model

Arbeitspapier

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 veri fication 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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Center for Mathematical Economics Working Papers ; No. 667

Klassifikation und Themen

• Thema: SIRS model ; optimal control ; viscosity solution ; non-smooth verification theorem ; epidemic ; optimal vaccination

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Federico, Salvatore ; Ferrari, Giorgio ; Torrente, Maria-Laura
• Ereignis: Veröffentlichung
• (wer): Bielefeld University, Center for Mathematical Economics (IMW)
• (wo): Bielefeld
• (wann): 2022

Weitere Informationen

• Handle: http://hdl.handle.net/10419/273043
• URN: urn:nbn:de:0070-pub-29637146
• Letzte Aktualisierung: 10.03.2025, 11:44 MEZ