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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 667

Classification and Topics

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

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Federico, Salvatore ; Ferrari, Giorgio ; Torrente, Maria-Laura
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2022

Further information

• Handle: http://hdl.handle.net/10419/273043
• URN: urn:nbn:de:0070-pub-29637146
• Last update: 10.03.2025, 11:44 AM CET