Epidemic spreading on heterogeneous probabilistic activity driven network model

<p indent=0mm>Human history is accompanied by all kinds of epidemic diseases. Yet, the research progress in epidemic spreading is unexpectedly slow. In the last few decades, by applying the theory of complex networks, the study on epidemic spreading has obtained great success. In this review, we briefly introduce the important progresses on epidemic spreading in complex networks. We mainly focus on the following four aspects: (1) epidemic spreading based on contact network model; (2) epidemic spreading based on meta-population model; (3) the prediction of epidemic spreading; (4) the control of epidemic spreading. These achievements make us deeply understand the epidemic spreading in the real world, and make it possible for us to predict and control the real epidemics.

Epidemic spreading on biological evolution networks.

The co-evolution of epidemic and information spread within multilayer networks is a current hot topic in network science. During epidemic outbreaks, the accompanying information exhibits both outbreak and reception game behaviors; yet, these complex phenomena have been scarcely addressed in existing research. In this paper, we model information outbreaks using activated individuals who transmit messages to their neighbors, while also considering the game behaviors of information receivers. By focusing on these two factors, we establish a multilayer network model featuring both information outbreaks and reception games. Employing the microscopic Markov chain method, we analyze the propagation dynamics within this network and derive epidemic thresholds, corroborating these results with Monte Carlo simulations. Our findings indicate that information outbreaks suppress epidemic outbreaks, whereas increased costs of information reception promote epidemic spread. Smooth information dissemination further inhibits the transmission of the epidemic. Additionally, we observe that heterogeneity in the network structure between the virtual and physical layers reduces the ultimate scale of epidemic infection, with the virtual layer exerting a more substantial influence. These insights are crucial for elucidating the co-evolutionary mechanisms of spread within multilayer networks and for developing effective epidemic prevention and control strategies.

Undirected Congruence Model: Topological characteristics and epidemic spreading

Complex networks are often used to model the network of individuals for analyzing various problems in human networks e.g. information diffusion and epidemic spreading. Various epidemic spreading models are proposed for analyzing and understanding the spreading of infectious diseases in human contact networks. In the classical epidemiological model, a susceptible person becomes infected instantly after getting in contact with the infected person. However, this scenario is not realistic. In real, a healthy person become infected with some delay in time not spontaneously after contacting with the infected person. Therefore, research is needed for creating more realistic models to study the dynamics of epidemics in the human population with delay. In order to handle delays in the infection process, we propose an epidemic spreading SIR (Susceptible-Infected-Recovered) model in human contact networks as complex network. We introduce time delay parameter in infection to handle the process to become a node infected after some delay. The critical threshold is derived for epidemic spreading on large human contact network considering the delay in infection. We perform simulations on the proposed SIR model on different underlying complex network topologies, which represents the real world scenario, e.g., random geometric network with and without mobile agents. The simulation results are validated in accordance with our theoretical description which shows that increment in delay decreases the critical threshold of epidemic spreading rate and the disease persists for the longer time.

The global spread of COVID-19 causes great losses to human society. Accurate calculation of the scale of epidemic spread is of great significance for the implementation of corresponding epidemic prevention measures. However, the existing method ignores the group formed by social relations of the population, which reduces the accuracy of the epidemic spread number calculation. In this paper, we propose an epidemic model based on intra- and inter-group interactions. Firstly, we construct a dual network model of epidemic spread based on intra- and inter-group interactions. The network describes how epidemics spread intra- and inter-group. To capture the intergroup influences, we construct a model for social mobility to calculate the inter-group spread rate. Secondly, we propose a computational model for the epidemic spread. We calculate the infection probability of groups in the upper layer network by using a continuous-time Markov chain (CTMC). We describe a dynamic evolution of the intra-group infection in the underlying network based on the mean field equation. And the number of infections in the population is calculated by integrating intra- and inter-group effects. Finally, we implement an epidemic spread simulation system to visualize the spread process. The experimental results show that the model can analyze the epidemic spread process more accurately.

Recent studies have shown that many real-world systems can be described by multi-layer complex networks. In this paper, the concept of layers is introduced to construct a traffic-driven SIR epidemic spreading model on “logical-physical” layered network. Based on the peak density of infected nodes and the ultimate density of recovered nodes, we investigate the features of epidemic spreading on layered network. Through numerical simulations, it is shown that traffic flow greatly influences the intensity and scope of epidemic spreading. By comparing the effects of four kinds of two-layer networks generated by ER random network model and BA scale-free network model on epidemic spreading, we found that the homogeneity of logical or physical network structure can promote the spread of epidemic more than heterogeneous networks. This work may be of service to design traffic-driven epidemic prevention and control strategies.

This contribution presents a model for dynamic networks of physical contacts among large populations and their application for reproducing complex patterns in epidemic spread. The networks are constructed from statistical data on demography, geography, organizational structure and contact behavior. Due to the heterogeneous nature of the data and by construction, rich topological characteristics such as overlapping communities, layering along multiple dimensions and multiplex dynamics on different time scales can be observed. The generated dynamic networks can furthermore be regarded as subgraphs or derivatives of latent social networks. General results and observations form social network theory apply naturally and are used for explaining dynamic effects in epidemics. An exemplaric analysis investigates the impact of weak ties and effects of communities with decreased immunization on epidemic spread. Optimized implementation and visualization techniques turn out to be a key asset for dynamic simulation of contacts within large populations.

