We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents. Broken links are either permanently removed or reconnected with the rest of the population. Thus, the network coevolves with the population as the infection progresses. We show that a moderate reconnection frequency is enough to completely suppress the infection. A partial, rather weak isolation of infected agents suffices to eliminate the endemic state.
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using macroscopic parameters that do not accurately represent person-to-person variability. To address this issue, we present a dynamic network model that provides a straightforward way to incorporate both disease transmission dynamics at the individual scale as well as the full spatiotemporal history of infection at the population scale. We find that disease spreads …
We introduce an epidemic spreading model on a network using concepts from percolation theory. The model is motivated by discussing the standard SIR model, with extensions to describe effects of lockdowns within a population. The underlying ideas and behavior of the lattice model, implemented using the same lockdown scheme as for the SIR scheme, are discussed in detail and illustrated with extensive simulations. A comparison between both models is presented for the case of COVID-19 data from the USA. Both fits to the empirical data are very good, but some differences emerge between the two appr…
We propose to use the mean time between infections (MTBI) metric as obtained from a recently introduced non-homogeneous Markov stochastic model. Different types of parameter calibration are performed. We estimate the MTBI using data from different time windows and from the whole stage history and compare the results. In order to detect waves and stages in the input data, a preprocessing filtering technique is applied. The results of applying this indicator to the COVID-19 reported data of infections from Argentina, Germany and the United States are shown. We find that the MTBI behaves similarl…
Northwestern University（西北大学）；NSF-Simons National Institute for Theory and Mathematics in Biology（NSF-西蒙斯生物理论与数学国家研究所）；Northwestern Institute on Complex Systems, Northwestern University（西北大学复杂系统研究所）；Department of Engineering Sciences and Applied Mathematics, Northwestern University（西北大学工程科学与应用数学系）
By the end of July 2020, the COVID-19 pandemic had infected more than seventeen million people and had spread to almost all countries worldwide. In response, many countries all over the world have used different methods to reduce the infection rate, such as including case isolation, the closure of schools and universities, banning public events, and mostly forcing social distancing, including local and national lockdowns. We use a Monte-Carlo (MC) based algorithm to predict the virus infection rate for different population densities using the most recent epidemic data in our work. We test the …
We investigate spreading and recovery of disease in a square lattice, and in particular, emphasize the role of the initial distribution of infected patches in the network, on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, infected core patches (ICP), infected peripheral patches (IPP) and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically…
Optimal Allocation of Resources for Suppressing Epidemic Spreading on Networks
有效配置有限的医疗资源是控制网络流行病传播的关键。基于易感-感染-易感模型，在每个节点的治愈率与其医疗资源正相关的条件下，解决了如何最好地分配有限的资源以使患病率最小的优化问题.利用猝灭平均场理论和异质平均场（HMF）理论，证明了当每个节点的治愈率与其度成正比时，传染病的爆发将得到最大程度的抑制，在此条件下，有效感染率$λ$存在一个最大阈值$λ_c^{opt}=1/\left\langle k \right\rangle$，其中$\left\langle k \right\rangle$为底层网络的平均度.对于弱感染区域（$λ\gtrsimλ_c^{opt}$），本文将摄动理论与拉格朗日乘子法（LMM）相结合，导出了治愈率最优分配的解析表达式，并得到了相应的最小患病率。对于一般感染域（$λ>λ_c^{opt}$），利用HMF理论和LMM将高维优化问题转化为低维非线性方程组的数值求解。与直觉相反，在强感染区域，低度节点应比高度节点分配更多的医疗资源，以最大限度地降低患病率。最后，我们使用模拟退火来验证理论结果。
State government-mandated social distancing measures have helped to slow down the growth of the COVID-19 pandemic in the United States. Current predictive models of the development of COVID-19, especially after mitigation efforts, are largely based on extrapolating the data from other countries. Since most states enforced stay-at-home orders towards the end of March, their effect should be reflected in the death and infection counts at the end of April. Using the data available until April 25th, we investigate the change in the infection rate due to the mitigation efforts, and project death an…
Since the outbreak of COVID-19, many data analyses have been done. Some of them are based on the classical epidemiological approach that assumes an exponential growth, but a few studies report that a power-law scaling may provide a better fit to the currently available data. Hereby, we examine the data in China (01/20/2020--02/24/2020), and indeed find that the growth closely follows a power-law kinetics over a significantly wide time period. The exponents are $2.48(20)$, $2.21(6)$ and $4.26(12)$ for the number of confirmed infections, deaths and cured cases, respectively, indicating an underl…
