Optimal vaccination in a SIRS epidemic model

DOI10.1007/S00199-022-01475-9arXiv2206.03284OpenAlexW4312059531MaRDI QIDQ6131948

Author name not available (Why is that?)

Publication date: 18 April 2024

Published in: Economic Theory (Search for Journal in Brave)

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 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 emph{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.

Full work available at URL: https://arxiv.org/abs/2206.03284

zbMATH Keywords

optimal control viscosity solution SIRS model epidemic optimal vaccination non-smooth verification theorem

Mathematics Subject Classification ID

Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Optimality conditions for problems involving ordinary differential equations (49K15) Medical epidemiology (92C60)