设计连贯且高效的传染病应对政策及其相关措施，不仅需要对流行病传播动力学建模，还需对个体行为建模，因为后者对前者有极强影响。本研究针对这一问题提出了一个考虑人口社会结构的理论模型。该模型基于SIR仓室模型的平均场博弈（Mean Field Game）版本，其中个体按年龄组划分，并在不同场景中发生互动。这种社会异质性既能复现现实情境，又能保持实际可用性。在我们的博弈论方法中，个体可以通过在感染风险与隔离成本之间进行权衡，选择限制自身社交接触。所有个体的选择与优化行为通过一组耦合方程形成纳什均衡，我们推导了这组方程并进行了数值求解。随后，我们将该场景下人口承担的总体成本与社会最优成本（即从社会视角出发的最优成本）进行对比，并研究了在政府机构实施封控的约束性纳什均衡下，两种成本之间的差距可被部分缩小的机制。最后，我们考察了人口规模N的有限性，以及外部事件终结流行病的时间T所带来的影响，证明这些参数的变化可能导致最优策略选择中出现一阶相变。本文中所有用于缓解流行病的策略均属于非药物干预（NPI），我们提供了一个理论框架，可用于评估取决于流行病特征与社会限制成本的公共政策指导方针。
英文摘要：
The design of coherent and efficient policies to address infectious diseases and their consequences requires to model not only epidemics dynamics, but also individual behaviors, as the latter has a strong influence on the former. In our work, we provide a theoretical model for this problem, taking into account the social structure of a population. This model is based on a Mean Field Game version of a SIR compartmental model, in which individuals are grouped by their age class and interact together in different settings. This social heterogeneity allows to reproduce realistic situations while remaining usable in practice. In our game theoretical approach, individuals can choose to limit their contacts by making a trade-off between the risks incurred by infection and the cost of being confined. The aggregation of all these individual choices and optimizations forms a Nash equilibrium through a system of coupled equations that we derive and solve numerically. The global cost born by the population within this scenario is then compared to its societal optimum counterpart (i.e. the optimal cost from the society viewpoint), and we investigate how the gap between these two costs can be partially bridged within a constrained Nash equilibrium for which a governmental institution would impose lockdowns. Finally we consider the consequences of the finiteness of the population size $N$, or of a time $T$ at which an external event would end the epidemic, and show that the variation of these parameters could lead to first order phase transitions in the choice of optimal strategies. In this paper, all the strategies considered to mitigate epidemics correspond to non-pharmaceutical interventions (NPI), and we provide here a theoretical framework within which guidelines for public policies depending on the characteristics of an epidemic and on the cost of restrictions on the society could be assessed.
We highlight the usefulness of city-scale agent-based simulators in studying various non-pharmaceutical interventions to manage an evolving pandemic. We ground our studies in the context of the COVID-19 pandemic and demonstrate the power of the simulator via several exploratory case studies in two metropolises, Bengaluru and Mumbai. Such tools become common-place in any city administration's tool kit in our march towards digital health.
The drivers behind regional differences of SARS-CoV-2 spread on finer spatio-temporal scales are yet to be fully understood. Here we develop a data-driven modelling approach based on an age-structured compartmental model that compares 116 Austrian regions to a suitably chosen control set of regions to explain variations in local transmission rates through a combination of meteorological factors, non-pharmaceutical interventions and mobility. We find that more than 60% of the observed regional variations can be explained by these factors. Decreasing temperature and humidity, increasing cloudine…
When an unprecedented infectious disease with high mortality and transmissibility emerges, immediate usage of vaccines or medicines is hardly available. Thus, many health authorities rely on non-pharmaceutical interventions through traceable fixed contacts. However, in reality, there is an additional type of transmission routes to the regular and fixed contacts: the random anonymous infection cases where non-pharmaceutical interventions are hardly feasible. In our study, such realistic situations are implemented by the susceptible-infected-recovered model with isolation on multiplex networks. …
Mathematical modeling of epidemic spreading has been widely adopted to estimate the threats of epidemic diseases (i.e., the COVID-19 pandemic) as well as to evaluate epidemic control interventions. The indoor place is considered to be a significant epidemic spreading risk origin, but existing widely-used epidemic spreading models are usually limited for indoor places since the dynamic physical distance changes between people are ignored, and the empirical features of the essential and non-essential travel are not differentiated. In this paper, we introduce a pedestrian-based epidemic spreading…
When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet compe…
The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It h…
Since December 2019, A novel coronavirus (2019-nCoV) has been breaking out in China, which can cause respiratory diseases and severe pneumonia. Mathematical and empirical models relying on the epidemic situation scale for forecasting disease outbreaks have received increasing attention. Given its successful application in the evaluation of infectious diseases scale, we propose a Susceptible-Undiagnosed-Infected-Removed (SUIR) model to offer the effective prediction, prevention, and control of infectious diseases. Our model is a modified susceptible-infected-recovered (SIR) model that injects u…
Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first…
