Hub nodes inhibit the outbreak of epidemic under voluntary vaccination

Haifeng Zhang,Jie Zhang,Changsong Zhou,Binghong Wang,Michael Small

doi:10.1088/1367-2630/12/2/023015

Abstract

It is commonly believed that epidemic spreading on scale-free networks is difficult to control and that the disease can spread even with a low infection rate, lacking an epidemic threshold. In this paper, we study epidemic spreading on complex networks under the framework of game theory, in which a voluntary vaccination strategy is incorporated. In particular, individuals face the ‘dilemma’ of vaccination: they have to decide whether or not to vaccinate according to the trade-off between the risk and the side effects or cost of vaccination. Remarkably and quite excitingly, we find that disease outbreak can be more effectively inhibited on scale-free networks than on random networks. This is because the hub nodes of scale-free networks are more inclined to take self-vaccination after balancing the pros and cons. This result is encouraging as it indicates that real-world networks, which are often claimed to be scale free, can be favorably and easily controlled under voluntary vaccination. Our work provides a way of understanding how to prevent the outbreak of diseases under voluntary vaccination, and is expected to provide valuable information on effective disease control and appropriate decision-making.

Highlights

In real-world epidemic spreading, where vaccination has always been adopted as an effective control strategy, we are naturally led to the following question: Will the above result hold under circumstances where the vaccination strategy is considered? To answer this, we consider the spreading of epidemics on various complex networks with the decision of whether or not to vaccinate by balancing the risk of infection and the risk/cost of vaccination
We study the epidemic spreading process on two typical complex networks: the scale-free BA network proposed by Barabási–Albert (BA) in 1999 [22], and the random network, which was first defined by Erdös and Rényi in 1959 [30]
We present a more practical framework to explore the spreading of epidemics on complex networks under voluntary vaccination, where individuals chose vaccination by balancing the payoff of vaccination and non-vaccination

Summary

Methods

We adopt the susceptible–infected–susceptible (SIS) epidemiological model to investigate the role of voluntary vaccination. In the SIS model, each susceptible (S) node is infected with probability β at each time step if it is connected to an infected (I) node. If a susceptible node has kinf infectious neighbors, the total probability λ that the node becomes infected is λ = 1 − (1 − β)kinf. When the epidemic is present, each individual has to decide whether or not to vaccinate by balancing the perceived risk of infection from neighbors versus the cost of vaccination. We assume that each individual has full recognition of the risk of infection and we set λperc = λ. For individuals who always seek personal interest, they will attempt to minimize their own cost/risk by balancing the gain and loss of vaccination. We find that the results obtained from equation (4) are quite similar to those from equation (3)

Main results

Conclusions and discussions