The dynamics of herd immunity depend crucially on the interaction between collective social behavior and disease transmission, but the role of heterogeneity in this context frequently remains unclear. Here, we dissect this co-evolutionary feedback by coupling a public goods game with an epidemic model on complex networks, including multiplex and real-world networks. Our results reveals a dichotomy in how heterogeneity shapes outcomes. We demonstrate that structural heterogeneity in social networks acts as a powerful catalyst for cooperation and disease suppression. This emergent effect is driven by highly connected hubs who, facing amplified personal risk, adopt protective strategies out of self-interest. In contrast, heterogeneity in individual infection costs proves detrimental, undermining cooperation and amplifying the epidemic. This creates a ``weakest link'' problem, where individuals with low perceived risk act as persistent free-riders and disease reservoirs, degrading the collective response. Our findings establish that heterogeneity is a double-edged sword: its impact is determined by whether it creates an asymmetry of influence (leverage points) or an asymmetry of motivation (weakest links), recommending disease intervention policies that facilitate cooperative transition in hubs (strengthening the leverage point) and homogenize incentives to weakest links.
In this paper, we investigate the epidemic spreading for SIR model in weighted scale-free networks with nonlinear infectivity, where the transmission rate in our analytical model is weighted. Concretely, we introduce the infectivity exponent $α$ and the weight exponent $β$ into the analytical SIR model, then examine the combination effects of $α$ and $β$ on the epidemic threshold and phase transition. We show that one can adjust the values of $α$ and $β$ to rebuild the epidemic threshold to a finite value, and it is observed that the steady epidemic prevalence $R$ grows in an exponential form …
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.
Cooperators forgo their interest to benefit others. Thus cooperation should not be favored by natural selection. It challenges the evolutionists, since cooperation is widespread. As one of the resolutions, information spreading has been revealed to play a key role in the emergence of cooperation. Individuals, however, are typically assumed to be passive in the information spreading. Here we assume that individuals are active to spread the information via self-recommendation. Individuals with higher intensities of self-recommendation are likely to have more neighbors. We find that i) eloquent c…
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…
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.
We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolising cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metaopoluation in the long time limit, as well as the relevant parameters characterising the epidemic threshold that separates an epidemic from a non-epidemic phase. W…
Despite extensive work on the interplay between traffic dynamics and epidemic spreading, the control of epidemic spreading by routing strategies has not received adequate attention. In this paper, we study the impact of efficient routing protocol on epidemic spreading. In the case of infinite node-delivery capacity, where the traffic is free of congestion, we find that that there exists optimal values of routing parameter, leading to the maximal epidemic threshold. This means that epidemic spreading can be effectively controlled by fine tuning the routing scheme. Moreover, we find that an incr…
We develop a generalized group-based epidemic model (GgroupEM) framework for any compartmental epidemic model (for example; susceptible-infected-susceptible, susceptible-infected-recovered, susceptible-exposed-infected-recovered). Here, a group consists of a collection of individual nodes. This model can be used to understand the important dynamic characteristics of a stochastic epidemic spreading over very large complex networks, being informative about the state of groups. Aggregating nodes by groups, the state space becomes smaller than the individual-based approach at the cost of aggregati…
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.
In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as "superspreaders", are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resourc…
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…
The disease spreading on complex networks is studied in SIR model. Simulations on empirical complex networks reveal two specific regimes of disease spreading: local containment and epidemic outbreak. The variables measuring the extent of disease spreading are in general characterized by a bimodal probability distribution. Phase diagrams of disease spreading for empirical complex networks are introduced. A theoretical model of disease spreading on m-ary tree is investigated both analytically and in simulations. It is shown that the model reproduces qualitative features of phase diagrams of dise…
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.
