# Pulse strategy for suppressing spreading on networks

## TL;DR

This paper introduces a pulse curing strategy for network epidemics, demonstrating it is more efficient than uniform curing by saving approximately 36.8% of curing operations, with a theoretical epidemic threshold derived from network eigenvalues.

## Contribution

The paper models a pulse curing strategy in network epidemics, deriving the epidemic threshold and showing its efficiency over uniform curing methods.

## Key findings

- Pulse curing saves about 36.8% of curing operations.
- The epidemic threshold is given by (1/λ₁) * ln(1/(1-p)).
- Pulse strategy is more efficient than uniform curing across network structures.

## Abstract

In networked spreading models, each node can infect its neighbors and cure spontaneously. The curing is assumed to occur uniformly over time. A pulse immunization/curing strategy is more efficient and broadly applied to suppressing spreading processes. We model the epidemic process by the basic Susceptible-Infected (SI) process with a pulse curing and incorporate the underlying contact network. The mean-field epidemic threshold of the pulse SI model is shown to be $\frac{1}{\lambda_1}\ln\frac{1}{1-p}$, where $\lambda_1$ and $p$ are the largest eigenvalue of the adjacency matrix and the fraction of nodes covered by each curing, respectively. Compared to the extensively studied uniform curing process, we show that the pulse curing strategy saves about $36.8$\%, i.e. $p\approx 0.632$, of the number of curing operations invariant to the network structure. Our results may help related policy makers to estimate the cost of controlling spreading processes.