The challenges presented by the COVID-19 epidemic have created a renewed interest in the development of new methods to combat infectious 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 are largely unknown. Here we study the critical percolation transition 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 test and illustrate our theoretical results using numerical simulations on infection trees and networks. 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.
We study the class of SIS epidemics on temporal networks and propose a new activity-driven and adaptive epidemic model that captures the impact of asymptomatic and infectious individuals in the network. In the proposed model, referred to as the A-SIYS epidemic, each node can be in three possible states: susceptible, infected without symptoms or asymptomatic and infected with symptoms or symptomatic. Both asymptomatic and symptomatic individuals are infectious. We show that the proposed A-SIYS epidemic captures several well-established epidemic models as special cases and obtain sufficient cond…
We investigate phase transitions associated with three control methods for epidemics on small world networks. Motivated by the behavior of SARS-CoV-2, we construct a theoretical SIR model of a virus that exhibits presymptomatic, asymptomatic, and symptomatic stages in two possible pathways. Using agent-based simulations on small world networks, we observe phase transitions for epidemic spread related to: 1) Global social distancing with a fixed probability of adherence. 2) Individually initiated social isolation when a threshold number of contacts are infected. 3) Viral shedding rate. The prim…
The detection and management of diseases become quite complicated when pathogens contain asymptomatic phenotypes amongst their ranks, as evident during the recent COVID-19 pandemic. Spreading of diseases has been studied extensively under the paradigm of Susceptible - Infected - Recovered - Deceased (SIRD) dynamics. Various game-theoretic approaches have also addressed disease spread, many of which consider S, I, R, and D as strategies rather than as states. Remarkably, most studies from the above approaches do not account for the distinction between the symptomatic or asymptomatic aspect of t…
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 …
Studies on how to model the interplay between diseases and behavioral responses (so-called coupled disease-behavior interaction) have attracted increasing attention. Owing to the lack of obvious clinical evidence of diseases, or the incomplete information related to the disease, the risks of infection cannot be perceived and may lead to inappropriate behavioral responses. Therefore, how to quantitatively analyze the impacts of asymptomatic infection on the interplay between diseases and behavioral responses is of particular importance. In this Letter, under the complex network framework, we st…
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…
Effective contact tracing is crucial to contain epidemic spreading without disrupting societal activities especially in the present time of coexistence with a pandemic outbreak. Large gatherings play a key role, potentially favouring superspreading events. However, the effects of tracing in large groups have not been fully assessed so far. We show that beside forward tracing, which reconstructs to whom disease spreads, and backward tracing, which searches from whom disease spreads, a third "sideward" tracing is always present, when tracing gatherings. This is an indirect tracing that detects i…
The ongoing COVID-19 pandemic is the first epidemic in human history in which digital contact-tracing has been deployed at a global scale. Tracking and quarantining all the contacts of individuals who test positive to a virus can help slowing-down an epidemic, but the impact of contact-tracing is severely limited by the generally low adoption of contact-tracing apps in the population. We derive here an analytical expression for the effectiveness of contact-tracing app installation strategies in a SIR model on a given contact graph. We propose a decentralised heuristic to improve the effectiven…
With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message--passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targete…
In this paper, we develop an extension of standard epidemiological models, suitable for COVID-19. This extension incorporates the transmission due to pre-symptomatic or asymptomatic carriers of the virus. Furthermore, this model also captures the spread of the disease due to the movement of people to/from different administrative boundaries within a country. The model describes the probabilistic rise in the number of confirmed cases due to the concomitant effects of (incipient) human transmission and multiple compartments. The associated parameters in the model can help architect the public he…
Contact tracing via digital tracking applications installed on mobile phones is an important tool for controlling epidemic spreading. Its effectivity can be quantified by modifying the standard methodology for analyzing percolation and connectivity of contact networks. We apply this framework to networks with varying degree distributions, numbers of application users, and probabilities of quarantine failures. Further, we study structured populations with homophily and heterophily and the possibility of degree-targeted application distribution. Our results are based on a combination of explicit…
