Epidemics and percolation in small-world networks

Optimal reduction of an epidemic outbreak size via temporary quarantine

Understanding the dynamics of an epidemic spread is crucial for effective control measures. During the COVID-19 pandemic, quarantines were implemented to minimize infections while mitigating social and economic impacts, raising the question of how to maximize quarantine efficiency. Previous research on periodic quarantines using the susceptible-infected-recovered (SIR) and similar models identified the optimal duration for periodic quarantines. However, the question of the optimal initiation time for a single quarantine was not addressed. Here, we use the SIR model in order to determine the optimal quarantine initiation time, by computing the optimal susceptible fraction at the onset of the quarantine, which minimizes the total outbreak size. Our analysis extends from a well-mixed scenario to strongly heterogeneous social networks. We show that the optimal quarantine initiation time is closely related to the so-called "herd immunity" threshold, occurring at the onset of epidemic decline. Importantly, providing a methodology for identifying the optimal quarantine initiation time across different network structures, entails significant implications for epidemic control.

Susceptible-infected-susceptible process on Erdős-Rényi graphs: Determining the infected fraction

There are many methods to estimate the quasistationary infected fraction of the SIS process on (random) graphs. A challenge is to adequately incorporate correlations, which is especially important in sparse graphs. Methods typically are either significantly biased in sparse graphs, or computationally very demanding already for small network sizes. The former applies to heterogeneous mean field and to the N-intertwined mean field approximation, the latter to most higher order approximations. In this paper we introduce a method to determine the infected fraction in sparse graphs, which we test on Erdős-Rényi graphs. Our method is based on degree pairs, does take into account correlations, and gives accurate estimates. At the same time, computations are very feasible and can easily be done even for large networks.

Weighted-ensemble network simulations of the susceptible-infected-susceptible model of epidemics

The presence of erratic or unstable paths in standard kinetic Monte Carlo simulations significantly undermines the accurate simulation and sampling of transition pathways. While typically reliable methods, such as the Gillespie algorithm, are employed to simulate such paths, they encounter challenges in efficiently identifying rare events due to their sequential nature and reliance on exact Monte Carlo sampling. In contrast, the weighted-ensemble method effectively samples rare events and accelerates the exploration of complex reaction pathways by distributing computational resources among multiple replicas, where each replica is assigned a weight reflecting its importance, and evolves independently from the others. Here, we implement the highly efficient and robust weighted-ensemble method to model susceptible-infected-susceptible dynamics on large heterogeneous population networks, and explore the interplay between stochasticity and contact heterogeneity, which ultimately gives rise to disease clearance. Studying a wide variety of networks characterized by fat-tailed asymmetric degree distributions, we are able to compute the mean time to extinction and quasistationary distribution around it in previously inaccessible parameter regimes.

Optimizing Contact Network Topological Parameters of Urban Populations Using the Genetic Algorithm

This paper explores the application of complex network models and genetic algorithms in epidemiological modeling. By considering the small-world and Barabási-Albert network models, we aim to replicate the dynamics of disease spread in urban environments. This study emphasizes the importance of accurately mapping individual contacts and social networks to forecast disease progression. Using a genetic algorithm, we estimate the input parameters for network construction, thereby simulating disease transmission within these networks. Our results demonstrate the networks' resemblance to real social interactions, highlighting their potential in predicting disease spread. This study underscores the significance of complex network models and genetic algorithms in understanding and managing public health crises.

Impact of community structure on the spread of epidemics on time-varying multiplex networks

Community structure plays a crucial role in realistic networks and different communities can be created by groups of interest and activity events, and exploring the impact of community properties on collective dynamics is an active topic in the field of network science. Here, we propose a new coupled model with different time scales for online social networks and offline epidemic spreading networks, in which community structure is added into online social networks to investigate its role in the interacting dynamics between information diffusion and epidemic spreading. We obtain the analytical equations of epidemic threshold by MMC (Microscopic Markov Chain) method and conduct a large quantities of numerical simulations using Monte Carlo simulations in order to verify the accuracy of the MMC method, and more valuable insights are also obtained. The results indicate that an increase in the probability of the mobility of an individual can delay the spread of epidemic-related information in the network, as well as delaying the time of the peak of the infection density in the network. However, an increase in the contact ability of mobile individuals produces a facilitating effect on the spread of epidemics. Finally, it is also found that the stronger the acceptance of an individual to information coming from a different community, the lower the infection density in the network, which suggests that it has an inhibitory effect on the disease spreading.

CCTFv2: Modeling Cyber Competitions

Cyber competitions are usually team activities, where team performance not only depends on the members' abilities but also on team collaboration. This seems intuitive, especially given that team formation is a well-studied discipline in competitive sports and project management, but unfortunately, team performance and team formation strategies are rarely studied in the context of cybersecurity and cyber competitions. Since cyber competitions are becoming more prevalent and organized, this gap becomes an opportunity to formalize the study of team performance in the context of cyber competitions. This work follows a cross-validating two-approach methodology. The first is the computational modeling of cyber competitions using Agent-Based Modeling. Team members are modeled, in NetLogo, as collaborating agents competing over a network in a red team/blue team match. Members' abilities, team interaction and network properties are parametrized (inputs), and the match score is reported as output. The second approach is grounded in the literature of team performance (not in the context of cyber competitions), where a theoretical framework is built in accordance with the literature. The results of the first approach are used to build a causal inference model using Structural Equation Modeling. Upon comparing the causal inference model to the theoretical model, they showed high resemblance, and this cross-validated both approaches. Two main findings are deduced: first, the body of literature studying teams remains valid and applicable in the context of cyber competitions. Second, coaches and researchers can test new team strategies computationally and achieve precise performance predictions. The targeted gap used methodology and findings which are novel to the study of cyber competitions.