This paper introduces a dynamic panel SIR (DP-SIR) model to investigate the impact of non-pharmaceutical interventions (NPIs) on the COVID-19 transmission dynamics with panel data from 9 countries across the globe. By constructing scenarios with different combinations of NPIs, our empirical findings suggest that countries may avoid the lockdown policy with imposing school closure, mask wearing and centralized quarantine to reach similar outcomes on controlling the COVID-19 infection. Our results also suggest that, as of April 4th, 2020, certain countries such as the U.S. and Singapore may requ…
Metapopulation epidemic models describe epidemic dynamics in networks of spatially distant patches connected with pathways for migration of individuals. In the present study, we deal with a susceptible-infected-recovered (SIR) metapopulation model where the epidemic process in each patch is represented by an SIR model and the mobility of individuals is assumed to be a homogeneous diffusion. Our study focuses on two types of patches including high-risk and low-risk ones, in order to evaluate intervention strategies for epidemic control. We theoretically analyze the intervention threshold, indic…
We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov Chain Monte Carlo (MCMC) methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model …
Protecting interventions of many types (both pharmaceutical and non-pharmaceutical) can be deployed against the spreading of a communicable disease, as the worldwide COVID-19 pandemic has dramatically shown. Here we investigate in detail the effects at the population level of interventions that provide an asymmetric protection between the people involved in a single interaction. Masks of different filtration types, either protecting mainly the wearer or the contacts of the wearer, are a prominent example of these interventions. By means of analytical calculations and extensive simulations of s…
Adherence to the non-pharmaceutical interventions (NPIs) put in place to mitigate the spreading of infectious diseases is a multifaceted problem. Socio-demographic, socio-economic, and epidemiological factors can influence the perceived susceptibility and risk which are known to affect behavior. Furthermore, the adoption of NPIs is dependent upon the barriers, real or perceived, associated with their implementation. We study the determinants of NPIs adherence during the first wave of the COVID-19 Pandemic in Colombia, Ecuador, and El Salvador. Analyses are performed at the level of municipalit…
The customary perspective to reason about epidemic mitigation in temporal networks hinges on the identification of nodes with specific features or network roles. The ensuing individual-based control strategies, however, are difficult to carry out in practice and ignore important correlations between topological and temporal patterns. Here we adopt a mesoscopic perspective and present a principled framework to identify collective features at multiple scales and rank their importance for epidemic spread. We use tensor decomposition techniques to build an additive representation of a temporal net…
Infectious diseases and human behavior are intertwined. On one side, our movements and interactions are the engines of transmission. On the other, the unfolding of viruses might induce changes to our daily activities. While intuitive, our understanding of such feedback loop is still limited. Before COVID-19 the literature on the subject was mainly theoretical and largely missed validation. The main issue was the lack of empirical data capturing behavioral change induced by diseases. Things have dramatically changed in 2020. Non-pharmaceutical interventions (NPIs) have been the key weapon again…
Recently, the world has witnessed the most severe pandemic (COVID-19) in this century. Studies on epidemic prediction and simulation have received increasing attention. However, the current methods suffer from three issues. First, most of the current studies focus on epidemic prediction, which can not provide adequate support for intervention policy making. Second, most of the current interventions are based on population groups rather than fine-grained individuals, which can not make the measures towards the infected people and may cause waste of medical resources. Third, current simulations …
Epidemic spread in a population is traditionally modeled via compartmentalized models which represent the free evolution of disease in absence of any intervention policies. In addition, these models assume full observability of disease cases and do not account for under-reporting. We present a mathematical model, namely PolSIRD, which accounts for the under-reporting by introducing an observation mechanism. It also captures the effects of intervention policies on the disease spread parameters by leveraging intervention policy data along with the reported disease cases. Furthermore, we allow ou…
Non-pharmaceutical interventions (NPIs) such as quarantine, self-isolation, social distancing, and virus-contact tracing can greatly reduce the spread of the virus during a pandemic. In the wave of the COVID-19 pandemic, many countries have implemented various NPIs for infection control and mitigation. However, the stringency of the NPIs and the resulting impact among different countries remain unclear due to the lack of quantitative factors. In this study we took a further step to incorporate the effect of the NPIs into the pandemic dynamics model using the concept of policy intensity factor …
The implementation of governmental Non-Pharmaceutical Interventions (NPIs) has been the primary means of controlling the spread of the COVID-19 disease. The intended effect of these NPIs has been to reduce mobility. A strong reduction in mobility is believed to have a positive effect on the reduction of COVID-19 transmission by limiting the opportunity for the virus to spread in the population. Due to the huge costs of implementing these NPIs, it is essential to have a good understanding of their efficacy. Using global mobility data, released by Apple and Google, and ACAPS NPI data, we investi…