This contribution presents a model for dynamic networks of physical contacts among large populations and their application for reproducing complex patterns in epidemic spread. The networks are constructed from statistical data on demography, geography, organizational structure and contact behavior. Due to the heterogeneous nature of the data and by construction, rich topological characteristics such as overlapping communities, layering along multiple dimensions and multiplex dynamics on different time scales can be observed. The generated dynamic networks can furthermore be regarded as subgraphs or derivatives of latent social networks. General results and observations form social network theory apply naturally and are used for explaining dynamic effects in epidemics. An exemplaric analysis investigates the impact of weak ties and effects of communities with decreased immunization on epidemic spread. Optimized implementation and visualization techniques turn out to be a key asset for dynamic simulation of contacts within large populations.

Traffic-driven epidemic spreading with non-uniform origin and destination selection

The individual behaviors driven by information diffusion show an undeniable impact on the process of epidemic spreading and have been continuously evolving with the dynamic processes. In this paper, a novel weighted co-evolving multiplex network model is proposed to describe the interaction between information diffusion in online social networks and epidemic spreading in adaptive physical contact networks. Considering the difference in the connections between individuals, the heterogeneous rewiring rate, which is proportional to the strength of the connection, is introduced in our model. The simulation results show that the maximum infection scale decreases as the information acceptance probability grows, and the final infection decreases as the rewiring behaviors increase. Interestingly, an infection peak appears in our model due to the interaction between information diffusion and epidemic spread.

Epidemic spreading processes on dynamic multiplex networks provide a more accurate description of natural spreading processes than those on single layered networks. To describe the influence of different individuals in the awareness layer on epidemic spreading, we propose a two-layer network-based epidemic spreading model, including some individuals who neglect the epidemic, and we explore how individuals with different properties in the awareness layer will affect the spread of epidemics. The two-layer network model is divided into an information transmission layer and a disease spreading layer. Each node in the layer represents an individual with different connections in different layers. Individuals with awareness will be infected with a lower probability compared to unaware individuals, which corresponds to the various epidemic prevention measures in real life. We adopt the micro-Markov chain approach to analytically derive the threshold for the proposed epidemic model, which demonstrates that the awareness layer affects the threshold of disease spreading. We then explore how individuals with different properties would affect the disease spreading process through extensive Monte Carlo numerical simulations. We find that individuals with high centrality in the awareness layer would significantly inhibit the transmission of infectious diseases. Additionally, we propose conjectures and explanations for the approximately linear effect of individuals with low centrality in the awareness layer on the number of infected individuals.

Networks with links representing different relationships have attracted much attention in recent years. Previous studies mostly focused on the analyses of network topology and evolution, multi-relation pattern mining, detection of overlapping communities, and cascading failure. However, epidemic spreading on multi-relation networks remains a largely unexplored area. We propose a binary-relation network model, representing working and friendship relationships, to reveal the effect of multiple relationships on the epidemic spreading. A link representing a closer relationship carries a higher weight. For reactive infection process in a multi-relation network, the threshold of outbreak is suppressed, making the epidemic harder to control. Comparing the networks with different structural heterogeneities such as the Watts-Strogatz (WS), Erdös-Rènyi and Barabási-Albert networks, the WS network is affected most significantly. Interestingly, the relative changes in the thresholds on the three networks are found to be independent of the structure. For contact infection process, an increase in the weight of the closer relationship can raise the outbreak threshold significantly and reduce the prevalence. As the fraction of closer relationship varies, an optimal fraction corresponding to a maximum outbreak threshold and minimum prevalence emerges. With an increase in the weight of the closer relationship, the proportion of links corresponding to the optimal value decreases. Most interestingly, the optimal proportions of closer-relation links on the three networks are almost the same, and thus they are independent of the network topology. This study not only contributes to the better understanding of epidemic spreading dynamics on multi-relation networks, but also provides a new perspective for research on multi-relation networks.

Human contact behaviors involve both dormant and active processes. The dormant (active) process goes from the disappearance (creation) to the creation (disappearance) of an edge. The dormant (active) time is the elapsed time since the edge became dormant (active). Many empirical studies have revealed that dormant and active times in human contact behaviors tend to show a long-tailed distribution. Previous researches focused on the impact of the dormant process on spreading dynamics. However, the epidemic spreading happens on the active process. This raises the question of how the active process affects epidemic spreading in complex networks. Here, we propose a novel time-varying network model in which the distributions of both the dormant time and active time of edges are adjustable. We develop a pairwise approximation method to describe the spreading dynamical processes in the time-varying networks. Through extensive numerical simulations, we find that the epidemic threshold is proportional to the mean dormant time and inversely proportional to the mean active time. The attack rate decreases with the increase of mean dormant time and increases with the increase of mean active time. It is worth noting that the epidemic threshold and the attack rate (e.g., the infected density in the steady state) are independent of the heterogeneities of the dormant time distribution and the active time distribution. Increasing the heterogeneity of the dormant time distribution accelerates epidemic spreading while increasing the heterogeneity of the active time distribution slows it down.

Epidemic trajectories and awareness diffusion among unequals in simplicial complexes