The ongoing SARS-CoV-2 pandemic has been holding the world hostage for more than a year now. Mobility is key to viral spreading and its restriction is the main non-pharmaceutical interventions to fight the virus expansion. Previous works have shown a connection between the structural organization of cities and the movement patterns of their residents. This puts urban centers in the focus of epidemic surveillance and interventions. Here we show that the organization of urban flows has a tremendous impact on disease spreading and on the amenability of different mitigation strategies. By studying anonymous and aggregated intra-urban flows in a variety of cities in the United States and other countries, and a combination of empirical analysis and analytical methods, we demonstrate that the response of cities to epidemic spreading can be roughly classified in two major types according to the overall organization of those flows. Hierarchical cities, where flows are concentrated primarily between mobility hotspots, are particularly vulnerable to the rapid spread of epidemics. Nevertheless, mobility restrictions in such types of cities are very effective in mitigating the spread of a virus. Conversely, in sprawled cities which present many centers of activity, the spread of an epidemic is much slower, but the response to mobility restrictions is much weaker and less effective. Investing resources on early monitoring and prompt ad-hoc interventions in more vulnerable cities may prove helpful in containing and reducing the impact of future pandemics.
In this study, we develop the mathematical model to understand the coupling between the spreading dynamics of infectious diseases and the mobility dynamics through urban transportation systems. We first describe the mobility dynamics of the urban population as the process of leaving from home, traveling to and from the activity locations, and engaging in activities. We then embed the susceptible-exposed-infectious-recovered (SEIR) process over the mobility dynamics and develops the spatial SEIR model with travel contagion (Trans-SEIR), which explicitly accounts for contagions both during trave…
We combine a pedestrian dynamics model with a contact tracing method to simulate the initial spreading of a highly infectious airborne disease in a confined environment. We focus on a medium size population (up to 1000 people) with a small number of infectious people (1 or 2) and the rest of the people is divided between immune and susceptible. We adopt a space-continuous model that represents pedestrian dynamics by the forces acting on them, i.e. a microscopic force-based model. Once discretized, the model results in a high-dimensional system of second order ordinary differential equations. B…
Urban areas with larger and more connected populations offer an auspicious environment for contagion processes such as the spread of pathogens. Empirical evidence reveals a systematic increase in the rates of certain sexually transmitted diseases (STDs) with larger urban population size. However, the main drivers of these systemic infection patterns are still not well understood, and rampant urbanization rates worldwide makes it critical to advance our understanding on this front. Using confirmed-cases data for three STDs in US metropolitan areas, we investigate the scaling patterns of infecti…
We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all thr…
Epidemic modeling in complex networks has become one of the latest topics in recent times. The Susceptible-Infectious-Recovered (SIR) model and its variants are often used for epidemic modeling. One important issue in epidemic modeling is the determination of the spreading ability of the nodes in the network. Thus, for example, can be detected in the early stages. In this study, we developed a centrality measure called Lexical Sorting Centrality (LSC) that distinguishes the spreading ability of the nodes. Using other centrality measures calculated for the nodes, LSC sorts the nodes in a way si…
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…
Infectious diseases are a significant threat to human society which was over sighted before the incidence of COVID-19, although according to the report of the World Health Organisation (WHO) about 4.2 million people die annually due to infectious disease. Due to recent COVID-19 pandemic, more than 2 million people died during 2020 and 96.2 million people got affected by this devastating disease. Recent research shows that applying individual interactions and movements data could help managing the pandemic though modelling the spread of infectious diseases on social contact networks. Infectious…
We investigate what structural aspects of a collection of twelve empirical temporal networks of human contacts are important to disease spreading. We scan the entire parameter spaces of the two canonical models of infectious disease epidemiology -- the Susceptible-Infectious-Susceptible (SIS) and Susceptible-Infectious-Removed (SIR) models. The results from these simulations are compared to reference data where we eliminate structures in the interevent intervals, the time to the first contact in the data, or the time from the last contact to the end of the sampling. The picture we find is that…
Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. In order to study the interplay between small-scale commuting flows and long-range airline traffic in shaping the spatio-temporal pattern of a global epidemic we i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms; ii) integrate in a worldwide structured me…
We investigate a fermionic susceptible-infected-susceptible model with mobility of infected individuals on uncorrelated scale-free networks with power-law degree distributions $P (k) \sim k^{-γ}$ of exponents $2<γ<3$. Two diffusive processes with diffusion rate $D$ of an infected vertex are considered. In the \textit{standard diffusion}, one of the nearest-neighbors is chosen with equal chance while in the \textit{biased diffusion} this choice happens with probability proportional to the neighbor's degree. A non-monotonic dependence of the epidemic threshold on $D$ with an optimum diffusion ra…
