Since the beginning of the COVID-19 spreading, the number of studies on the epidemic models increased dramatically. It is important for policymakers to know how the disease will spread and what are the effects of the policies and environment on the spreading. In this paper, we propose two extensions to the standard SIR model: (a) we consider the prevention measures adopted based on the current severity of the infection. Those measures are adaptive and change over time; (b) multiple cities and regions are considered, with population movements between those cities and regions, while taking into account that each region may have different prevention measures. Although the adaptive measures and mobility of the population were often observed during the pandemic, these effects are rarely explicitly modeled and studied in the classical epidemic models. The model we propose gives rise to a plateau phenomenon: the number of people infected by the disease stays at the same level during an extended period of time. We show what are conditions need to be met in order for the spreading to exhibit a plateau period in a single city. In addition, this phenomenon is interdependent when considering multiple cities. We verify from the real-world data that the plateau phenomenon does exist in many regions of the world in the current COVID-19 development. Finally, we provide theoretical analysis on the plateau phenomenon for the single-city model and derive a series of results on the emergence and the ending of the plateau, as well as on the height and length of the plateau. Our theoretical results match well with our experimental findings.
Since the 21st century, the global outbreaks of infectious diseases such as SARS in 2003, H1N1 in 2009, and H7N9 in 2013, have become the critical threat to the public health and a hunting nightmare to the government. Understanding the propagation in large-scale metapopulations and predicting the future outbreaks thus become crucially important for epidemic control and prevention. In the literature, there have been a bulk of studies on modeling intra-city epidemic propagation but with the single population assumption (homogeneity). Some recent works on metapopulation propagation, however, focu…
The adoption of prophylaxis attitudes, such as social isolation and use of face masks, to mitigate epidemic outbreaks strongly depends on the support of the population. In this work, we investigate a susceptible-infected-recovered (SIR) epidemic model, in which the epidemiological perception of the environment can adapt the behavior of susceptible individuals towards preventive behavior. {Two compartments of susceptible individuals are considered, to distinguish those that adopt or not prophylaxis attitudes.} Two rules, depending on local and global epidemic prevalence, for the spread of the e…
Contagious diseases can spread quickly in human populations, either through airborne transmission or if some other spreading vectors are abundantly accessible. They can be particularly devastating if the impact on individuals' health has severe consequences on the number of hospitalizations or even deaths. Common countermeasures to contain the epidemic spread include introducing restrictions on human interactions or their mobility in general which are often associated with an economic and social cost. In this paper, we present a targeted model of optimal social distancing on metapopulation net…
PeopleTraffic is a proposed initiative to develop a real-time, open-data population density mapping tool open to public institutions, private companies and the civil society, providing a common framework for infection spreading prevention. The system is based on a real-time people' locations gathering and mapping system from available 2G, 3G and 4G mobile networks operators, enforcing privacy-by-design through the adoption of an innovative data anonymizing algorithm inspired by quantum information de-localizing processes. Besides being originally targeted to help balancing social distancing re…
It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, i.e. constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models we demonstrate the emergence of a new long timescale governing the epidemic in broad agreement with empirical data. Our model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multip…
This manuscript proposes a model of $n$ distinct populations interaction structured SEIR to describe the spread of COVID-19 pandemic diseases. The proposed model has the flexibility to include geographically separated communities as well as taking into account aging population groups and their interactions. We show that distinct assumptions on the dynamics of the proposed model lead to a plateau-like curve of the infected population, reflecting collected data from large countries like Brazil. Such observations aim to the following conjecture: " Covid-19 diseased diffusion from the capitals to …
Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such a dynamical pattern is compatible with critical Susceptible-Infected-Removed (SIR) dynamics. In traditional analyses of the critical SIR model, the critical dynamical regime is started from a single infected node. The application of containment measures to an ongoing epidemic, however, has the effect to make the system enter in its critical regime with a num…
In the face of serious infectious diseases, governments endeavour to implement containment measures such as public vaccination at a macroscopic level. Meanwhile, individuals tend to protect themselves by avoiding contacts with infections at a microscopic level. However, a comprehensive understanding of how such combined strategy influences epidemic dynamics is still lacking. We study a susceptible-infected-susceptible epidemic model with imperfect vaccination on dynamic contact networks, where the macroscopic intervention is represented by random vaccination of the population and the microscop…
There were 27 novel coronavirus pneumonia cases found in Wuhan, China in December 2019, named as 2019-nCoV temporarily and COVID-19 formally by WHO on 11 February, 2020. In December 2019 and January 2020, COVID-19 has spread in large scale among the population, which brought terrible disaster to the life and property of the Chinese people. In this paper, we will first analyze the feature and pattern of the virus transmission, and discuss the key impact factors and uncontrollable factors of epidemic transmission based on public data. Then the virus transmission can be modelled and used for the …
In December 2019, COVID-19 were detected in Wuhan City, Hubei Province of China. SARS-CoV-2 rapidly spread to the whole Chinese mainland with the people during the Chinese Spring Festival Travel Rush. As of 19 February 2020, 74576 confirmed cases of COVID-19 had been reported in Chinese Mainland. What kind of cities have more confirmed cases, and is there any relationship between GDP and confirmed cases? In this study, we explored the relationship between the confirmed cases of COVID-19 and GDP at the prefectural-level, found a positive correlation between them. This finding warns high GDP are…
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…
The mobility patterns of individuals in China during the early outbreak of the COVID-19 pandemic exhibit reversible changes -- in many regions, the mobility first decreased significantly and later restored. Based on this observation, here we study the classical SIR model on a particular type of time-varying network where the links undergo a freeze-recovery process. We first focus on an isolated network and find that the recovery mechanism could lead to the resurgence of an epidemic. The influence of link freezing on epidemic dynamics is subtle. In particular, we show that there is an optimal v…
