# Second-Order Moment-Closure for Tighter Epidemic Thresholds

## TL;DR

This paper introduces a second-order moment-closure method to derive tighter lower bounds on the decay rate of infected nodes in SIS epidemic models, improving containment strategies in complex networks.

## Contribution

We develop a second-order moment-closure approach that provides more accurate lower bounds on epidemic decay rates than existing first-order methods.

## Key findings

- Second-order bounds are tighter than first-order bounds.
- Numerical simulations show improved containment strategies.
- The method enhances understanding of epidemic dynamics in networks.

## Abstract

In this paper, we study the dynamics of contagious spreading processes taking place in complex contact networks. We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible-infected-susceptible (SIS) stochastic spreading process. A precise quantification of this decay rate is crucial for designing efficient strategies to contain epidemic outbreaks. However, existing lower-bounds on the decay rate based on first-order mean-field approximations are often accompanied by a large error resulting in inefficient containment strategies. To overcome this deficiency, we derive a lower-bound based on a second-order moment-closure of the stochastic SIS processes. The proposed second-order bound is theoretically guaranteed to be tighter than existing first-order bounds. We also present various numerical simulations to illustrate how our lower-bound drastically improves the performance of existing first-order lower-bounds in practical scenarios, resulting in more efficient strategies for epidemic containment.