# Controlling distant contacts to reduce disease spreading on disordered complex networks

## TL;DR

This paper investigates how controlling distant contacts in disordered social networks can effectively reduce disease spread, especially when close contacts are predominant, by developing a targeted mitigation strategy based on contact duration modifications.

## Contribution

The study introduces a novel mitigation approach that selectively reduces distant contact durations and analyzes its effectiveness using branching theory and simulations in disordered networks.

## Key findings

- Reducing distant contact durations can prevent epidemics even with long close contacts.
- The strategy's effectiveness increases as the density of close contacts decreases.
- A threshold of close contact density determines the success of epidemic prevention.

## Abstract

In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic. This property, called disorder, is usually associated with contact times between individuals and can be modeled by a weighted network, where the weights are related to normalized contact times $\omega$. In this paper, we study the SIR model for disease spreading when both close and distant types of interactions are present. We develop a mitigation strategy that reduces only the time duration of distant contacts, which are easier to alter in practice. Using branching theory, supported by simulations, we found that the effectiveness of the strategy increases when the density $f_1$ of close contacts decreases. Moreover, we found a threshold $\tilde{f}_1 = T_c / \beta$ below which the strategy can bring the system from an epidemic to a non-epidemic phase, even when close contacts have the longest time durations.