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Session S25 - New Methods and Emerging Applications in Dynamics, Networks, and Control

Monday, July 12, 16:15 ~ 16:45 UTC-3

Optimal control of diseases in prison populations through screening policies of new inmates

Victor Riquelme

Universidad de Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We study an optimal control problem of a communicable disease in a prison population. To control the spread of the disease inside a prison, we consider an active case-finding strategy, consisting of screening a proportion of new inmates at the entry point, followed by a treatment depending on the results of this procedure. The control variable consists then in the coverage of the screening applied to new inmates. The disease dynamics is modeled by an SIS (susceptible-infected-susceptible) model, typically used to represent diseases that do not confer immunity after infection. We determine the optimal strategy that minimizes a combination between the cost of the screening/treatment at the entrance and the cost of maintaining infected individuals inside the prison, in a given time horizon. Using the Pontryagin Maximum Principle and Hamilton-Jacobi-Bellman equation, among other tools, we provide the complete synthesis of an optimal feedback control, consisting of a bang-bang strategy with at most two switching times and no singular arc trajectory, characterizing different profiles depending on model parameters.

Joint work with Pedro Gajardo (Universidad Técnica Federico Santa María, Chile) and Diego Vicencio (Universidad Técnica Federico Santa María, Chile).

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