Two novel immunization strategies for epidemic control in directed scale-free networks with nonlinear infectivity

TL;DR

This paper introduces two innovative immunization strategies for epidemic control in directed scale-free networks, significantly increasing epidemic thresholds and outperforming traditional methods through theoretical analysis and numerical validation.

Contribution

It proposes combined and duplex immunization strategies, providing the first comprehensive analysis tailored to directed networks and demonstrating their superior effectiveness over existing schemes.

Findings

Duplex immunization outperforms traditional schemes in epidemic threshold increase.

Targeting nodes with large out-degrees is more effective for immunization.

Numerical results confirm the theoretical advantages of the proposed strategies.

Abstract

In this paper, we propose two novel immunization strategies, i.e., combined immunization and duplex immunization, for SIS model in directed scale-free networks, and obtain the epidemic thresholds for them with linear and nonlinear infectivities. With the suggested two new strategies, the epidemic thresholds after immunization are greatly increased. For duplex immunization, we demonstrate that its performance is the best among all usual immunization schemes with respect to degree distribution. And for combined immunization scheme, we show that it is more effective than active immunization. Besides, we give a comprehensive theoretical analysis on applying targeted immunization to directed networks. For targeted immunization strategy, we prove that immunizing nodes with large out-degrees are more effective than immunizing nodes with large in-degrees, and nodes with both large out-degrees and large in-degrees are more worthy to be immunized than nodes with only large out-degrees or large in-degrees. Finally, some numerical analysis are performed to verify and complement our theoretical results. This work is the first to divide the whole population into different types and embed appropriate immunization scheme according to the characteristics of the population, and it will benefit the study of immunization and control of infectious diseases on complex networks.