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It has been demonstrated that the propagation of information and awareness regarding a disease can assist in containing the outbreak of epidemics. Previous models for this coevolving usually introduced the dependence between these two processes by setting a lower but time-independent infection rate for individuals with awareness. However, a realistic scenario can be more complicated, as individual vigilance and the adopted protective measures may depend on the extent of the discussion on the disease, whereas individuals may be irrational or lack relevant knowledge, leading to improper measures being taken. These can introduce a time-varying dependence between epidemic dynamics and awareness prevalence and may weaken the effect of spreading awareness in containing a pandemic. To better understand this effect, we introduce a nonlinear dependence of the epidemic infection rate on awareness prevalence, focusing on the effect of different forms of dependence on the coevolving dynamics. We demonstrate that a positive correlation between vigilance and awareness prevalence can enhance the effect of information spreading in suppressing epidemics. However, this enhancement can be weakened if some individuals are irrational. Our results demonstrate the importance of rational behavior in the strategy of containing epidemics by propagation of disease information.

Fighting a pandemic is a major challenge. Therefore, understanding the dynamics of epidemic spreading and determining an efficient strategy to contain a pandemic have attracted considerable attention in complex networks [_{1}N_{1}) [

One of the characteristics of modern living is the omnipresence of information. Reading news, browsing webpages, and participating in online social networks have become important parts of our daily lives. Messages received through these activities can influence our decision making, can change our behaviors, and, as a result, may also impact the pattern of epidemic spreading [

Recent studies on the coevolution dynamics between information and disease spreading usually assume that the response of individuals to messages is independent of time, and the response to information is manifested by a relatively lower infection rate for individuals with awareness. However, a realistic situation can be more complicated: an individual may not immediately take the highest level of protective measures when he/she receives information regarding the epidemic. The level of protective measures is usually upgraded when individuals become more vigilant or frightened. Recently, it has been demonstrated that this vigilance (or fear) is related to the prevalence of public discussion on epidemics [

(a) Number of existing cases of COVID-19 in China (red line), number of discussions about COVID-19 (M) (green line), and disinfection on

Previous studies on the coevolving dynamics of information and epidemic spreading usually assume that individuals are rational and can take proper protective measures. However, during a pandemic, not all individuals are rational. Irrational behaviors, such as irrational beliefs [

In this study, based on the framework of the coevolving dynamics of information and disease spreading in two-layer networks, we consider the effect of dependence between individual vigilance and the prevalence of the discussion. Using brief analytics and numerical simulations, we demonstrate that a positive dependence can assist in containing the spread of the epidemic. In some cases, strong individual vigilance can suppress the size of the final outbreak even without increasing the awareness of the population. However, irrational individuals can weaken this suppressive effect. In some extreme cases, when most individuals are irrational, the spreading of information can no longer suppress epidemics.

The remainder of this paper is organized as follows. In Section

The model contains two components, as shown in Figure

Schematic of the model. The dynamics of information spreading are described using the UAU model in the information network. The epidemic spreading process is described by the SIS model in the contagion network.

To incorporate the dependence between individual vigilance and the prevalence of awareness of the disease, we now investigate two specific forms of dependence, where

Dependence 1:

Dependence 2:

Notably, the dynamics of the model are similar to those of the model in [

In the model, each individual can be unaware (

Probability trees for the transition for the possible states at each time step for the model. The four possible states are aware-infected (

We denote by

The stationary state of the system can be estimated by the stationary state in equation (

To quantitatively study the effect of different forms of dependence between individual vigilance and the prevalence of the discussion on the spread of the epidemic, we now focus on the two functional forms by comparing the results of a simulation with the theoretical estimation from equation (

As described in the model, individuals with awareness will take protective measures, leading to a reduced infection rate

(a) Plots of the function

Regarding the second form of

(a) Plots of the function

Figures

We have demonstrated that the dependence of

Dependence 1:

Dependence 2:

Accordingly, disease awareness can reduce the infection rate for rational individuals but increase the infection rate for irrational individuals.

Figure

For the first form of dependence, where

For the second form of dependence, where

For the first form of dependence, where

For the first form of dependence, where

These results demonstrate the importance of maintaining rationality in containing epidemics, as the efficiency of the strategy of inducing individuals to become aware of the disease and take protective measures depends on the ratio of individuals who can take proper measures. If most individuals cannot take proper protective measures, the spread of awareness cannot assist in containing the epidemic. Thus, irrational population is also a factor that may affect the spread of the pandemic.

In modern society, online communication and social media have become important sources of information. Accordingly, relevant information can be spread faster during a pandemic. Individuals can become vigilant about the spread of the disease and take protective measures. Therefore, the process of information propagation can suppress epidemics to a certain extent. In a more realistic scenario, the vigilance of individuals who are aware of the disease is not constant. The level of vigilance and protective measures may change with awareness prevalence. Therefore, investigating the effect of the dependence of individual vigilance on awareness prevalence may lead to a deeper understanding of the coevolution dynamics between epidemic spreading and information spreading.

In this study, we investigated the effect of various forms of dependence between individual vigilance and the spread of awareness of a disease. For rational individuals, vigilance and the level of protective measures increase with the prevalence of discussion. We demonstrated that this positive dependence can enhance the effect of information spreading in suppressing epidemics, as shown in Figures

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This study was supported by the National Social Science Foundation of China, “Risk Communication and Effectiveness Evaluation in Public Crises” (20AXW008).

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