For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. We present an extended model for disease spread based on combining an SIR model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. The model shows interesting nonequilibrium phase separation associated with a reduction of the number of infections, and …
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…
Passenger contact in public transit (PT) networks can be a key mediate in the spreading of infectious diseases. This paper proposes a time-varying weighted PT encounter network to model the spreading of infectious diseases through the PT systems. Social activity contacts at both local and global levels are also considered. We select the epidemiological characteristics of coronavirus disease 2019 (COVID-19) as a case study along with smart card data from Singapore to illustrate the model at the metropolitan level. A scalable and lightweight theoretical framework is derived to capture the time-v…
In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders - rather than favoring - the global diseas…
Resource support between individuals is of particular importance in controlling or mitigating epidemic spreading, especially during pandemics. Whereas there remains the question of how we can protect ourselves from being infected while helping others by donating resources in fighting against the epidemic. To answer the question, we propose a novel resource allocation model by considering the awareness of self-protection of individuals. In the model, a tuning parameter is introduced to quantify the reaction strength of individuals when they are aware of the disease. And then, a coupled model of…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission rates to the nodes results in the heterogeneity, which in turn causes the segregation of nodes in terms of various sub populations. The aim of the study is to gain microscopic insight into the effect of interactions among various sub populations in the spreading processes of disease over such networks. The discrete time Markov chain method based upon the suscep…
Albeit epidemic models have evolved into powerful predictive tools for the spread of diseases and opinions, most assume memoryless agents and independent transmission channels. We develop an infection mechanism that is endowed with memory of past exposures and simultaneously incorporates the joint effect of multiple infectious sources. Analytic equations and simulations of the susceptible-infected-susceptible model in unstructured substrates reveal the emergence of an additional phase that separates the usual healthy and endemic ones. This intermediate phase shows fundamentally distinct charac…
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…
One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thom…
Recently, many empirical studies uncovered that animal foraging, migration and human traveling obey Levy flights with an exponent around -2. Inspired by the deluge of H1N1 this year, in this paper, the effects of Levy flights' mobility pattern on epidemic spreading is studied from a network perspective. We construct a spatial weighted network which possesses Levy flight spatial property under a restriction of total energy. The energy restriction is represented by the limitation of total travel distance within a certain time period of an individual. We find that the exponent -2 is the epidemic …
In spite of the extensive previous efforts on traffic dynamics and epidemic spreading in complex networks, the problem of traffic-driven epidemic spreading on {\em correlated} networks has not been addressed. Interestingly, we find that the epidemic threshold, a fundamental quantity underlying the spreading dynamics, exhibits a non-monotonic behavior in that it can be minimized for some critical value of the assortativity coefficient, a parameter characterizing the network correlation. To understand this phenomenon, we use the degree-based mean-field theory to calculate the traffic-driven epid…
We consider a standard \textit{susceptible-infected-susceptible} (SIS) model to study behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual epidemic behavior with a critical threshold $λ_{c}$ below which infectious diseases die out. Whereas for the spreading rate $λ$ far above $λ_{c}$, it was found that the density of infected individuals $ρ$ as a function of $λ$ has the property $ρ\approx F(K)(\ln λ- \ln λ_{c})$.
This article reviews and presents various solved and open problems in the development, analysis, and control of epidemic models. We are interested in presenting a relatively concise report for new engineers looking to enter the field of spreading processes on complex networks.
We propose a theoretical framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze both the classical Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models within this framework, and compare macroscopic and microscopic indicators of th…
The mobility patterns of individuals in China during the early outbreak of the COVID-19 pandemic exhibit reversible changes -- in many regions, the mobility first decreased significantly and later restored. Based on this observation, here we study the classical SIR model on a particular type of time-varying network where the links undergo a freeze-recovery process. We first focus on an isolated network and find that the recovery mechanism could lead to the resurgence of an epidemic. The influence of link freezing on epidemic dynamics is subtle. In particular, we show that there is an optimal v…
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of its time in localized environments and has easily identifiable mobility patterns --such as workplaces, university campuses or schools-- it is of critical importance to identify the factors controlling the rate of disease spread. Here we present a discrete-time, metapopulation-based model to describe the transmission of SIS-like diseases that take place in co…
Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role relations. In addition, we perform detailed analysis of two representative metrics, outbreak threshold and epidemic prevalence, on SIS and SIR models. Both theoretical and simulation results find good agreements with each other. Furthermore, experiments show that, on fully mixed networks, the weight distribution on edges would not affect the epidemic results …
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-removed (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach we derive, in the long time limit, analytical pre…
Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model considering the two key ingredients, in which the contacts are grouped into two classes: strong contacts and normal ones. Next, we present a unified edge-based compartmental approach to the spread dynamics on Erdös-Rényi (ER) networks and validate its results by extensive numerical simulations. In case that epidemic is totally drug-resistant, we both numeric…
The impact that information diffusion has on epidemic spreading has recently attracted much attention. As a disease begins to spread in the population, information about the disease is transmitted to others, which in turn has an effect on the spread of disease. In this paper, using empirical results of the propagation of H7N9 and information about the disease, we clearly show that the spreading dynamics of the two-types of processes influence each other. We build a mathematical model in which both types of spreading dynamics are described using the SIS process in order to illustrate the influe…
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…
We investigate the spread of diseases, computer viruses or information on complex networks and also immunization strategies to prevent or control the spread. When an entire population cannot be immunized and the effect of immunization is not perfect, we need the targeted immunization with immunization rate. Under such a circumstance we calculate epidemic thresholds for the SIR and SIS epidemic models. It is shown that, in scale-free networks, the targeted immunization is effective only if the immunization rate is equal to one. We analyze here epidemic spreading on directed complex networks, bu…
In this work we consider a model of epidemic spreading coupled with an opinion dynamics in a fully-connected population. Regarding the opinion dynamics, the individuals may be in two distinct states, namely in favor or against a vaccination campaign. Individuals against the vaccination follow a standard SIS model, whereas the pro-vaccine individuals can also be in a third compartment, namely Vaccinated. In addition, the opinions change according to the majority-rule dynamics in groups with three individuals. We also consider that the vaccine can give permanent or temporary immunization to the …
Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread some infected packets by biased random walks to their neighbor nodes causing the infection of the susceptible nodes that receive the packets. An infected node get recovered from infection with a fixed probability. Simulation and analytical results on model and real-world networks show that the epidemic spreading becomes intense and wide with the increase of del…
Bipartite networks are composed of two types of nodes and there are no links between nodes of the same type. Thus the study of epidemic spread and control on such networks is relevant to sexually transmitted diseases (STDs). When entire populations of two types cannot be immunized and the effect of immunization is not perfect, we have to consider the targeted immunization with immunization rates. We derive the epidemic thresholds of SIR and SIS models with immunization and illustrate the results with STDs on heterosexual contact networks.