Interaction patterns among individuals play vital roles in spreading infectious diseases. Understanding these patterns and integrating their impact in modeling diffusion dynamics of infectious diseases are important for epidemiological studies. Current network-based diffusion models assume that diseases transmit through interactions where both infected and susceptible individuals are co-located at the same time. However, there are several infectious diseases that can transmit when a susceptible individual visits a location after an infected individual has left. Recently, we introduced a diffus…
We are facing a common serious issue, infectious diseases, and trying to suppress the spreading of infection. We need less contact with each other to decrease the chance of infection, but this means loss of economic activity, as well. This tradeoff is inevitable in our society, because we still need direct communication and commuting, so far. The focus of our paper is the structure of society, on which we have direct contacts. We study on spreading process with artificial sosiety model, where each agent has daily cycle and go office and back home, every day. At the same time, infection spreads…
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in…
With the exponential growth in the world population and the constant increase in human mobility, the danger of outbreaks of epidemics is rising. Especially in high density urban areas such as public transport and transfer points, where people come in close proximity of each other, we observe a dramatic increase in the transmission of airborne viruses and related pathogens. It is essential to have a good understanding of the `transmission highways' in such areas, in order to prevent or to predict the spreading of infectious diseases. The approach we take is to combine as much information as is …
Non-pharmaceutical measures such as social distancing, can play an important role to control an epidemic in the absence of vaccinations. In this paper, we study the impact of social distancing on epidemics for which it is executable. We use a mathematical model combining human mobility and disease spreading. For the mobility dynamics, we design an agent based model consisting of pedestrian dynamics with a novel type of force to resemble social distancing in crowded sites. For the spreading dynamics, we consider the compartmental SIE dynamics plus an indirect transmission with the footprints of…
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 paper, we study into the impact of the preference of an individual for public transport on the spread of infectious disease, through a quantity known as the public mobility. Our theoretical and numerical results based on a constructed model reveal that if the average public mobility of the agents is fixed, an increase in the diversity of the agents' public mobility reduces the epidemic threshold, beyond which an enhancement in the rate of infection is observed. Our findings provide an approach to improve the resistance of a society against infectious disease, while preserving the utili…
The study proposes a modeling framework for investigating the disease dynamics with adaptive human behavior during a disease outbreak, considering the impacts of both local observations and global information. One important application scenario is that commuters may adjust their behavior upon observing the symptoms and countermeasures from their physical contacts during travel, thus altering the trajectories of a disease outbreak. We introduce the heterogeneous mean-field (HMF) approach in a multiplex network setting to jointly model the spreading dynamics of the infectious disease in the cont…
In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian and economic impact, it is important to develop models to estimate the probability of a worldwide pandemic. In this paper, we propose a model of disease spreading in a structural modular complex network (having communities) and study how the number of bridge nodes $n$ that connect communities affects disease spread. We find that our model can be described at…
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Science and Technology of China（中国科学技术大学）
Infectious diseases usually originate from a specific location within a city. Due to the heterogenous distribution of population and public facilities, and the structural heterogeneity of human mobility network embedded in space, infectious diseases break out at different locations would cause different transmission risk and control difficulty. This study aims to investigate the impact of initial outbreak locations on the risk of spatiotemporal transmission and reveal the driving force behind high-risk outbreak locations. First, integrating mobile phone location data, we built a SLIR (suscepti…
Currently, the global situation of COVID-19 is aggravating, pressingly calling for efficient control and prevention measures. Understanding spreading pattern of COVID-19 has been widely recognized as a vital step for implementing non-pharmaceutical measures. Previous studies investigated such an issue in large-scale (e.g., inter-country or inter-state) scenarios while urban spreading pattern still remains an open issue. Here, we fill this gap by leveraging the trajectory data of 197,808 smartphone users (including 17,808 anonymous confirmed cases) in 9 cities in China. We find a universal spre…
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…
There has been much recent interest in screening populations for an infectious disease. Here, we present a stochastic-control model, wherein the optimum screening policy is provably difficult to find, but wherein Thompson sampling has provably optimal performance guarantees in the form of Bayesian regret. Thompson sampling seems applicable especially to diseases, for which we do not understand the dynamics well, such as to the super-spreading COVID-19.
We investigate the spreading of information through Twitter messaging related to the spread of Ebola in western Africa using epidemic based dynamic models. Diffusive spreading leads to NLPDE models and fixed point analysis yields systems of NLODE models. When tweets are mapped as connected nodes in a graph and are treated as a time sequenced Markov chain, TSMC, then by the Kurtz theorem these specific paths can be identified as being near solutions to systems of ordinary differential equations that in the large N limit retain many of the features of the original Tweet dynamics. Constraints on …
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.
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 $ρ\approx F(K)(\ln λ- \ln λ_{c})$.