Infection propagator approach to compute epidemic thresholds on temporal networks: impact of immunity and of limited temporal resolution
一个传播过程的流行病阈值表明了发生广泛传播制度的条件，从而代表了网络对流行病的脆弱性的预测。这种阈值取决于疾病的自然史和网络的接触模式及其时间变化。基于（Valdano et al. PRX 2015）中引入的易感-感染-易感模型的理论框架，我们在这里制定了一种感染传播因子方法来计算流行病阈值，该方法考虑了关于每次接触的不同感染力，免疫力的存在以及时间网络的有限时间分辨率的更现实的影响。我们将这种方法应用到两个时间网络模型和一个经验数据集的学校接触。我们发现，永久或暂时的免疫不影响估计的流行阈值，通过感染传播者的方法。与数值计算结果的比较表明，分析预测的良好协议。聚集的时间网络迅速恶化的预测，除了缓慢的疾病，一旦异质性的链接被保留。权重拓扑相关性被认为是关键因素，以提高预测的准确性。
To evaluate the effectiveness of the containment on the epidemic spreading of the new Coronavirus disease 2019, we carry on an analysis of the time evolution of the infection in a selected number of different Countries, by considering well-known macroscopic growth laws, the Gompertz law, and the logistic law. We also propose here a generalization of Gompertz law. Our data analysis permits an evaluation of the maximum number of infected individuals. The daily data must be compared with the obtained fits, to verify if the spreading is under control. From our analysis it appears that the spreadin…
We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped to a branching process spreading in a random time-sensitive environment, determined by the dynamics of the underlying primary infection. When both epidemics follow the Susceptible-Infective-Recovered model, we show that in order to survive, it is necessary for the secondary infection to evolve on a timescale that is closely matched to that of the primary infe…
We study Covid-19 spreading dynamics underlying 84 curves of daily Covid-19 infection rates pertaining to 84 districts belonging to the largest seven cities in Taiwan during her pristine surge period. Our computational developments begin with selecting and extracting 18 features from each smoothed district-specific curve. This step of computing effort allows unstructured data to be converted into structured data, with which we then demonstrate asymmetric growth and decline dynamics among all involved curves. Specifically, based on Theoretical Information measurements of conditional entropy and…
In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we assume to be related to the fraction of infected neighbours, as introduced by Bagnoli et al., PRE 76:061904 (2007). We re-derive previous results using a self-organized method, that automatically gives the percolation threshold in just one simulation. We then extend the model to multiplex networks considering that people get infected by contacts in real life but…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $R_0$ which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an a…
During pandemic events, strategies such as social distancing can be fundamental to curb viral spreading. Such actions can reduce the number of simultaneous infections and mitigate the disease spreading, which is relevant to the risk of a healthcare system collapse. Although these strategies can be suggested, their actual implementation may depend on the population perception of the disease risk. The current COVID-19 crisis, for instance, is showing that some individuals are much more prone than others to remain isolated, avoiding unnecessary contacts. With this motivation, we propose an epidem…
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…
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…
The recent outbreak of a novel coronavirus and its rapid spread underlines the importance of understanding human mobility. Enclosed spaces, such as public transport vehicles (e.g. buses and trains), offer a suitable environment for infections to spread widely and quickly. Investigating the movement patterns and the physical encounters of individuals on public transit systems is thus critical to understand the drivers of infectious disease outbreaks. For instance previous work has explored the impact of recurring patterns inherent in human mobility on disease spread, but has not considered othe…
The COVID-19 pandemic has posed significant challenges in modeling its complex epidemic transmissions, infection and contagion, which are very different from known epidemics. The challenges in quantifying COVID-19 complexities include effectively modeling its process and data uncertainties. The uncertainties are embedded in implicit and high-proportional undocumented infections, asymptomatic contagion, social reinforcement of infections, and various quality issues in the reported data. These uncertainties become even more apparent in the first two months of the COVID-19 pandemic, when the rele…
