Many real networks are embedded in a metric space: the interactions among individuals depend on their spatial distances and usually take place among their nearest neighbors. In this paper, we introduce a modified susceptible-infected-susceptible (SIS) model to study geographical effects on the spread of diseases by assuming that the probability of a healthy individual infected by an infectious one is inversely proportional to the Euclidean distance between them. It is found that geography plays a more important role than hubs in disease spreading: the more geographically constrained the network is, the more highly the epidemic prevails.
In this paper, we study the control of the traffic-driven epidemic spreading by immunization strategy. We consider the random, degree-based and betweeness-based immunization strategies, respectively. It is found that the betweeness-based immunization strategy can most effectively prevent the outbreak of traffic-driven epidemic. Besides, we find that the critical number of immune nodes above which epidemic dies out is increased with the enhancement of the spreading rate and the packet-generation rate.
Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity o…
We study the traffic-driven epidemic spreading on scale-free networks with tunable degree distribution. The heterogeneity of networks is controlled by the exponent $γ$ of power-law degree distribution. It is found that the epidemic threshold is minimized at about $γ=2.2$. Moreover, we find that nodes with larger algorithmic betweenness are more likely to be infected. We expect our work to provide new insights into the effect of network structures on traffic-driven epidemic spreading.
The design of routing strategies for traffic-driven epidemic spreading has received increasing attention in recent years. In this paper, we propose an adaptive routing strategy that incorporates topological distance with local epidemic information through a tunable parameter $h$. In the case where the traffic is free of congestion, there exists an optimal value of routing parameter $h$, leading to the maximal epidemic threshold. This means that epidemic spreading can be more effectively controlled by adaptive routing, compared to that of the static shortest path routing scheme. Besides, we fin…
We introduce non-Markovian SIR epidemic spreading model inspired by the characteristics of the COVID-19, by considering discrete- and continuous-time versions. The incubation period, delayed infectiousness and the distribution of the recovery period are modeled with general functions. By taking corresponding choice of these functions, it is shown that the model reduces to the classical Markovian case. The epidemic threshold is analytically determined for arbitrary functions of infectivity and recovery and verified numerically. The relevance of the model is shown by modeling the first wave of t…
We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we study the epidemic size of Susceptible-Infected-Recovered, SIR, models and the epidemic threshold of Susceptible-Infected-Susceptible, SIS, models. Interestingly, we find that while the presence of tightly connected clusters inhibit SIR processes, it speeds up SIS diseases. In this case, we observe that heterogeneous temporal connectivity patterns and modular st…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading, using the Susceptible-Infected-Susceptible (SIS) model, in simplicial complexes. In particular, we analyze the dynamics of SIS in complex networks characterized by pairwise interactions (links), and three-body interactions (filled triangles, also known as 2-simplices). This higher-order description of the epidemic spreading is analytically formulated using a mi…
The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single epidemic spreading episode. At variance, real data from different cities over the world suggest that, besides a major single peak trait of infected density, a finite probability exists for a pattern made of two (or multiple) peaks. We show that such a latter feature is fully distinctive of a multilayered network of interactions, and reveal that actually a t…
We present a contact-based model to study the spreading of epidemics by means of extending the dynamic message passing approach to temporal networks. The shift in perspective from node- to edge-centric quantities enables accurate modelling of Markovian susceptible-infected-recovered outbreaks on time-varying trees, i.e., temporal networks with a loop-free underlying topology. On arbitrary graphs, the proposed contact-based model incorporates potential structural and temporal heterogeneities of the underlying contact network and improves analytic estimations with respect to the individual-based…
Changs in individual behavior often entangles with the dynamic interaction of individuals, which complicates the epidemic process and brings great challenges for the understanding and control of the epidemic. In this work, we consider three kinds of typical behavioral changes in epidemic process that is, self-quarantine of infected individuals, self-protection of susceptible individuals, and social distancing between them. We connect the behavioral changes with individual's social attributes by the activity-driven network with attractiveness. A mean-field theory is established to derive an ana…
Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of the infection channels are still not fully understood. Here we apply the SIR model and study analytically and numerically the epidemic spread on a recently developed spatial modular model imitating the structure of cities in a country. The model assumes that inside a city the infection channels connect many different locations, while the infection channels be…
We investigate a fermionic susceptible-infected-susceptible model with mobility of infected individuals on uncorrelated scale-free networks with power-law degree distributions $P (k) \sim k^{-γ}$ of exponents $2<γ<3$. Two diffusive processes with diffusion rate $D$ of an infected vertex are considered. In the \textit{standard diffusion}, one of the nearest-neighbors is chosen with equal chance while in the \textit{biased diffusion} this choice happens with probability proportional to the neighbor's degree. A non-monotonic dependence of the epidemic threshold on $D$ with an optimum diffusion ra…
We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transi…
Identifying super-spreaders in epidemics is important to suppress the spreading of disease especially when the medical resource is limited.In the modern society, the information on epidemics transmits swiftly through various communication channels which contributes much to the suppression of epidemics. Here we study on the identification of super-spreaders in the information-disease coupled spreading dynamics. Firstly, we find that the centralities in physical contact layer are no longer effective to identify super-spreaders in epidemics, which is due to the suppression effects from the inform…
A central feature of an emerging infectious disease in a pandemic scenario is the spread through geographical scales and the impacts on different locations according to the adopted mitigation protocols. We investigated a stochastic epidemic model with the metapopulation approach in which patches represent municipalities. Contagion follows a stochastic compartmental model for municipalities; the latter, in turn, interact with each other through recurrent mobility. As a case of study, we consider the epidemic of COVID-19 in Brazil performing data-driven simulations. Properties of the simulated e…