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 …
The spreading of an infectious disease can trigger human behavior responses to the disease, which in turn plays a crucial role on the spreading of epidemic. In this study, to illustrate the impacts of the human behavioral responses, a new class of individuals, $S^F$, is introduced to the classical susceptible-infected-recovered ($SIR$) model. In the model, $S^F$ state represents that susceptible individuals who take self-initiate protective measures to lower the probability of being infected, and a susceptible individual may go to $S^F$ state with a response rate when contacting an infectious …
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…
The COVID-19 pandemic has evolved over time through multiple spatial and temporal dynamics. The varying extent of interactions among different geographical areas can result to a complex pattern of spreading so that influences between these areas can be hard to discern. Here, we use cross-correlation analysis to detect synchronous evolution and potential inter-influences in the time evolution of new COVID-19 cases at the county level in the USA. Our analysis identified two main time periods with distinguishable features in the behavior of correlations. In the first phase, there were few strong …
The current outbreak of the coronavirus disease 2019 (COVID-19) is an unprecedented example of how fast an infectious disease can spread around the globe (especially in urban areas) and the enormous impact it causes on public health and socio-economic activities. Despite the recent surge of investigations about different aspects of the COVID-19 pandemic, we still know little about the effects of city size on the propagation of this disease in urban areas. Here we investigate how the number of cases and deaths by COVID-19 scale with the population of Brazilian cities. Our results indicate small…
The mitigation of an infectious disease spreading has recently gained considerable attention from the research community. It may be obtained by adopting sanitary measurements social rules, together with an extensive vaccination campaign. Vaccination is currently the primary way for mitigating the Coronavirus Disease (COVID-19) outbreak without severe lockdown. Its effectiveness also depends on the number and timeliness of administrations and thus demands strict prioritization criteria. Almost all countries have prioritized similar classes of exposed workers obtaining to maximize the survival o…
Improved mobility not only contributes to more intensive human activities but also facilitates the spread of communicable disease, thus constituting a major threat to billions of urban commuters. In this study, we present a multi-city investigation of communicable diseases percolating among metro travelers. We use smart card data from three megacities in China to construct individual-level contact networks, based on which the spread of disease is modeled and studied. We observe that, though differing in urban forms, network layouts, and mobility patterns, the metro systems of the three cities …
The emergence due to the outbreak of the COVID-19 disease, caused by the SARS-CoV-2 virus, suddenly erupted at the beginning of 2020 in China and soon spread worldwide. This has caused an outstanding increase on research about the virus itself and, more in general, epidemics in many scientific fields. In this work we focus on the dynamics of the epidemic spreading and how it can be affected by the individual variability in compliance with social norms, i.e., in the adoption of health and hygienic social norms by population's members.
The dense social contact networks and high mobility in congested urban areas facilitate the rapid transmission of infectious diseases. Typical mechanistic epidemiological models are either based on uniform mixing with ad-hoc contact processes or need real-time or archived population mobility data to simulate the social networks. However, the rapid and global transmission of the novel coronavirus (SARS-CoV-2) has led to unprecedented lockdowns at global and regional scales, leaving the archived datasets to limited use. While it is often hypothesized that population density is a significant driv…
We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a …
Only a fast and global transformation towards decarbonization and sustainability can keep the Earth in a civilization-friendly state. As hotspots for (green) innovation and experimentation, cities could play an important role in this transition. They are also known to profit from each other's ideas, with policy and technology innovations spreading to other cities. In this way, cities can be conceptualized as nodes in a globe-spanning learning network. The dynamics of this process are important for society's response to climate change and other challenges, but remain poorly understood on a macr…
Urbanization drives the epidemiology of infectious diseases to many threats and new challenges. In this research, we study the interplay between human mobility and dengue outbreaks in the complex urban environment of the city-state of Singapore. We integrate both stylized and mobile phone data-driven mobility patterns in an agent-based transmission model in which humans and mosquitoes are represented as agents that go through the epidemic states of dengue. We monitor with numerical simulations the system-level response to the epidemic by comparing our results with the observed cases reported d…
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…
The symptoms of many infectious diseases influence their host to withdraw from social activity limiting their own potential to spread. Successful transmission therefore requires the onset of infectiousness to coincide with a time when its host is socially active. Since social activity and infectiousness are both temporal phenomena, we hypothesize that diseases are most pervasive when these two processes are synchronized. We consider disease dynamics that incorporate a behavioral response that effectively shortens the infectious period of the disease. We apply this model to data collected from …
Many real networks are embedded in a metric space: the interactions among individuals depend on their spatial distances and usually take place among their nearest neighbors. In this paper, we introduce a modified susceptible-infected-susceptible (SIS) model to study geographical effects on the spread of diseases by assuming that the probability of a healthy individual infected by an infectious one is inversely proportional to the Euclidean distance between them. It is found that geography plays a more important role than hubs in disease spreading: the more geographically constrained the networ…
