Narrow Results

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number $R_0$ of the model and studied the influence of orders a and b on $R_0$. Second, we found that frSIS has a disease-free equilibrium point $E_0$ and an endemic equilibrium point $E^{\ast }$. Moreover, we proved frSIS global stability of the model using $R_0$. If $R_0<1$, the model of $E_0$ is globally asymptotically stable. If $R_0>1$, the model of $E^{\ast }$ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease.

In this paper, two definitions about traffic congestion are proposed. We describe the traffic congestion spreading with the SEIR model of a complex small-world network. In addition, the relationships among the congestion factor, the number of average infection, the average recover rate and the infection rate are given by simulations in general traffic congestion conditions.

In this paper, we introduce the effect of neighbors on the infection of packets by computer virus in the SI and SIR models using the minimal traffic routing protocol. We have applied this model to the Barabasi–Albert network to determine how intrasite and extrasite infection rates affect virus propagation through the traffic flow of information packets in both the free-flow and the congested phases. The numerical results show that when we change the intrasite infection rate ${\lambda }_1$ while keeping constant the extrasite infection rate ${\lambda }_2$, we get normal behavior in the congested phase: in the network, the proportion of infected packets increases to reach a peak and then decreases resulting in a simultaneous increase of the recovered packets. In contrast, when the intrasite infection rate ${\lambda }_1$ is kept fixed, an increase of the extrasite infection rate results in two regimes: The first one is characterized by an increase of the proportion of infected packets until reaching some peak value and then decreases smoothly. The second regime is characterized by an increase of infected packets to some stationary value.

Over the past few decades, the study of epidemic propagation has caught widespread attention from many areas. The field of graphs contains a wide body of research, yet only a few studies explore epidemic propagation’s dynamics in “signed” networks. Motivated by this problem, in this paper we propose a new epidemic propagation model for signed networks, denoted as S-SIS. To explain our analysis, we utilized the mean field theory to demonstrate the theoretical results. When we compare epidemic propagation through negative links to those only having positive links, we find that a higher proportion of infected nodes actually spreads at a relatively small infection rate. It is also found that when the infection rate is higher than a certain value, the overall spreading in a signed network begins showing signs of suppression. Finally, in order to verify our findings, we apply the S-SIS model on Erdös–Rényi random network and scale-free network, and the simulation results is well consist with the theoretical analysis.