Cost-optimal seeding strategy during a botanical pandemic in domesticated fields

Botanical pandemics cause enormous economic damage and food shortages around the globe. However, since botanical pandemics are here to stay in the short-medium term, domesticated field owners can strategically seed their fields to optimize each session's economic profit. In this work, we propose a novel epidemiological-economic mathematical model that describes the economic profit from a field of plants during a botanical pandemic. We describe the epidemiological dynamics using a spatiotemporal extended susceptible-infected-recovered epidemiological model with a non-linear output economic model. We provide an algorithm to obtain an optimal grid-formed seeding strategy to maximize economic profit, given field and pathogen properties. We show that the recovery and basic infection rates have a similar economic influence. Unintuitively, we show that a larger farm does not promise higher economic profit. Our results demonstrate a significant benefit of using the proposed seeding strategy and shed more light on the dynamics of the botanical pandemic.

Scaling laws of failure dynamics on complex networks

The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes. Most notably, we show that the spatial structure of damage governs the emergence of the localized to mean field transition: as the network gets gradually randomized failed clusters formed on locally regular patches merge through long range links generating a percolation like transition which reduces the load concentration on the network. The results may help to design network structures with an improved robustness against cascading failure.

Extended-range percolation in complex networks

Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted path of nodes between them. In a variety of more recent data transmission protocols, such as the communication of noisy data via error-correcting repeaters, both in classical and quantum networks, the requirement of an uninterrupted path is too strict: two nodes may be able to communicate even if all paths between them have interruptions or gaps consisting of nodes that may corrupt the message. In such a case a different approach is needed. We develop the theoretical framework for extended-range percolation in networks, describing the fundamental connectivity properties relevant to such models of information transfer. We obtain exact results, for any range R, for infinite random uncorrelated networks and we provide a message-passing formulation that works well in sparse real-world networks. The interplay of the extended range and heterogeneity leads to novel critical behavior in scale-free networks.

Study on the regional risk classification method for the prevention and control of emerging infectious diseases based on directed graph theory

Background

Emerging infectious diseases are a class of diseases that are spreading rapidly and are highly contagious. It seriously affects social stability and poses a significant threat to human health, requiring urgent measures to deal with them. Its outbreak will very easily lead to the large-scale spread of the virus, causing social problems such as work stoppages and traffic control, thereby causing social panic and psychological unrest, affecting human activities and social stability, and even endangering lives. It is essential to prevent and control the spread of infectious diseases effectively.

Purpose

We aim to propose an effective method to classify the risk level of a new epidemic region by using graph theory and risk classification methods to provide a theoretical reference for the comprehensive evaluation and determination of epidemic prevention and control, as well as risk level classification.

Methods

Using the graph theory method, we first define the network structure of social groups and construct the risk transmission network of the new epidemic region. Then, combined with the risk classification method, the classification of high, medium, and low risk levels of the new epidemic region is discussed from two cases with common and looped graph nodes, respectively. Finally, the reasonableness of the classification method is verified by simulation data.

Results

The directed weighted scale-free network can better describe the transmission law of an epidemic. Moreover, the proposed method of classifying the risk level of a region by using the correlation function between two regions and the risk value of the regional nodes can effectively evaluate the risk level of different regions in the new epidemic region. The experiments show that the number of medium and high risk nodes shows no increasing trend. The number of high-risk regions is relatively small compared to medium-risk regions, and the number of low-risk regions is the largest.

Conclusions

It is necessary to distinguish scientifically between the risk level of the epidemic area and the neighboring regions so that the constructed social network model of the epidemic region's spread risk can better describe the spread of the epidemic risk in the social network relations.

Universality of explosive percolation under product and sum rule

We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which M candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other M-1 candidate edges are being discarded. These two rules are prototypical "explosive" percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.e., M=2. Here we investigate whether the claimed PR-SR universality is valid for higher-order models with M larger than 2. Based on traditional finite-size scaling theory and largest-gap scaling, we obtain the percolation threshold and the critical exponents of the order parameter, susceptibility, and the derivative of entropy for PR and SR for M from 2 to 9. Our results strongly suggest PR-SR universality, for any fixed M.

Site percolation in distorted square and simple cubic lattices with flexible number of neighbors

This paper exhibits a Monte Carlo study on site percolation using the Newmann-Ziff algorithm in distorted square and simple cubic lattices where each site is allowed to be directly linked with any other site if the Euclidean separation between the pair is at most a certain distance d, called the connection threshold. Distorted lattices are formed from regular lattices by a random but controlled dislocation of the sites with the help of a parameter α, called the distortion parameter. The distinctive feature of this study is the relaxation of the restriction of forming bonds with only the nearest neighbors. Owing to this flexibility and the intricate interplay between the two parameters α and d, the site percolation threshold may either increase or decrease with distortion. The dependence of the percolation threshold on the average degree of a site has been explored to show that the obtained results are consistent with those on percolation in regular lattices with an extended neighborhood and continuum percolation.