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effect…
Estimating the population-level effects of non-pharmaceutical interventions when transmission rates of COVID-19 vary by orders of magnitude from one contact to another
Emergent dilemma and periodic oscillation in the nonlinear interplay between epidemic and behavior
Beihang University（北京航空航天大学）；Key laboratory of Mathematics, Informatics and Behavioral Semantics, Beihang University（北京航空航天大学数学、信息与行为语义重点实验室）；Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University（北京航空航天大学未来区块链与隐私计算高级创新中心）；State Key Laboratory of Complex & Critical Software Environment, Beihang University（北京航空航天大学复杂与关键软件环境国家重点实验室）；Beijing Academy of Blockchain and Edge Computing（北京区块链与边缘计算研究院）；School of Mathematical Sciences, Beihang University（北京航空航天大学数学科学学院）；School of Logistics, Beijing Wuzi University（北京物资学院物流学院）；Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新学院）
The pandemic caused by the novel Coronavirus SARS-CoV2 has been responsible for life threatening health complications, and extreme pressure on healthcare systems. While preventive and definite curative medical interventions are yet to arrive, Non-Pharmaceutical Interventions (NPIs) like physical isolation, quarantine and drastic social measures imposed by governing agencies are effective in arresting the spread of infections in a population. In densely populated countries like India, lockdown interventions are partially effective due to social and administrative complexities. Using detailed de…
Once an epidemic outbreak has been effectively contained through non-pharmaceutical interventions, a safe protocol is required for the subsequent release of social distancing restrictions to prevent a disastrous resurgence of the infection. We report individual-based numerical simulations of stochastic susceptible-infectious-recovered model variants on four distinct spatially organized lattice and network architectures wherein contact and mobility constraints are implemented. We robustly find that the intensity and spatial spread of the epidemic recurrence wave can be limited to a manageable e…
The coronavirus disease 2019 (COVID-19) pandemic has quickly become a global public health crisis unseen in recent years. It is known that the structure of the human contact network plays an important role in the spread of transmissible diseases. In this work, we study a structure aware model of COVID-19 CGEM. This model becomes similar to the classical compartment-based models in epidemiology if we assume the contact network is a Erdos-Renyi (ER) graph, i.e. everyone comes into contact with everyone else with the same probability. In contrast, CGEM is more expressive and allows for plugging i…
The SARS-CoV-2 pandemic has caused significant mortality and morbidity worldwide, sparing almost no community. As the disease will likely remain a threat for years to come, an understanding of the precise influences of human demographics and settlement, as well as the dynamic factors of climate, susceptible depletion, and intervention, on the spread of localized epidemics will be vital for mounting an effective response. We consider the entire set of local epidemics in the United States; a broad selection of demographic, population density, and climate factors; and local mobility data, trackin…
We propose a deterministic compartmental model of infectious disease which considers the test-kits as an important ingredient for the suppression and mitigation of epidemics. A rigorous simulation (with analytical argument) is provided to reveal the effective reduction of final outbreak size and peak of infection as a function of basic reproduction number in a single patch. Further, to study the impact of long and short-distance human migration among the patches, we have considered heterogeneous networks where the linear diffusive connectivity is determined by the network link structure. We nu…
Reverse Engineering the Reproduction Number: A Framework for Data-Driven Counterfactual Analysis, Strategy Evaluation, and Feedback Control of Epidemics
We develop a minimalist compartmental model to study the impact of mobility restrictions in Italy during the Covid-19 outbreak. We show that an early lockdown shifts the epidemic in time, while that beyond a critical value of the lockdown strength, the epidemic tend to restart after lifting the restrictions. As a consequence, specific mitigation strategies must be introduced. We characterize the relative importance of different broad strategies by accounting for two fundamental sources of heterogeneity, i.e. geography and demography. First, we consider Italian regions as separate administrativ…
Understanding how to effectively control an epidemic spreading on a network is a problem of paramount importance for the scientific community. The ongoing COVID-19 pandemic has highlighted the need for policies that mitigate the spread, without relying on pharmaceutical interventions, that is, without the medical assurance of the recovery process. These policies typically entail lockdowns and mobility restrictions, having thus nonnegligible socio-economic consequences for the population. In this paper, we focus on the problem of finding the optimum policies that "flatten the epidemic curve" wh…
