Control of Overpopulated Tails in Kinetic Epidemic Models

TL;DR

This paper develops kinetic control strategies for epidemic models, focusing on managing contact distributions with overpopulated tails to influence epidemic progression effectively.

Contribution

It introduces two control protocols within kinetic epidemic models and derives their macroscopic effects, demonstrating their effectiveness through numerical simulations.

Findings

Control strategies can steer epidemic dynamics effectively.

Controlled models mitigate overpopulated contact tails.

Numerical results confirm the approach's effectiveness.

Abstract

We introduce model-based transition rates for controlled compartmental models in mathematical epidemiology, with a focus on the effects of control strategies applied to interacting multi-agent systems describing contact formation dynamics. In the framework of kinetic control problems, we compare two prototypical control protocols: one additive control directly influencing the dynamics and another targeting the interaction strength between agents. The emerging controlled macroscopic models are derived for an SIR compartmentalization to illustrate their impact on epidemic progression and contact interaction dynamics. Numerical results show the effectiveness of this approach in steering the dynamics and controlling epidemic trends, even in scenarios where contact distributions exhibit an overpopulated tail.