Critical behavior of the diffusive susceptible-infected-recovered model

The critical behavior of the nondiffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the two-dimensional lattice, we show that diffusion for all agents, while rendering this symmetry destroyed, constitutes a singular perturbation that induces asymptotically distinct dynamical and stationary critical behavior from the nondiffusive model. In particular, the manifested crossover behavior in the effective mean-square radius exponents reveals that slow crossover behavior in general diffusive multispecies reaction systems may be ascribed to the interference of multiple length scales and timescales at early times.

A novel methodology concentrating on risk propagation to conduct a risk analysis based on a directed complex network

A novel methodology is proposed in the present study to describe the risk propagation process by quantitatively evaluating the criticality and sensitivity of risk events according to complex network theory, based on which risk matrices are developed to interrupt the risk propagation process by setting up safety barriers. The applicability and accuracy of the improved k-shell decomposition algorithm and risk flow model for calculating the criticality proposed in this study are verified by the susceptible-infected-recovered (SIR) simulation, which is widely regarded as a benchmark for complex networks (CN) issues. The results confirm the advantages of the proposed methodologies considering comprehensively various comparison indicators. The sensitivity of the nodes is quantified by running an SIR simulation with a variable infection rate and recovery rate. Finally, the criticality and sensitivity of risk events contribute to the development of risk matrices with three different risk scenarios, based on which the applicability and effectiveness of safety barriers are qualitatively analyzed to interrupt the risk propagation process. The framework and methodologies proposed in this study could well present the risk propagation process within CNs and are proven to have a great potential for studies on safety barriers.

Early Detection and Control of the Next Epidemic Wave Using Health Communications: Development of an Artificial Intelligence-Based Tool and Its Validation on COVID-19 Data from the US

Social media networks highly influence on a broad range of global social life, especially in the context of a pandemic. We developed a mathematical model with a computational tool, called EMIT (Epidemic and Media Impact Tool), to detect and control pandemic waves, using mainly topics of relevance on social media networks and pandemic spread. Using EMIT, we analyzed health-related communications on social media networks for early prediction, detection, and control of an outbreak. EMIT is an artificial intelligence-based tool supporting health communication and policy makers decisions. Thus, EMIT, based on historical data, social media trends and disease spread, offers an predictive estimation of the influence of public health interventions such as social media-based communication campaigns. We have validated the EMIT mathematical model on real world data combining COVID-19 pandemic data in the US and social media data from Twitter. EMIT demonstrated a high level of performance in predicting the next epidemiological wave (AUC = 0.909, F₁ = 0.899).

Tracking the Progression and Influence of Beta-Amyloid Plaques Using Percolation Centrality and Collective Influence Algorithm: A Study Using PET Images

Background

The study of brain networks, particularly the spread of disease, is made easier thanks to the network theory. The aberrant accumulation of beta-amyloid plaques and tau protein tangles in Alzheimer's disease causes disruption in brain networks. The evaluation scores, such as the mini-mental state examination (MMSE) and neuropsychiatric inventory questionnaire, which provide a clinical diagnosis, are affected by this build-up.

Purpose

The percolation of beta-amyloid/tau tangles and their impact on cognitive tests are still unspecified.

Methods

Percolation centrality could be used to investigate beta-amyloid migration as a characteristic of positron emission tomography (PET)-image-based networks. The PET-image-based network was built utilizing a public database containing 551 scans published by the Alzheimer's Disease Neuroimaging Initiative. Each image in the Julich atlas has 121 zones of interest, which are network nodes. Furthermore, the influential nodes for each scan are computed using the collective influence algorithm.

Results

For five nodal metrics, analysis of variance (ANOVA; P < .05) reveals the region of interest (ROI) in gray matter (GM) Broca's area for Pittsburgh compound B (PiB) tracer type. The GM hippocampus area is significant for three nodal metrics in the case of florbetapir (AV45). Pairwise variance analysis of the clinical groups reveals five to twelve statistically significant ROIs for AV45 and PiB, respectively, that can distinguish between pairs of clinical situations. Based on multivariate linear regression, the MMSE is a trustworthy evaluation tool.

Conclusion

Percolation values suggest that around 50 of the memory, visual-spatial skills, and language ROIs are critical to the percolation of beta-amyloids within the brain network when compared to the other extensively used nodal metrics. The anatomical areas rank higher with the advancement of the disease, according to the collective influence algorithm.

Topic selectivity and adaptivity promote spreading of short messages

Why is the Twitter, with its extremely length-limited messages so popular ? Our work shows that short messages focused on a single topic may have an inherent advantage in spreading through social networks, which may explain the popularity of a service featuring only short messages. We introduce a new explanatory model for information propagation through social networks that includes selectivity of message consumption depending on their content, competition for user's attention between messages and message content adaptivity through user-introduced changes. Our agent-based simulations indicate that the model displays inherent power-law distribution of number of shares for different messages and that the popular messages are very short. The adaptivity of messages increases the popularity of already popular messages, provided the users are neither too selective nor too accommodating. The distribution of message variants popularity also follows a power-law found in real information cascades. The observed behavior is robust against model parameter changes and differences of network topology.