The COVID-19 infection cases have surged globally, causing devastations to both the society and economy. A key factor contributing to the sustained spreading is the presence of a large number of asymptomatic or hidden spreaders, who mix among the susceptible population without being detected or quarantined. Here we propose an effective non-pharmacological intervention method of detecting the asymptomatic spreaders in contact-tracing networks, and validated it on the empirical COVID-19 spreading network in Singapore. We find that using pure physical spreading equations, the hidden spreaders of …
For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. We present an extended model for disease spread based on combining an SIR model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. The model shows interesting nonequilibrium phase separation associated with a reduction of the number of infections, and …
We study the interaction between epidemic spreading and a vaccination process. We assume that, similar to the disease spreading, also the vaccination process occurs through direct contact, i.e., it follows the standard susceptible-infected-susceptible (SIS) dynamics. The two competing processes are asymmetrically coupled as vaccinated nodes can directly become infected at a reduced rate with respect to susceptible ones. We study analytically the model in the framework of mean-field theory finding a rich phase-diagram. When vaccination provides little protection toward infection, two continuous…
A key characteristic of the spread of infectious diseases is their ability to use efficient transmission paths within contact graphs. This enables the pathogen to maximise infection rates and spread within a target population. In this work, we devise techniques to localise infections and decrease infection rates based on a principled analysis of disease transmission paths within human-contact networks (proximity graphs). Experimental results of disease spreading shows that that at low visibility rates contact tracing slows disease spreading. However to stop disease spreading, contact tracing r…
How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the Susceptible-Infected-Recovered (SIR) model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability $ω$- and then get infected -with probability …
Various coarse-grained models have been proposed to study the spreading dynamics in the network. A microscopic theory is needed to connect the spreading dynamics with the individual behaviors. In this letter, we unify the description of different spreading dynamics on complex networks by decomposing the microscopic dynamics into two basic processes, the aging process and the contact process. A microscopic dynamical equation is derived to describe the dynamics of individual nodes on the network. The hierarchy of a duration coarse-grained (DCG) approach is obtained to study duration-dependent pr…
Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real scenarios, the distribution of these times are not necessarily exponential. To overcome this limitation, we first introduce a generalized susceptible-infected-susceptible (SIS) spreading model that allows transmission and recovery times to follow phase-type distributions. In this context, we derive a lower bound on the exponential decay rate towards the infection-fr…
In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-09/03/2020$. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-(confirmed) infected-recovered-deaths model indicates that the kinetic parameter that des…
In this paper we study the spatial spread of the COVID-19 infection in Lebanon. We inspect the spreading of the daily new infections across the 26 administrative districts of the country, and implement Moran's $I$ statistics in order to analyze the tempo-spatial clustering of the infection in relation to various variables parameterized by adjacency, proximity, population, population density, poverty rate and poverty density, and we find out that except for the poverty rate, the spread of the infection is clustered and associated to those parameters with varying magnitude for the time span betw…
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of its time in localized environments and has easily identifiable mobility patterns --such as workplaces, university campuses or schools-- it is of critical importance to identify the factors controlling the rate of disease spread. Here we present a discrete-time, metapopulation-based model to describe the transmission of SIS-like diseases that take place in co…
Corona Virus Disease 2019 (COVID-19), due to its extremely high infectivity, has been spreading rapidly around the world and bringing huge influence to socioeconomic development as well as people's daily life. Taking for example the virus transmission that may occur after college students return to school, we analyze the quantitative influence of the key factors on the virus spread, including crowd density and self-protection. One Campus Virus Infection and Control Simulation model (CVICS) of the novel coronavirus is proposed in this paper, fully considering the characteristics of repeated con…
