Optimal control and the value of information for a stochastic epidemiological SIS-model

• Published in: Journal of mathematical analysis and applications 2019-08, Vol.476 (2), p.665-695
• Main Authors: Grandits, Peter, Kovacevic, Raimund M., Veliov, Vladimir M.
• Format: Article
• Language: English
• Subjects: Epidemiology; Fokker-Planck equation; Hamilton-Jacobi-Bellman equation; Optimal control; SIS models; Stochastic differential equations
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2019.04.005

We analyze a continuous time stochastic SIS epidemiological model, describing the transmission dynamics of infectious diseases where infected individuals can become susceptible again after recovery. The infectivity period of infected individuals can be influenced dynamically by a decision maker, with the aim to minimize the expected aggregated economic costs due to illness and drug treatment. This stochastic control problem is investigated under two alternative assumptions about the information available. If a complete and exact measurement of the size of the infected population is available at any time, then the optimal control is sought in a state-feedback form and the related Hamilton-Jacobi-Bellman (HJB) equation can be used. If no state measurement is available, then the optimal control is sought in an open-loop form and the problem can be reformulated as an optimal control problem for the Kolmogorov forward equation. In both cases, deriving optimality conditions requires non-standard arguments due to the degeneracy of the involved HJB and Kolmogorov equations. Based on the obtained theoretical results, the role of the information pattern is numerically investigated.