We create a network model to study the spread of an epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for two kinds of agents - poor and non-poor. Under non-intervention, peak caseload is maximised, but no differences are observed in infection rates across poor and non-poor. Introducing interventions to control spread, peak caseloads are reduced, but both cumulative infection rates and current infection rates are systematically higher for the poor than for non-poor, across all scenarios. Larger populations, higher fractions of poor, and …
Instituto Federal do Norte de Minas Gerais (IFNMG)（北米纳斯吉拉斯联邦学院）；Federal University of Minas Gerais（米纳斯吉拉斯联邦大学）；Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）；Universidade Federal de Ouro Preto（奥罗普雷托联邦大学）
The COVID-19 pandemic due to the SARS-CoV-2 coronavirus has directly impacted the public health and economy worldwide. To overcome this problem, countries have adopted different policies and non-pharmaceutical interventions for controlling the spread of the virus. This paper proposes the COVID-ABS, a new SEIR (Susceptible-Exposed-Infected-Recovered) agent-based model that aims to simulate the pandemic dynamics using a society of agents emulating people, business and government. Seven different scenarios of social distancing interventions were analyzed, with varying epidemiological and economic…
The pandemic of COVID-19 has caused severe public health consequences around the world. Many interventions of COVID-19 have been implemented. It is of great public health and societal importance to evaluate the effects of interventions in the pandemic of COVID-19. In this paper, with help of synthetic control method, regression discontinuity and a Susceptible-Infected and infectious without isolation-Hospitalized in isolation-Removed (SIHR) model, we evaluate the horizontal and longitudinal effects of stringent interventions implemented in Wenzhou, a representative urban city of China, where s…
PyRoss is an open-source Python library that offers an integrated platform for inference, prediction and optimisation of NPIs in age- and contact-structured epidemiological compartment models. This report outlines the rationale and functionality of the PyRoss library, with various illustrations and examples focusing on well-mixed, age-structured populations. The PyRoss library supports arbitrary structured models formulated stochastically (as master equations) or deterministically (as ODEs) and allows mid-run transitioning from one to the other. By supporting additional compartmental subdivisi…
In this paper we conduct a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a scale-free network and that each infected individual in the network gains a temporary immunity after its infectious period is over. After the temporary immunity period is over, the individual becomes susceptible to the virus again. When the underlying contact network is embedded in Euclidean geometry, we model three different intervention strategies that aim to contr…
As infectious disease outbreaks emerge, public health agencies often enact vaccination and social distancing measures to slow transmission. Their success depends on not only strategies and resources, but also public adherence. Individual willingness to take precautions may be influenced by global factors, such as news media, or local factors, such as infected family members or friends. Here, we compare three modes of epidemiological decision-making in the midst of a growing outbreak. Individuals decide whether to adopt a recommended intervention based on overall disease prevalence, the proport…
Investigating the effect of adaptive optimal control function in epidemic dynamics: predictions and strategy evolution based on SIR/V game theoretic framework
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…
The spread of COVID-19 has been thwarted in most countries through non-pharmaceutical interventions. In particular, the most effective measures in this direction have been the stay-at-home and closure strategies of businesses and schools. However, population-wide lockdowns are far from being optimal carrying heavy economic consequences. Therefore, there is nowadays a strong interest in designing more efficient restrictions. In this work, starting from a recent kinetic-type model which takes into account the heterogeneity described by the social contact of individuals, we analyze the effects of…
Voluntary nonpharmaceutical intervention as a feedback-evolving game
CEFE, Univ Montpellier, CNRS, EPHE, IRD（法国国家科学研究中心、高等教育与研究学院、热带研究所）；Institute of Tropical Medicine, Nagasaki University（长崎大学热带医学研究所）；Multidisciplinary Pandemic Research Center, Nagasaki University（长崎大学多学科流行病研究中心）；National Institute of Genetics（国立遗传学研究所）；SOKENDAI（综合研究大学院大学）；The University of Queensland（昆士兰大学）；Yokohama National University（横滨国立大学）；The University of Tokyo（东京大学）
The reproductive number R_0 (and its value after initial disease emergence R) has long been used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic virus SARS-CoV-2, the causative agent of COVID-19. We address some of these misconceptions, namely, how R changes over time, varies over space, and relates to epidemic size by referencing the mathematical definition of R an…
We propose a targeted intervention protocol where recovery is restricted to individuals that have the least number of infected neighbours. Our recovery strategy is highly efficient on any kind of network, since epidemic outbreaks are minimal when compared to the baseline scenario of spontaneous recovery. In the case of spatially embedded networks, we find that an epidemic stays strongly spatially confined with a characteristic length scale undergoing a random walk. We demonstrate numerically and analytically that this dynamics leads to an epidemic spot with a flat surface structure and a radiu…