Contacts between people are the absolute drivers of contagious respiratory infections. For this reason, limiting and tracking contacts is a key strategy for the control of the COVID-19 epidemic. Digital contact tracing has been proposed as an automated solution to scale up traditional contact tracing. However, the required penetration of contact tracing apps within a population to achieve a desired target in the control of the epidemic is currently under discussion within the research community. In order to understand the effects of digital contact tracing, several mathematical models have bee…
Effectiveness of probabilistic contact tracing in epidemic containment: the role of super-spreaders and transmission path reconstruction
Politecnico di Torino（都灵理工大学）；Italian Institute for Genomic Medicine（意大利基因组医学研究所）；Politecnico di Milano（米兰理工大学）；Universidad Complutense（康普顿斯大学）；Collegio Carlo Alberto（卡洛·阿尔贝托学院）
Contact tracing has been extensively studied from different perspectives in recent years. However, there is no clear indication of why this intervention has proven effective in some epidemics (SARS) and mostly ineffective in some others (COVID-19). Here, we perform an exhaustive evaluation of random testing and contact tracing on novel superspreading random networks to try to identify which epidemics are more containable with such measures. We also explore the suitability of positive rates as a proxy of the actual infection statuses of the population. Moreover, we propose novel ideal strategie…
In this study, we address three important challenges related to disease transmissions such as the COVID-19 pandemic, namely, (a) providing an early warning to likely exposed individuals, (b) identifying individuals who are asymptomatic, and (c) prescription of optimal testing when testing capacity is limited. First, we present a dynamic-graph based SEIR epidemiological model in order to describe the dynamics of the disease propagation. Our model considers a dynamic network that accounts for the interactions between individuals over time, such as the ones obtained by manual or automated contact…
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…
To trace or not to trace: analytical insights from network-based contact-tracing models
Tampere University（坦佩雷大学）；University of Trento（特伦托大学）；Universidad Nacional Autonóma de México（墨西哥国立自治大学）；Eötvös Loránd University（厄特沃什·罗兰大学）；National Laboratory for Health Security（国家健康安全实验室）；Northeastern University London（东北大学伦敦分校）；Northeastern University（东北大学）
The Covid-19 pandemic is ongoing worldwide, and the damage it has caused is unprecedented. For prevention, South Korea has adopted a local quarantine strategy rather than a global lockdown. This approach not only minimizes economic damage, but it also efficiently prevents the spread of the disease. In this work, the spread of COVID-19 under local quarantine measures is modeled using the Susceptible-Exposed-Infected-Recovered model on complex networks. In this network approach, the links connected to isolated people are disconnected and then reinstated when they are released. This link dynamics…
The Covid-19 epidemic of the novel coronavirus (severe acute respiratory syndrome SARS - CoV-2) has been spreading around the world. While different containment policies using non-pharmaceutical interventions have been applied, their efficiency are not known quantitatively. We show that the doubling time Td(t) with the success s factor, the characteristic time of the exponential growth of Td(t) in the arrested regime, is a reliable tool for early predictions of epidemic spread time evolution and it provides a quantitative measure of the success of different containment measures. The efficiency…
We investigate the evolution of epidemics over dynamical networks when nodes choose to interact with others in a selfish and decentralized manner. Specifically, we analyze the susceptible-asymptomatic-infected-recovered (SAIR) epidemic in the framework of activity-driven networks with heterogeneous node degrees and time-varying activation rates, and derive both individual and degree-based mean-field approximations of the exact state evolution. We then present a game-theoretic model where nodes choose their activation probabilities in a strategic manner using current state information as feedba…
After the blockade that many nations suffered to stop the growth of the incidence curve of COVID-19 during the first half of 2020, they face the challenge of resuming their social and economic activity. The rapid airborne transmissibility of SARS-CoV-2, and the absence of a vaccine, calls for active containment measures to avoid the propagation of transmission chains. The best strategy up to date, popularly known as Test-Track-Treat (TTT), consist in testing the population for diagnosis, track the contacts of those infected, and treat by quarantine all these cases. The dynamical process that b…
Mumbai, amongst the most densely populated cities in the world, has witnessed the fourth largest number of cases and the largest number of deaths among all the cities in India (as of 28th October 2020). Along with the rest of India, lockdowns (of varying degrees) have been in effect in Mumbai since March 25, 2020. Given the large economic toll on the country from the lockdown and the related restrictions on mobility of people and goods, swift opening of the economy especially in a financial hub such as Mumbai becomes critical. In this report, we use the IISc-TIFR agent based simulator to devel…
