Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/273043 
Year of Publication: 
2022
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 667
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
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.
Subjects: 
SIRS model
optimal control
viscosity solution
non-smooth verification theorem
epidemic
optimal vaccination
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

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