Optimal control on a network: optimization of vaccination strategies
Maria Soledad Aronna (FGV-Rio)

This talk discusses a mathematical model for optimal vaccination strategies in interconnected cities and metropolitan areas, considering commuting patterns. It is a compartmental model with a vaccination rate for each city, acting as a control function. The commuting patterns are incorporated through a weighted adjacency matrix and a parameter that selects day and night periods. The optimal control problem is formulated to minimize a functional cost that balances the number of hospitalizations and vaccines, including restrictions of a weekly availability cap and an application capacity of vaccines per unit of time. The key findings of this work are sharp bounds for the basic reproduction number. Theoretical analysis and numerical simulations provide insights into disease dynamics and the effectiveness of control measures.