Modified Heider balance on Erdös-Rényi networks

The lack of signed random networks in standard balance studies has prompted us to extend the Hamiltonian of the standard balance model. Random networks with tunable parameters are suitable for better understanding the behavior of standard balance as an underlying dynamics. Moreover, the standard balance model in its original form does not allow preserving tensed triads in the network. Therefore, the thermal behavior of the balance model has been investigated on a fully connected signed network recently. It has been shown that the model undergoes an abrupt phase transition with temperature. Considering these two issues, we examine the thermal behavior of the structural balance model defined on Erdös-Rényi random networks within the range of their connected regime. We provide a mean-field solution for the model. We observe a first-order phase transition with temperature for a wide range of connection probabilities. We detect two transition temperatures, T_{cold} and T_{hot}, characterizing a hysteresis loop. We find that with decreasing the connection probability, both T_{cold} and T_{hot} decrease. However, the slope of decreasing T_{hot} with decreasing connection probability is larger than the slope of decreasing T_{cold}. Hence, the hysteresis region gets narrower until it disappears in a certain connection probability. We provide a phase diagram in the temperature-tie density plane to accurately observe the metastable or coexistence region behavior. Then we justify our mean-field results with a series of Monte Carlo simulations.

Micro-level social structures and the success of COVID-19 national policies

Similar policies in response to the COVID-19 pandemic have resulted in different success rates. Although many factors are responsible for the variances in policy success, our study shows that the micro-level structure of person-to-person interactions-measured by the average household size and in-person social contact rate-can be an important explanatory factor. To create an explainable model, we propose a network transformation algorithm to create a simple and computationally efficient scaled network based on these micro-level parameters, as well as incorporate national-level policy data in the network dynamic for SEIR simulations. The model was validated during the early stages of the COVID-19 pandemic, which demonstrated that it can reproduce the dynamic ordinal ranking and trend of infected cases of various European countries that are sufficiently similar in terms of some socio-cultural factors. We also performed several counterfactual analyses to illustrate how policy-based scenario analysis can be performed rapidly and easily with these explainable models.

Estimation of the basic reproduction number of COVID-19 from the incubation period distribution

The estimates of the future course of spreading of the SARS-CoV-2 virus are frequently based on Markovian models in which the duration of residence in any compartment is exponentially distributed. Accordingly, the basic reproduction number R 0 is also determined from formulae where it is related to the parameters of such models. The observations show that the start of infectivity of an individual appears nearly at the same time as the onset of symptoms, while the distribution of the incubation period is not an exponential. Therefore, we propose a method for estimation of R 0 for COVID-19 based on the empirical incubation period distribution and assumed very short infectivity period that lasts only few days around the onset of symptoms. We illustrate this venerable approach to estimate R 0 for six major European countries in the first wave of the epidemic. The calculations show that even if the infectivity starts 2 days before the onset of symptoms and stops instantly when they appear (immediate isolation), the value of R 0 is larger than that from the classical, SIR model. For more realistic cases, when only individuals with mild symptoms spread the virus for few days after onset of symptoms, the respective values are even larger. This implies that calculations of R 0 and other characteristics of spreading of COVID-19 based on the classical, Markovian approaches should be taken very cautiously.

Exactly solvable percolation problems

We propose a simple percolation criterion for arbitrary percolation problems. The basic idea is to decompose the system of interest into a hierarchy of neighborhoods, such that the percolation problem can be expressed as a branching process. The criterion provides the exact percolation thresholds for a large number of exactly solved percolation problems, including random graphs, small-world networks, bond percolation on two-dimensional lattices with a triangular hypergraph, and site percolation on two-dimensional lattices with a generalized triangular hypergraph, as well as specific continuum percolation problems. The fact that the range of applicability of the criterion is so large bears the remarkable implication that all the listed problems are effectively treelike. With this in mind, we transfer the exact solutions known from duality to random lattices and site-bond percolation problems and introduce a method to generate simple planar lattices with a prescribed percolation threshold.

Simple model of epidemic dynamics with memory effects

We introduce a compartment model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states S=susceptible, I=infected, or R=recovered (SIR model). In state R an individual is assumed to stay immune within a finite-time interval. In the first part, we introduce a random lifetime or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and not captured by the classical standard SIR model.

Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number z and site thresholds p_{c} for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting z versus 1/p_{c} and z versus -1/ln(1-p_{c}) using the data of d'Iribarne et al. [J. Phys. A 32, 2611 (1999)JPHAC50305-447010.1088/0305-4470/32/14/002] and others. The results show that all the plots overlap on a line with a slope consistent with the theoretically predicted asymptotic value of zp_{c}∼4η_{c}=4.51235, where η_{c} is the continuum threshold for disks. In three dimensions, precise site and bond thresholds for bcc and fcc lattices with 2nd and 3rd NN, and bond thresholds for the sc lattice with up to the 13th NN, are obtained by Monte Carlo simulations, using an efficient single-cluster growth method. For site percolation, the values of thresholds for different types of lattices with compact neighborhoods also collapse together, and linear fitting is consistent with the predicted value of zp_{c}∼8η_{c}=2.7351, where η_{c} is the continuum threshold for spheres. For bond percolation, Bethe-lattice behavior p_{c}=1/(z-1) is expected to hold for large z, and the finite-z correction is confirmed to satisfy zp_{c}-1∼a_{1}z^{-x}, with x=2/3 for three dimensions as predicted by Frei and Perkins [Electron. J. Probab. 21, 56 (2016)1083-648910.1214/16-EJP6] and by Xu et al. [Phys. Rev. E 103, 022127 (2021)2470-004510.1103/PhysRevE.103.022127]. Our analysis indicates that for compact neighborhoods, the asymptotic behavior of zp_{c} has universal properties, depending only on the dimension of the system and whether site or bond percolation but not on the type of lattice.

Epidemic Risk Assessment by a Novel Communication Station Based Method

The COVID-19 pandemic has caused serious consequences in the last few months and trying to control it has been the most important objective. With effective prevention and control methods, the epidemic has been gradually under control in some countries and it is essential to ensure safe work resumption in the future. Although some approaches are proposed to measure people's healthy conditions, such as filling health information forms or evaluating people's travel records, they cannot provide a fine-grained assessment of the epidemic risk. In this paper, we propose a novel epidemic risk assessment method based on the granular data collected by the communication stations. We first compute the epidemic risk of these stations in different intervals by combining the number of infected persons and the way they pass through the station. Then, we calculate the personnel risk in different intervals according to the station trajectory of the queried person. This method could assess people's epidemic risk accurately and efficiently. We also conduct extensive simulations and the results verify the effectiveness of the proposed method.

Exchange on dynamic encounter networks allows plant mitochondria to collect complete sets of mitochondrial DNA products despite their incomplete genomes

Mitochondria in plant cells usually contain less than a full copy of the mitochondrial DNA (mtDNA) genome. Here, we asked whether mitochondrial dynamics may allow individual mitochondria to 'collect' a full set of mtDNA-encoded gene products over time, by facilitating exchange between individuals akin to trade on a social network. We characterise the collective dynamics of mitochondria in Arabidopsis hypocotyl cells using a recent approach combining single-cell time-lapse microscopy, video analysis and network science. We use a quantitative model to predict the capacity for sharing genetic information and gene products through the networks of encounters between mitochondria. We find that biological encounter networks support the emergence of gene product sets over time more readily than a range of other possible network structures. Using results from combinatorics, we identify the network statistics that determine this propensity, and discuss how features of mitochondrial dynamics observed in biology facilitate the collection of mtDNA-encoded gene products.

Epidemics with asymptomatic transmission: Subcritical phase from recursive contact tracing

The challenges presented by the COVID-19 epidemic have created a renewed interest in the development of new methods to combat infectious diseases, and it has shown the importance of preparedness for possible future diseases. A prominent property of the SARS-CoV-2 transmission is the significant fraction of asymptomatic transmission. This may influence the effectiveness of the standard contact tracing procedure for quarantining potentially infected individuals. However, the effects of asymptomatic transmission on the epidemic threshold of epidemic spreading on networks have rarely been studied explicitly. Here we study the critical percolation transition for an arbitrary disease with a nonzero asymptomatic rate in a simple epidemic network model in the presence of a recursive contact tracing algorithm for instant quarantining. We find that, above a certain fraction of asymptomatic transmission, standard contact tracing loses its ability to suppress spreading below the epidemic threshold. However, we also find that recursive contact tracing opens a possibility to contain epidemics with a large fraction of asymptomatic or presymptomatic transmission. In particular, we calculate the required fraction of network nodes participating in the contact tracing for networks with arbitrary degree distributions and for varying recursion depths and discuss the influence of recursion depth and asymptomatic rate on the epidemic percolation phase transition. We anticipate recursive contact tracing to provide a basis for digital, app-based contact tracing tools that extend the efficiency of contact tracing to diseases with a large fraction of asymptomatic transmission.

Group size and modularity interact to shape the spread of infection and information through animal societies

Social interactions between animals can provide many benefits, including the ability to gain useful environmental information through social learning. However, these social contacts can also facilitate the transmission of infectious diseases through a population. Animals engaging in social interactions therefore face a trade-off between the potential informational benefits and the risk of acquiring disease. Theoretical models have suggested that modular social networks, associated with the formation of groups or sub-groups, can slow spread of infection by trapping it within particular groups. However, these social structures will not necessarily impact the spread of information in the same way if its transmission follows a "complex contagion", e.g. through individuals disproportionally copying the majority (conformist learning). Here we use simulation models to demonstrate that modular networks can promote the spread of information relative to the spread of infection, but only when the network is fragmented and group sizes are small. We show that the difference in transmission between information and disease is maximised for more well-connected social networks when the likelihood of transmission is intermediate. Our results have important implications for understanding the selective pressures operating on the social structure of animal societies, revealing that highly fragmented networks such as those formed in fission-fusion social groups and multilevel societies can be effective in modulating the infection-information trade-off for individuals within them.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00265-021-03102-4.