Connecting the different scales of epidemic dynamics, from individuals to communities to nations, remains one of the main challenges of disease modeling. Here, we revisit one of the largest public health efforts deployed against a localized epidemic: the 2014-2016 Ebola Virus Disease (EVD) epidemic in Sierra Leone. We leverage the data collected by the surveillance and contact tracing protocols of the Sierra Leone Ministry of Health and Sanitation, the US Centers for Disease Control and Prevention, and other responding partners to validate a network epidemiology framework connecting the popula…
Quarantining and contact tracing are popular ad hoc practices for mitigating epidemic outbreaks. However, few mathematical theories are currently available to asses the role of a network in the effectiveness of these practices. In this paper, we study how the final size of an epidemic is influenced by the procedure that combines contact tracing and quarantining on a network null model: the configuration model. Namely, we suppose that infected vertices may self-quarantine and trace their infector with a given success probability. A traced infector is, in turn, less likely to infect others. We s…
The possibility to analyze, quantify and forecast epidemic outbreaks is fundamental when devising effective disease containment strategies. Policy makers are faced with the intricate task of drafting realistically implementable policies that strike a balance between risk management and cost. Two major techniques policy makers have at their disposal are: epidemic modeling and contact tracing. Models are used to forecast the evolution of the epidemic both globally and regionally, while contact tracing is used to reconstruct the chain of people who have been potentially infected, so that they can…
Contact tracing and quarantine are well established non-pharmaceutical epidemic control tools. The paper aims to clarify the impact of these measures in COVID-19 epidemic. A new deterministic model is introduced (SEIRQ: susceptible, exposed, infectious, removed, quarantined) with Q compartment capturing individuals and releasing them with delay. We obtain a simple rule defining the reproduction number $\mathcal{R}$ in terms of quarantine parameters, ratio of diagnosed cases and transmission parameters. The model is applied to the epidemic in Poland in March - April 2020, when social distancing…
Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume mass-action contact patterns and undirected contact networks, meaning that the individuals most likely to spread the disease are also the most at risk to receive it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproduction number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees ("risk" and "spread"), including their heterogeneity and the correlation between them. …
Motivated by the importance of individual differences in risk perception and behavior change in people's responses to infectious disease outbreaks (particularly the ongoing COVID-19 pandemic), we propose a heterogeneous Disease-Behavior-Information (hDBI) transmission model, in which people's risk of getting infected is influenced by information diffusion, behavior change, and disease transmission. We use both a mean-field approximation and Monte Carlo simulations to analyze the dynamics of the model. Information diffusion influences behavior change by allowing people to be aware of the diseas…
Given the growth of urbanization and emerging pandemic threats, more sophisticated models are required to understand disease propagation and investigate the impacts of intervention strategies across various city types. We introduce a fully mechanistic, activity-based and highly spatio-temporally resolved epidemiological model which leverages on person-trajectories obtained from integrated mobility demand and supply models in full-scale cities. Simulating COVID-19 evolution in two full-scale cities with representative synthetic populations and mobility patterns, we analyze activity-based contac…
With more than 1.7 million COVID-19 deaths, identifying effective measures to prevent COVID-19 is a top priority. We developed a mathematical model to simulate the COVID-19 pandemic with digital contact tracing and testing strategies. The model uses a real-world social network generated from a high-resolution contact data set of 180 students. This model incorporates infectivity variations, test sensitivities, incubation period, and asymptomatic cases. We present a method to extend the weighted temporal social network and present simulations on a network of 5000 students. The purpose of this wo…
Discovering and isolating infected individuals is a cornerstone of epidemic control. Because many infectious diseases spread through close contacts, contact tracing is a key tool for case discovery and control. However, although contact tracing has been performed widely, the mathematical understanding of contact tracing has not been fully established and it has not been clearly understood what determines the efficacy of contact tracing. Here, we reveal that, compared with "forward" tracing---tracing to whom disease spreads, "backward" tracing---tracing from whom disease spreads---is profoundly…
The COVID-19 epidemic has swept the world for over a year. However, a large number of infectious asymptomatic COVID-19 cases (\textit{ACC}s) are still making the breaking up of the transmission chains very difficult. Efforts by epidemiological researchers in many countries have thrown light on the clinical features of ACCs, but there is still a lack of practical approaches to detect ACCs so as to help contain the pandemic. To address the issue of ACCs, this paper presents a neural network model called Spatio-Temporal Episodic Memory for COVID-19 (\textit{STEM-COVID}) to identify ACCs from cont…