We study the perception of COVID-2019 epidemic in Polish society using quantitative analysis of its digital footprints on the Internet (on Twitter, Google, YouTube, Wikipedia and electronic media represented by Event Registry) from January 2020 to 12.03.2020 (before and after official introduction to Poland on 04.03.2020). To this end we utilize data mining, social network analysis, natural language processing techniques. Each examined internet platform was analyzed for representativeness and composition of the target group. We identified three temporal major cluster of the interest before dis…
In 2020, the COVID-19 pandemic spreads all over the world. In order to alleviate the spread of the epidemic, various blockade policies have been implemented in many areas. In order to formulate a better epidemic prevention policy for urban energy consumption of the commercial tourism cities, this paper first analyses the energy characteristics of Macao during the epidemic period from two aspects, based on the energy consumption data of Macao. On this basis, the power consumption characteristics of commercial tourism cities during the epidemic were analyzed. Then, this paper provides analysis o…
Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important role in epidemic dynamics and is also affected by behavioral changes, but there are many situations in which real mobility data is incomplete or inaccessible. We present a model for epidemic spreading in temporal networks of mobile agents that incorporates local behavioral responses. Susceptible agents are allowed to move towards the opposite direction of infe…
The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modeling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive an explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega functi…
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…
In this article we develop a highly integrated effective degree approach to modeling epidemic and awareness spreading processes on multiplex networks coupled with awareness-dependent adaptive rewiring. This approach keeps track of the number of nearest neighbors in each state of an individual; consequently, it allows for the integration of changes in local contacts into the multiplex network model. We derive a formula for the threshold condition of contagion outbreak; also, we provide a lower bound for the threshold parameter to indicate the effect of adaptive rewiring. The threshold analysis …
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…
Most researches on adaptive networks mainly concentrate on the properties of steady state, but neglect transient dynamics. In this study, we pay attention to the emergence of community structures in transient process and the effects of community-based control strategies on epidemic spreading. First, by normalizing modularity $Q$, we investigate the evolution of community structures during the transient process, and find that very strong community structures are induced by rewiring mechanism in the early stage of epidemic spreading, which remarkably delays the outbreaks of epidemic. Then we stu…
The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are exceptionally rare to find in any context, especially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers, interconnected through a fraction $q$ of shar…
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on scale-free networks, the density of the recovered individuals in the present model shows a threshold behavior. We obtain the analytical results using the mean-field theory and find that the threshold value equals 1/A, indicating that the threshold value is independent of the topology of the underlying network. The simulations agree well with the analytic resul…
A Strategy Transfer and Decision Support Approach for Epidemic Control in Experience Shortage Scenarios
University of Science and Technology Beijing（北京科技大学）；Tsinghua University（清华大学）；Chinese Academy of Sciences（中国科学院）；Central South Architectural Design Institute Co.（中南建筑设计院股份有限公司）；Shanxi University（山西大学）；Shanghai Jiao Tong University（上海交通大学）
Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission. In this article we study how the spreading of knowledge of a disease affects the propagation of that disease in a population of interacting individuals. For that, we analyze the interaction between two different processes on multiplex networks: the propagation of an epidemic using the susceptible-infected-susceptible dynamics and the dissemination of information about the disease --and its prevention methods-- using the unaware-aware-unaware dynamics, …
Exploring the impact of social stress on the adaptive dynamics of COVID-19: Typing the behavior of naïve populations faced with epidemics
Lobachevsky State University of Nizhny Novgorod（下诺夫哥罗德国立大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Samara State Medical University（萨马拉国立医科大学）；Institut Curie（居里研究所）；PSL Research University（巴黎文理研究大学）；INSERM U900（法国国家健康与医学研究院 U900）；Center for Computational Biology, Mines ParisTech（巴黎矿业学院计算生物学中心）；University of Leicester（莱斯特大学）；Evotec（Evotec公司）
The data analysis on deaths in the Lombardy Region and of both the provinces of Bergamo and Brescia shows a twofold aspect on the trend of the epidemic: - all the data show a bias linked to the event of March 10th (day for which the Lombardy region data is partial) and the subsequent change in the way in which positive cases and deaths are calculated; - following the containment measures of the Prime Minister's Decree of March 11th, the spread of the epidemic, although still exponential in nature, has a reduced multiplication coefficient. Our analysis concludes that the situation is not yet co…
The constrained outbreak of COVID-19 in Mainland China has recently been regarded as a successful example of fighting this highly contagious virus. Both the short period (in about three months) of transmission and the sub-exponential increase of confirmed cases in Mainland China have proved that the Chinese authorities took effective epidemic prevention measures, such as case isolation, travel restrictions, closing recreational venues, and banning public gatherings. These measures can, of course, effectively control the spread of the COVID-19 pandemic. Meanwhile, they may dramatically change t…
Numerous real-world systems, for instance, the communication platforms and transportation systems, can be abstracted into complex networks. Containing spreading dynamics (e.g., epidemic transmission and misinformation propagation) in networked systems is a hot topic in multiple fronts. Most of the previous strategies are based on the immunization of nodes. However, sometimes, these node--based strategies can be impractical. For instance, in the train transportation networks, it is dramatic to isolating train stations for flu prevention. On the contrary, temporarily suspending some connections …
As the COVID19 spreads across the world, prevention measures are becoming the essential weapons to combat the pandemic in the period of crisis. The lockdown measure is the most controversial one as it imposes an overwhelming impact on our economy and society. Especially when and how to enforce the lockdown measures are the most challenging questions considering both economic and epidemiological costs. In this paper, we extend the classic SIR model to find optimal decision making to balance between economy and people's health during the outbreak of COVID-19. In our model, we intend to solve a t…