Balancing capacity and epidemic spread in the global airline network

The structure of complex networks has long been understood to play a role in transmission and spreading phenomena on a graph. Such networks form an important part of the structure of society, including transportation networks. As society fights to control the COVID-19 pandemic, an important question is how to choose the optimum balance between the full opening of transport networks and the control of epidemic spread. In this work we investigate the interplay between network dismantling and epidemic spread rate as a proxy for the imposition of travel restrictions to control disease spread. For network dismantling we focus on the weighted and unweighted forms of metrics that capture the topological and informational structure of the network. Our results indicate that there is benefit to a directed approach to imposing travel restrictions, but we identify that more detailed models of the transport network are necessary for definitive results.

A cluster-based model of COVID-19 transmission dynamics

Many countries have manifested COVID-19 trajectories where extended periods of constant and low daily case rate suddenly transition to epidemic waves of considerable severity with no correspondingly drastic relaxation in preventive measures. Such solutions are outside the scope of classical epidemiological models. Here, we construct a deterministic, discrete-time, discrete-population mathematical model called cluster seeding and transmission model, which can explain these non-classical phenomena. Our key hypothesis is that with partial preventive measures in place, viral transmission occurs primarily within small, closed groups of family members and friends, which we label as clusters. Inter-cluster transmission is infrequent compared with intra-cluster transmission but it is the key to determining the course of the epidemic. If inter-cluster transmission is low enough, we see stable plateau solutions. Above a cutoff level, however, such transmission can destabilize a plateau into a huge wave even though its contribution to the population-averaged spreading rate still remains small. We call this the cryptogenic instability. We also find that stochastic effects when case counts are very low may result in a temporary and artificial suppression of an instability; we call this the critical mass effect. Both these phenomena are absent from conventional infectious disease models and militate against the successful management of the epidemic.

The Impact of Contact Structure and Mixing on Control Measures and Disease-Induced Herd Immunity in Epidemic Models: A Mean-Field Model Perspective

The contact structure of a population plays an important role in transmission of infection. Many 'structured models' capture aspects of the contact pattern through an underlying network or a mixing matrix. An important observation in unstructured models of a disease that confers immunity is that once a fraction [Formula: see text] has been infected, the residual susceptible population can no longer sustain an epidemic. A recent observation of some structured models is that this threshold can be crossed with a smaller fraction of infected individuals, because the disease acts like a targeted vaccine, preferentially immunising higher-risk individuals who play a greater role in transmission. Therefore, a limited 'first wave' may leave behind a residual population that cannot support a second wave once interventions are lifted. In this paper, we set out to investigate this more systematically. While networks offer a flexible framework to model contact patterns explicitly, they suffer from several shortcomings: (i) high-fidelity network models require a large amount of data which can be difficult to harvest, and (ii) very few, if any, theoretical contact network models offer the flexibility to tune different contact network properties within the same framework. Therefore, we opt to systematically analyse a number of well-known mean-field models. These are computationally efficient and provide good flexibility in varying contact network properties such as heterogeneity in the number contacts, clustering and household structure or differentiating between local and global contacts. In particular, we consider the question of herd immunity under several scenarios. When modelling interventions as changes in transmission rates, we confirm that in networks with significant degree heterogeneity, the first wave of the epidemic confers herd immunity with significantly fewer infections than equivalent models with less or no degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect may become much more subtle. Indeed, modifying the structure disproportionately can shield highly connected nodes from becoming infected during the first wave and therefore make the second wave more substantial. We strengthen this finding by using an age-structured compartmental model parameterised with real data and comparing lockdown periods implemented either as a global scaling of the mixing matrix or age-specific structural changes. Overall, we find that results regarding (disease-induced) herd immunity levels are strongly dependent on the model, the duration of the lockdown and how the lockdown is implemented in the model.

Complex network analysis of the thermal lens signal: a Markov model approach

The paper reports a novel, to the best of my knowledge, complex network-based Markov model approach to analyze the thermal lens (TL) signal. The complex network is constructed by segmenting the experimental and fitted TL signals into three regions. Here, a new parameter, degree of fluctuation, is introduced to analyze the Markov transition probability matrix (M) and the increase of system enthalpy leading to increased Brownian motion. The spread of data about the diagonal elements of M distinguishes the experimental and fitted data and appears as an increased number of edges in the complex network. Thus, the system's network displays the transient heat flow giving information about the Brownian motion in the medium.

Small-world effects in a modified epidemiological model with mutation and permanent immune mechanism

Pandemic with mutation and permanent immune spreading in a small-world network described is studied by a modified SIR model, with consideration of mutation-immune mechanism. First, a novel mutation-immune model is proposed to modify the classical SIR model to simulate the transmission of mutable viruses that can be permanently immunized in small-world networks. Then, the influences of the size, coordination number and disorder parameter of the small-world network on the spread of the epidemic are analyzed in detail. Finally, the influences of mutation cycle and infection rate on epidemic transmission in small-world network are investigated further. The results show that the structure of the small-world network and the virus mutation cycle have an important impact on the spread of the epidemic. For viruses that can be permanently immunized, virus mutation is equivalent to making the immune cycle of human beings from infinite to finite. The dynamical behavior of the modified SIR epidemic model changes from an irregular, low-amplitude evolution at small disorder parameter to a spontaneous state of wide amplitude oscillations at large disorder parameter. Moreover, similar transition can also be found in increasing mutation cycle parameter. The maximum valid variation mutation decreases with the increase of disorder parameter and coordination number, but increase with respect to system size. In addition above, as the infection rate increases, the fraction of the infected increases and then decreases. As the mutation cycle increases, the time-average fraction of the infected and the infection rate corresponding to the maximum time-average fraction of the infected also decrease. As one conclusion, the results could give a deep understanding Pandemic with mutation and permanent immune spreading, from viewpoint of small-world network.

