Social Distancing, Gathering, Search Games: Mobile Agents on Simple Networks.

Area of Science:

• Network Science
• Optimization Theory
• Epidemiology Modeling

Background:

• Social distancing is crucial during epidemics, requiring individuals to maintain physical separation.
• Previous models often lack dynamic agent movement and network-based optimization.

Purpose of the Study:

• To introduce and solve a novel optimization problem for achieving social distancing on networks.
• To determine the optimal movement strategy (laziness parameter) for agents to reach a socially distanced state efficiently.

Main Methods:

• Modeling social distancing as achieving a minimum pairwise graph distance (D) between agents.
• Utilizing lazy random walks, a Markov chain process, to simulate agent movement.
• Calculating the expected time to reach the socially distanced state as the absorption time of the Markov chain.

Main Results:

• The study identifies the optimal laziness parameter 'p' that minimizes the expected time to achieve social distancing.
• The same Markov chain framework can model related problems like the multi-rendezvous problem.
• The model extends predator-prey search games to multiple agents with distinct movement parameters.

Conclusions:

• Lazy random walks provide an effective framework for modeling and optimizing social distancing on networks.
• The research offers insights into efficient agent coordination for achieving separation or gathering.
• The findings have implications for epidemic control strategies and multi-agent coordination problems.