Initially emerged in the Chinese city Wuhan and subsequently spread almost worldwide causing a pandemic, the SARS-CoV-2 virus follows reasonably well the SIR (Susceptible-Infectious-Recovered) epidemic model on contact networks in the Chinese case. In this paper, we investigate the prediction accuracy of the SIR model on networks also for Italy. Specifically, the Italian regions are a metapopulation represented by network nodes and the network links are the interactions between those regions. Then, we modify the network-based SIR model in order to take into account the different lockdown measu…
This paper presents a discrete time probabilistic dynamic for simulating a contact-based epidemic spreading based on discrete time Markov chain process, in particular the attention is addressed to the susceptible-infectious-removed (SIR) model and the phase diagram of such model will be presented. Then, this report presents the set of equations that represent the optimal control strategies, by the means of Pontryagin's maximum principle, in two different cases a vaccination policy and a combined vaccination-hospitalization policy and show a numerical simulation, with the standard forward-backw…
The pattern formation and spatial spread of infectious populations are investigated using a kernel-based Susceptible-Infectious-Recovered (SIR) model applicable across a wide range of basic reproduction numbers $R_o$. The focus is on the role of geographic spreaders defined here as a portion of the infected population ($ϕ$) experiencing high mobility between identical communities. The spatial organization of the infected population and invasive front speeds ($c_{max}$) are determined when the infections are randomly initiated in space within multiple communities. For small but finite $ϕ$, scal…
The spatial propagation of many livestock infectious diseases critically depends on the animal movements among premises; so the knowledge of movement data may help us to detect, manage and control an outbreak. The identification of robust spreading features of the system is however hampered by the temporal dimension characterizing population interactions through movements. Traditional centrality measures do not provide relevant information as results strongly fluctuate in time and outbreak properties heavily depend on geotemporal initial conditions. By focusing on the case study of cattle disp…
Background: Animal trade plays an important role for the spread of infectious diseases in livestock populations. As a case study, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The central question is how infectious diseases can potentially spread within the system of trade contacts. We address this question by analyzing the underlying network of animal movements. Methodology/Findings: The considered pig trade dataset spans several years and is analyzed with respect to its potential to spread infectious diseases. Focusing on measurements of…
Population inhomogeneity, in the variation of the individual social contact networks and the individual infectious-recovery rates, renders the dynamics of infectious disease spreading uncertain. As a consequence the overlaying economical production network with its proper collaboration components is to extent impacted unpredictably. Our model proposes a `vector logistic' dynamical approach to SIS dynamics in a social contact network interacting with its economic capacity network. The probabilistic interpretation of the graph state in the vector logistic description provides a method to assess …
Infectious diseases that incorporate pre-symptomatic transmission are challenging to monitor, model, predict and contain. We address this scenario by studying a variant of a stochastic susceptible-exposed-infected-recovered model on arbitrary network instances using an analytical framework based on the method of dynamic message-passing. This framework provides a good estimate of the probabilistic evolution of the spread on both static and contact networks, offering a significantly improved accuracy with respect to individual-based mean-field approaches while requiring a much lower computationa…
Vaccination is an effective way to prevent and control the occurrence and epidemic of infectious diseases. However, many factors influence whether the residents decide to get vaccinated or not, such as the efficacy and side effects while individuals hope to obtain immunity through vaccination. In this paper, the public attitude toward vaccination is investigated, especially how it is influenced by the public estimation of vaccines efficacy and reliance on their neighbors' vaccination behavior. We find that improving people's trust in the vaccination greatly benefits increasing the vaccination …
A simple contagion process describes spreading of traffic jams in urban networks
University of New South Wales (UNSW)（新南威尔士大学）；Monash University（莫纳什大学）；K.N. Toosi University of Technology（K.N.托伊西理工大学）；CSIRO（澳大利亚联邦科学与工业研究组织）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of California, Berkeley（加利福尼亚大学伯克利分校）
The spatial structure of modern cities exhibits highly diverse patterns and keeps evolving under numerous constraints. Two key dimensions have recently achieved prominence in characterizing this diversity: heterogeneity and spreading. However, modern settlements do not fill the entire heterogeneity--spreading space. Yet, the dynamic mechanisms leading to emergence of the observed layouts are unclear. Here, we assess the heterogeneity and spreading of population density in 25 Australian and 175 US cities. We observe that larger cities tend to form a cluster with a low degree of spreading and a …
This paper focuses on studying and understanding of stochastic dynamics in population composition when the population is subject to rumor spreading. We undertake the study by first developing an individual Susceptible-Exposed-Infectious-Removed (iSEIR) model, an extension of the SEIR model, for summarizing rumor-spreading behaviors of interacting groups in the population. With this iSEIR model, the interacting groups may be regarded as nodes in a multiplex network. Then various properties of the dynamic behaviors of the interacting groups in rumor spreading can be drawn from samples of the mul…