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network, wherein the disease in one network can spread to the other. Theoretical analysis is provided for each model to reveal that the global epidemic threshold in the interconnected network is not larger than the epidemic thresholds for the two isolated layered networks. In particular, in an interconnected homogenous network, detailed theoretical analysis is prese…
Many progresses in the understanding of epidemic spreading models have been obtained thanks to numerous modeling efforts and analytical and numerical studies, considering host populations with very different structures and properties, including complex and temporal interaction networks. Moreover, a number of recent studies have started to go beyond the assumption of an absence of coupling between the spread of a disease and the structure of the contacts on which it unfolds. Models including awareness of the spread have been proposed, to mimic possible precautionary measures taken by individual…
Most studies of disease spreading consider the underlying social network as obtained without the contagion, though epidemic influences people's willingness to contact others: A "friendly" contact may be turned to "unfriendly" to avoid infection. We study the susceptible-infected disease-spreading model on signed networks, in which each edge is associated with a positive or negative sign representing the friendly or unfriendly relation between its end nodes. In a signed network, according to Heider's theory, edge signs evolve such that finally a state of structural balance is achieved, correspo…
Wireless networks are commonly used in public spaces, universities and public institutions and provide accurate and easily accessible information to monitor the mobility and behavior of users. Following the application of containment measures during the recent pandemic, we analyse extensive data from the WiFi network in a University Campus in Italy during three periods, corresponding to partial lockdown, partial opening, and almost complete opening. We measure the probability distributions of groups and link activation at Wi-Fi Access Points, investigating how different areas are used in the p…
A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can interchange during the epidemic. We apply the model to the COVID-19 case and demonstrate the predictive features of our model.
Although suppressing the spread of a disease is usually achieved by investing in public resources, in the real world only a small percentage of the population have access to government assistance when there is an outbreak, and most must rely on resources from family or friends. We study the dynamics of disease spreading in social-contact multiplex networks when the recovery of infected nodes depends on resources from healthy neighbors in the social layer. We investigate how degree heterogeneity affects the spreading dynamics. Using theoretical analysis and simulations we find that degree heter…
We propose a targeted intervention protocol where recovery is restricted to individuals that have the least number of infected neighbours. Our recovery strategy is highly efficient on any kind of network, since epidemic outbreaks are minimal when compared to the baseline scenario of spontaneous recovery. In the case of spatially embedded networks, we find that an epidemic stays strongly spatially confined with a characteristic length scale undergoing a random walk. We demonstrate numerically and analytically that this dynamics leads to an epidemic spot with a flat surface structure and a radiu…
We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all thr…
Epidemic spreading on physical contact network will naturally introduce the human awareness information diffusion on virtual contact network, and the awareness diffusion will in turn depress the epidemic spreading, thus forming the competing spreading processes of epidemic and awareness in a multiplex networks. In this paper, we study the competing dynamics of epidemic and awareness, both of which follow the SIR process, in a two-layer networks based on microscopic Markov chain approach and numerical simulations. We find that strong capacities of awareness diffusion and self-protection of indi…
Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic spreading dynamics influenced by spatial structure and human dynamics (including both human mobility and human interaction intensity). We propose a systematical model to depict nationwide epidemic spreading in Côte d'Ivoire, which integrates multiple factors, such as human mobility, human interaction intensity, and demographic features. We provide insights to …
In this paper, we study the interplay between individual behaviors and epidemic spreading in a dynamical network. We distribute agents on a square-shaped region with periodic boundary conditions. Every agent is regarded as a node of the network and a wireless link is established between two agents if their geographical distance is less than a certain radius. At each time, every agent assesses the epidemic situation and make decisions on whether it should stay in or leave its current place. An agent will leave its current place with a speed if the number of infected neighbors reaches or exceeds…
Just like the degrees of human and animal interaction networks, the distribution of the times between interactions is known to often be right-skewed and fat-tailed. Both these distributions affect epidemic dynamics strongly, but, as we show in this Letter, for very different reasons. Whereas the high degrees of the tail are critical for facilitating epidemics, it is the small interevent times that control the dynamics of epidemics. We investigate this effect both analytically and numerically for different versions of the Susceptible-Infected-Recovered model on different types of networks.
This paper presents a discrete time probabilistic dynamic for simulating a contact-based epidemic spreading based on discrete time Markov chain process, in particular the attention is addressed to the susceptible-infectious-removed (SIR) model and the phase diagram of such model will be presented. Then, this report presents the set of equations that represent the optimal control strategies, by the means of Pontryagin's maximum principle, in two different cases a vaccination policy and a combined vaccination-hospitalization policy and show a numerical simulation, with the standard forward-backw…
In this work, we aim to understand the influence of the heterogeneity of infection rates on the Susceptible-Infected-Susceptible (SIS) epidemic spreading. Employing the classic SIS model as the benchmark, we study the influence of the independently identically distributed infection rates on the average fraction of infected nodes in the metastable state. The log-normal, gamma and a newly designed distributions are considered for infection rates. We find that, when the recovery rate is small, i.e.\ the epidemic spreads out in both homogeneous and heterogeneous cases: 1) the heterogeneity of infe…
