The epidemic threshold of a social system is the ratio of infection and recovery rate above which disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the links of the graph. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. , we show that tipping from an epidemic to a non-epidemic state happens at a larger critical ratio between infection rate and recovery rate for WCNE and degree-homogenized networks than for those obtained by random removals.

https://link.springer.com/content/pdf/10.1140/epjs/s11734-021-00138-5.pdf