Social distancing mediated generalized model to predict epidemic spread of COVID-19

The extensive proliferation of recent coronavirus (COVID-19), all over the world, is the outcome of social interactions through massive transportation, gatherings and population growth. To disrupt the widespread of COVID-19, a mechanism for social distancing is indispensable. Also, to predict the effectiveness and quantity of social distancing for a particular social network, with a certain contagion, a generalized model is needed. In this manuscript, we propose a social distancing mediated generalized model to predict the pandemic spread of COVID-19. By considering growth rate as a temporal harmonic function damped with social distancing in generalized Richard model and by using the data of confirmed COVID-19 cases in China, USA and India, we find that, with time, the cumulative spread grows more rapidly due to weak social distancing as compared to the stronger social distancing, where it is explicitly decreasing. Furthermore, we predict the possible outcomes with various social distancing scenarios by considering highest growth rate as an initial state, and illustrate that the increase in social distancing tremendously decreases growth rate, even it tends to reach zero in lockdown regimes. Our findings not only provide epidemic growth scenarios as a function of social distancing but also provide a modified growth model to predict controlled information flow in any network.

Scale-free percolation in continuous space: quenched degree and clustering coefficient

Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuous-space version of scale-free percolation introduced in [14]. This is an undirected inhomogeneous random graph whose vertices are given by a Poisson point process in $\mathbb{R}^d$. Each vertex is equipped with a random weight, and the probability that two vertices are connected by an edge depends on their weights and on their distance. Under suitable conditions on the parameters of the model, we show that, for almost all realizations of the point process, the degree distributions of all the nodes of the graph follow a power law with the same tail at infinity. We also show that the averaged clustering coefficient of the graph is self-averaging. In particular, it is almost surely equal to the annealed clustering coefficient of one point, which is a strictly positive quantity.

Bistability and time crystals in long-ranged directed percolation

Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given by probabilistic cellular automata, which typically feature time-independent and short-ranged update rules. Here, we propose a simple cellular automaton with power-law interactions that gives rise to a bistable phase of long-ranged directed percolation whose long-time behaviour is not only dictated by the system dynamics, but also by the initial conditions. In the presence of a periodic modulation of the update rules, we find that the system responds with a period larger than that of the modulation for an exponentially (in system size) long time. This breaking of discrete time translation symmetry of the underlying dynamics is enabled by a self-correcting mechanism of the long-ranged interactions which compensates noise-induced imperfections. Our work thus provides a firm example of a classical discrete time crystal phase of matter and paves the way for the study of novel non-equilibrium phases in the unexplored field of driven probabilistic cellular automata.

Social interaction layers in complex networks for the dynamical epidemic modeling of COVID-19 in Brazil

We are currently living in a state of uncertainty due to the pandemic caused by the SARS-CoV-2 virus. There are several factors involved in the epidemic spreading, such as the individual characteristics of each city/country. The true shape of the epidemic dynamics is a large, complex system, considerably hard to predict. In this context, Complex networks are a great candidate for analyzing these systems due to their ability to tackle structural and dynamic properties. Therefore, this study presents a new approach to model the COVID-19 epidemic using a multi-layer complex network, where nodes represent people, edges are social contacts, and layers represent different social activities. The model improves the traditional SIR, and it is applied to study the Brazilian epidemic considering data up to 05/26/2020, and analyzing possible future actions and their consequences. The network is characterized using statistics of infection, death, and hospitalization time. To simulate isolation, social distancing, or precautionary measures, we remove layers and reduce social contact's intensity. Results show that even taking various optimistic assumptions, the current isolation levels in Brazil still may lead to a critical scenario for the healthcare system and a considerable death toll (average of 149,000). If all activities return to normal, the epidemic growth may suffer a steep increase, and the demand for ICU beds may surpass three times the country's capacity. This situation would surely lead to a catastrophic scenario, as our estimation reaches an average of 212,000 deaths, even considering that all cases are effectively treated. The increase of isolation (up to a lockdown) shows to be the best option to keep the situation under the healthcare system capacity, aside from ensuring a faster decrease of new case occurrences (months of difference), and a significantly smaller death toll (average of 87,000).

Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit

By means of extensive Monte Carlo simulation, we study extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearest neighbors for the simple cubic lattice. We find precise thresholds for 23 systems using a single-cluster growth algorithm. Site percolation on lattices with compact neighborhoods of connected sites can be mapped to problems of lattice percolation of extended objects of a given shape, such as disks and spheres, and the thresholds can be related to the continuum thresholds η_{c} for objects of those shapes. This mapping implies zp_{c}∼4η_{c}=4.51235 in two dimensions and zp_{c}∼8η_{c}=2.7351 in three dimensions for large z for circular and spherical neighborhoods, respectively, where z is the coordination number. Fitting our data for compact neighborhoods to the form p_{c}=c/(z+b) we find good agreement with this prediction, c=2^{d}η_{c}, with the constant b representing a finite-z correction term. We also examined results from other studies using this fitting formula. A good fit of the large but finite-z behavior can also be made using the formula p_{c}=1-exp(-2^{d}η_{c}/z), a generalization of a formula of Koza, Kondrat, and Suszcayński [J. Stat. Mech.: Theor. Exp. (2014) P110051742-546810.1088/1742-5468/2014/11/P11005]. We also study power-law fits which are applicable for the range of values of z considered here.

Incorporating social opinion in the evolution of an epidemic spread

The evolution of the COVID19 pandemic worldwide has shown that the most common and effective strategy to control it used worldwide involve imposing mobility constrains to the population. A determinant factor in the success of such policies is the cooperation of the population involved but this is something, at least, difficult to measure. In this manuscript, we propose a method to incorporate in epidemic models empirical data accounting for the society predisposition to cooperate with the mobility restriction policies.

A Markovian random walk model of epidemic spreading

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 the same node, there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations, we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.

"Stay nearby or get checked": A Covid-19 control strategy

This paper repurposes the classic insight from network theory that long-distance connections drive disease propagation into a strategy for controlling a second wave of Covid-19. We simulate a scenario in which a lockdown is first imposed on a population and then partly lifted while long-range transmission is kept at a minimum. Simulated spreading patterns resemble contemporary distributions of Covid- 19 across EU member states, German and Italian regions, and through New York City, providing some model validation. Results suggest that our proposed strategy may significantly reduce peak infection. We also find that post-lockdown flare-ups remain local longer, aiding geographical containment. These results suggest a tailored policy in which individuals who frequently travel to places where they interact with many people are offered greater protection, tracked more closely, and are regularly tested. This policy can be communicated to the general public as a simple and reasonable principle: Stay nearby or get checked.

Network inference from population-level observation of epidemics

Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e., the number of infected individuals at a finite set of discrete times of a single realisation of the epidemic), the only information likely to be available in real world settings. To tackle this, epidemics on networks are approximated by a Birth-and-Death process which keeps track of the number of infected nodes at population level. The rates of this surrogate model encode both the structure of the underlying network and disease dynamics. We use extensive simulations over Regular, Erdős–Rényi and Barabási–Albert networks to build network class-specific priors for these rates. We then use Bayesian model selection to recover the most likely underlying network class, based only on a single realisation of the epidemic. We show that the proposed methodology yields good results on both synthetic and real-world networks.

Identifying epidemic spreading dynamics of COVID-19 by pseudocoevolutionary simulated annealing optimizers

At the end of 2019, a new coronavirus (COVID-19) epidemic has triggered global public health concern. Here, a model integrating the daily intercity migration network, which constructed from real-world migration records and the Susceptible–Exposed–Infected–Removed model, is utilized to predict the epidemic spreading of the COVID-19 in more than 300 cities in China. However, the model has more than 1800 unknown parameters, which is a challenging task to estimate all unknown parameters from historical data within a reasonable computation time. In this article, we proposed a pseudocoevolutionary simulated annealing (SA) algorithm for identifying these unknown parameters. The large volume of unknown parameters of this model is optimized through three procedures co-adapted SA-based optimization processes, respectively. Our results confirm that the proposed method is both efficient and robust. Then, we use the identified model to predict the trends of the epidemic spreading of the COVID-19 in these cities. We find that the number of infections in most cities in China has reached their peak from February 29, 2020, to March 15, 2020. For most cities outside Hubei province, the total number of infected individuals would be less than 100, while for most cities in Hubei province (exclude Wuhan), the total number of infected individuals would be less than 3000.

A data-driven network model for the emerging COVID-19 epidemics in Wuhan, Toronto and Italy

The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modeling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the reported data for the COVID-19 epidemic in Wuhan (China), Toronto (Canada), and the Italian Republic using a Markov Chain Monte Carlo (MCMC) optimization algorithm. Our model fits all three regions well with narrow confidence intervals and could be adapted to simulate other megacities or regions. The model projections on the role of containment strategies can help inform public health authorities to plan control measures.

Self-isolation or borders closing: What prevents the spread of the epidemic better?

Pandemic propagation of COVID-19 motivated us to discuss the impact of the human network clustering on epidemic spreading. Today, there are two clustering mechanisms which prevent of uncontrolled disease propagation in a connected network: an "internal" clustering, which mimics self-isolation (SI) in local naturally arranged communities, and an "external" clustering, which looks like a sharp frontiers closing (FC) between cities and countries, and which does not care about the natural connections of network agents. SI networks are "evolutionarily grown" under the condition of maximization of small cliques in the entire network, while FC networks are instantly created. Running the standard SIR model on clustered SI and FC networks, we demonstrate that the evolutionary grown clustered network prevents the spread of an epidemic better than the instantly clustered network with similar parameters. We find that SI networks have the scale-free property for the degree distribution P(k)∼k^{η}, with a small critical exponent -2<η<-1. We argue that the scale-free behavior emerges as a result of the randomness in the initial degree distributions.