Ate Darabi PhD Proposal Review

Title:
Complex Delayed Networks and Their Application in Epidemic Analysis: Modeling, Analysis, and Strategic Management

Committee Members:
Prof. Milad Siami (Advisor)
Prof. Bahram Shafai
Prof. Rozhin Hajian

Abstract:
In the face of crowd-related disasters like pandemics and mass attacks, the complex dynamics of human interactions demand comprehensive modeling approaches. This proposal adopts a network-based perspective, leveraging the delayed Susceptible-Infected-Susceptible (SIS) model for epidemics and the Predator-Swarm-Guide (PSG) model for crowd movement, to gain insights into the dynamics of these critical situations.

In epidemic networks, time delays and uncertainties can significantly change the epidemic behavior and result in successive echoing waves of the spread between various population clusters. We examine these effects on linear SIS dynamics, evaluating network stability and performance loss. We prove that network performance loss is correlated with the structure of the underlying graph, intrinsic time delays, epidemic characteristics, and external shocks. This performance measure is then used to develop an optimal traffic restriction algorithm for network performance enhancement, resulting in reduced infection in the metapopulation.   An epidemic-based centrality index is also proposed to evaluate the impact of every subpopulation on network performance, and its asymptotic behavior is investigated. This index converges to local or eigenvector centralities under specific parameters. Moreover, given that epidemic-based centrality depends on the epidemic properties of the disease, it may yield distinct node rankings as the disease characteristics slowly change over time or as different types of infections spread. This unique characteristic of epidemic-based centrality enables it to adjust to various epidemic features. The derived centrality index is then adopted to improve the network robustness against external shocks on the epidemic network.

The PSG model addresses mass attack scenarios, considering individuals’ efforts to evade adversaries and seek guidance. Environmental factors like impermeable walls and psychological elements are incorporated into this model. The preliminary results highlight the role of coordinated cooperation in minimizing casualties. The objective is to reduce casualties through a hybrid motion optimization approach for individuals and the guiding agent.