We propose a stochastic SIR model with or without distributed time delay and we study the stability of disease-free equilibrium. The numerical simulation of the stochastic SIR model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold...

Rumor propagation is a typical form of social communication and plays a significant role in social life. In this paper, we studied the process of rumor propagation by accounting for the mechanism of forgetting in Barrat–Barthelemy–Vespignani (BBV) networks. First, we derived mean-field...

The problem of estimating a nonlinear state-space model whose state process is driven by an ordinary differential equation (ODE) or a stochastic differential equation (SDE), with discrete-time data is studied. A new estimation method is proposed based on minimizing the conditional least squares...

Public policies intended to induce behavioral change, specifically incentives to reduce interpersonal contacts or to “social distance,” increasingly play a prominent role in public disease response strategies as governments plan for and respond to major epidemics. I compare social distancing...

Microblog is one of the most popular communication channels on the Internet, and has already become the third largest source of news and public opinions in China. Although researchers have studied the information propagation in microblog using the epidemic models, previous studies have not...

Rumor is an important form of social interaction. However, spreading of harmful rumors could have a significant negative impact on the well-being of the society. In this paper, considering the counterattack mechanism of the rumor spreading, we introduce two new models:...

Spreading of certain infections in complex networks is effectively suppressed by using intelligent strategies for epidemic control. One such standard epidemiological strategy consists in tracing contacts of infected individuals. In this paper, we use a recently introduced generalization of the...

Rumor is an important form of social interaction, and its spreading has a significant impact on people’s lives. In the age of Web, people are using electronic media more frequently than ever before, and blog has become one of the main online social interactions. Therefore, it is essential to...

There are significant differences between rumor spreading and epidemic spreading in social networks, especially with consideration of the mutual effect of forgetting and remembering mechanisms. In this paper, a new rumor spreading model, Susceptible-Infected-Hibernator-Removed (SIHR) model, is...

Within the standard SIR model with spatial structure, we propose two models for the superspreader. In one model, superspreaders have intrinsically strong infectiousness. In other model, they have many social connections. By Monte Carlo simulation, we obtain the percolation probability, the...