The epidemic spreading has been widely studied when each node may get infected by an infected neighbor with the same rate. However, the infection rate between a pair of nodes is usually heterogeneous and even correlated with their nodal degrees in the contact network. We aim to understand how such correlated heterogeneous infection rates influence the spreading on different network topologies. Motivated by real-world datasets, we propose a correlated heterogeneous Susceptible-Infected-Susceptible model which assumes that the infection rate $β_{ij}(=β_{ji})$ between node $i$ and $j$ is correlat…
We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations of arrival times reveals a higher correlation compared to the shortest path approach used previously. In addition ou…
The interplay between traffic dynamics and epidemic spreading on complex networks has received increasing attention in recent years. However, the control of traffic-driven epidemic spreading remains to be a challenging problem. In this Brief Report, we propose a method to suppress traffic-driven epidemic outbreak by properly removing some edges in a network. We find that the epidemic threshold can be enhanced by the targeted cutting of links among large-degree nodes or edges with the largest algorithmic betweeness. In contrast, the epidemic threshold will be reduced by the random edge removal.…
We present a modified \emph{susceptible-infected-susceptible} (SIS) model on complex networks, small-world and scale-free, to study epidemic spreading with the effect of time delay which is introduced to the infected phase. Considering the topology of the network, both uniform and degree-dependent delays are studied during the contagion process. We find that the existence of time delay will enhance both outbreaks and prevalence of infectious diseases in the network.
A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epidemic spreading. In particular it is found that as in static networks, rewiring networks with degree distribution exponent $γ>3$ exhibit a threshold in the infection rate below which epidemics die out in the steady state. However the threshold is higher in the rewiring case. For $2<γ\leq 3$ no such threshold exists, but for small infection rate the s…
We study geographical effects on the spread of diseases in lattice-embedded scale-free networks. The geographical structure is represented by the connecting probability of two nodes that is related to the Euclidean distance between them in the lattice. By studying the standard Susceptible-Infected model, we found that the geographical structure has great influences on the temporal behavior of epidemic outbreaks and the propagation in the underlying network: the more geographically constrained the network is, the more smoothly the epidemic spreads.
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on th…
ETH Zürich（苏黎世联邦理工学院）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；University of Maribor（马里博尔大学）；China Medical University Hospital, China Medical University（中国医药大学附设医院，中国医药大学）；Alma Mater Europaea（欧洲母校大学）
In a non-sustainable, "over-populated" world, what might the use of nanotechnology-based targeted, autonomous weapons mean for the future of humanity? In order to gain some insights, we make a simplified game-theoretical thought experiment. We consider a population where agents play the public goods game, and where in parallel an epidemic unfolds. Agents that are infected defectors are killed with a certain probability and replaced by susceptible cooperators. We show that such "nanowars", even if aiming to promote good behavior and planetary health, fail not only to promote cooperation, but th…
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…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation, widely exploited for most of the models. Using discrete approach we investigate the epidemic threshold and the quasi-stationary distribution. The main result is a theorem about mixing time for the process, which scales like logarithm of the network size and which is proportional to the inverse of the distance from the epidemic threshold. In order to present…
University of Oxford（牛津大学）；Massachusetts Institute of Technology (MIT)（麻省理工学院）；TU Delft（代尔夫特理工大学）；German Aerospace Center (DLR)（德国航空航天中心）；Proxima Robotics srl（普罗xima机器人有限公司）
When an epidemic spreads into a population, it is often unpractical or impossible to have a continuous monitoring of all subjects involved. As an alternative, algorithmic solutions can be used to infer the state of the whole population from a limited amount of measures. We analyze the capability of deep neural networks to solve this challenging task. Our proposed architecture is based on Graph Convolutional Neural Networks. As such it can reason on the effect of the underlying social network structure, which is recognized as the main component in the spreading of an epidemic. We test the propo…
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…
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 recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, $i.e$, the network that sustain the functionality of a society. Then, we survey …
Pandemic distribution of COVID-19 in the world has motivated us to discuss combined effects of network clustering and adaptivity on epidemic spreading. We address the question concerning the choice of optimal mechanism for most effective prohibiting disease propagation in a connected network: adaptive clustering, which mimics self-isolation (SI) in local communities, or sharp instant clustering, which looks like frontiers closing (FC) between cities and countries. SI-networks are "adaptively grown" under condition of maximization of small cliques in the entire network, while FC-networks are "i…
