Speaker
Description
In recent years, there has been renewed interest in the modeling, analysis and control of epidemics. The classic SIR model presents limitations due to its assumption of fully mixed and homogeneous population. It is essential to consider network effects to account for heterogeneity in susceptibility, infectivity and interactions. In addition, different behavioral changes of the individuals may influence the epidemic. This talk first focuses on analyzing the SIR model on a network of interacting subpopulations. These subpopulations consist of homogeneously mixed individuals with differing activity rates, disease susceptibility and infectivity. In contrast to the classic SIR model, we show that infection curves can be multimodal in the single node. With rank-1 interaction matrix, we provide sufficient conditions for this multimodality and establish an upper bound on the number of monotonicity changes in the node-level infection curve. Additionally, we characterize the system's asymptotic behavior, with explicit expressions for limit equilibrium points and conditions for their stability. The second part of the talk analyzes a deterministic SIR model in which the transmission rate depends on the system state, reflecting behavioral adaptations in response to the epidemic. Under general conditions, we prove that the infection curve is unimodal. We then solve an optimal control problem to minimize intervention costs while keeping the infection curve below a desired threshold.
