Motivated by COVID-19, we develop and analyze a simple stochastic model for a disease spread in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for slowing down and reopening the society and we compare their efficiency in mitigating the spread of the virus from several different points of view. We find that in order to avoid overwhelming of the hospital system, a policy must impose a harsh lockdown or it must react swiftly (or both). While reacting swiftly is universally beneficial, being harsh pays off only when the country is patient about reopening and when the neighboring countries coordinate their mitigation efforts. Our work highlights the importance of acting decisively when closing down and the importance of patience and coordination between neighboring countries when reopening.
Lockdown procedures have been proven successful in mitigating the spread of the viruses in this COVID-19 pandemic, but they also have devastating impact on the economy. We use a modified Susceptible-Infectious-Recovered-Deceased model with time dependent infection rate to simulate how the infection is spread under lockdown. The economic cost due to the loss of workforce and incurred medical expenses is evaluated with a simple model. We find the best strategy, meaning the smallest economic cost for the entire course of the pandemic, is to keep the strict lockdown as long as possible.
We show that the dynamics of the number of deaths due to Covid in different countries is to a large extent universal once the origin of time is chosen to be the start of the lockdown, and the number of death is rescaled by the total number of deaths after the lockdown, itself a proxy of the number of infections at the start of the lockdown. Such a curve collapse is much less convincing when normalizing by the total population. Sweden, with its no-lockdown, light-touch approach, is the only outlier that deviates considerably from the average behavior. We argue that these model-free findings pro…
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 …
In this work, we present a stochastic discrete-time SEIR (Susceptible-Exposed-Infectious-Recovered) model adapted to describe the propagation of COVID-19 during a football tournament. Specifically, we are concerned about the re-start of the Spanish national football league, La Liga, which is currently -May 2020- stopped with 11 fixtures remaining. Our model includes two additional states of an individual, confined and quarantined, which are reached when an individual presents COVID-19 symptoms or has undergone a virus test with a positive result. The model also accounts for the interaction dyn…
We consider here an extended SIR model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the su…
We study mechanisms for reopening economic activities that explore the trade off between containing the spread of COVID-19 and maximizing economic impact. This is of current importance as many organizations, cities, and states are formulating reopening strategies. Our mechanisms, referred to as group scheduling, are based on partitioning the population into groups and scheduling each group on appropriate days with possible gaps (when all are quarantined). Each group interacts with no other group and, importantly, any person who is symptomatic in a group is quarantined. Specifically, our mechan…
During a pandemic, there are conflicting demands arising from public health and economic cost. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimise the economic damage of a lockdown while still containing infections. Our analysis is based on the SIR model, which we analyse using a clock set by the virus. This use of the "virus time" permits a clean mathematical formulation of our problem. We optimise the economic cost for a fixed health cost and arrive at a strategy for navigating the pandemic. This involves adjust…
To slow down the spread of Covid-19, administrative regions within Pakistan imposed complete and partial lockdown restrictions on socio-economic activities, religious congregations, and human movement. Here we examine the impact of regional lockdown strategies on Covid-19 outcomes. After conducting econometric analyses (Regression Discontinuity and Negative Binomial Regressions) on official data from the National Institute of Health (NIH) Pakistan, we find that the strategies did not lead to a similar level of Covid-19 caseload (positive cases and deaths) in all regions. In terms of reduction …
The nation-wide lockdown starting 25 March 2020, aimed at suppressing the spread of the COVID-19 disease, was extended until 31 May 2020 in three subsequent orders by the Government of India. The extended lockdown has had significant social and economic consequences and `lockdown fatigue' has likely set in. Phased reopening began from 01 June 2020 onwards. Mumbai, one of the most crowded cities in the world, has witnessed both the largest number of cases and deaths among all the cities in India (41986 positive cases and 1368 deaths as of 02 June 2020). Many tough decisions are going to be made…
The current COVID-19 pandemic and subsequent lockdowns have highlighted the close and delicate relationship between a country's public health and economic health. Macroeconomic models that use preexisting epidemic models to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We develop an SIR model of the COVID-19 pandemic that explicitly considers herd immunity, behavior-dependent transmission rates, remote workers, and indirect externalities of lockdown. This model is presented as an exit …
We are currently facing a highly critical case of a world-wide pandemic. The novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely contagious and the original outbreak from Asia has now spread to all continents. This situation will fruitfully profit from the study in regards of the spread of the virus, assessing effective countermeasures to weight the impact of the adopted strategies. The standard Susceptible-Infectious-Recovered (SIR) model is a very successful and widely used mathematical model for predicting the spread of an epidemic. We adopt the SIR model on a random …
We develop a Bayesian inference framework to quantify uncertainties in epidemiological models. We use SEIJR and SIJR models involving populations of susceptible, exposed, infective, diagnosed, dead and recovered individuals to infer from covid-19 data rate constants, as well as their variations in response to lockdown measures. To account for confinement, we distinguish two susceptible populations at different risk: confined and unconfined. We show that transmission and recovery rates within them vary in response to facts. A key unknown to predict the evolution of the epidemic is the fraction …
COVID-19 abatement strategies have risks and uncertainties which could lead to repeating waves of infection. We show -- as proof of concept grounded on rigorous mathematical evidence -- that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn -- while not eliminating the v…
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…
As Europe is facing the second wave of the CoViD-19 pandemic, each country should carefully review how it dealt with the first wave of outbreak. Lessons from the first experience should be useful to avoid indiscriminate closures and, above all, to determine universal (understandable) parameters to guide the introduction of containment measures to reduce the spreading of the virus. The use of few (effective) parameters is indeed of extreme importance to create a link between authorities and population, allowing the latter to understand the reason for some restrictions and, consequently, to allo…
The 2019 Novel Corona virus infection (COVID 19) is an ongoing public health emergency of international focus. Significant gaps persist in our knowledge of COVID 19 epidemiology, transmission dynamics, investigation tools and management, despite (or possibly because of) the fact that the outbreak is an unprecedented global threat. On the positive side, enough is currently known about the epidemic process to permit the construction of mathematical predictive models. In our work, we adapt a traditional SEIR epidemic model to the specific dynamic compartments and epidemic parameters of COVID 19, …
In this work, we provide a general mathematical formalism to study the optimal control of an epidemic, such as the COVID-19 pandemic, via incentives to lockdown and testing. In particular, we model the interplay between the government and the population as a principal-agent problem with moral hazard, à la Cvitanić, Possamaï, and Touzi [27], while an epidemic is spreading according to dynamics given by compartmental stochastic SIS or SIR models, as proposed respectively by Gray, Greenhalgh, Hu, Mao, and Pan [45] and Tornatore, Buccellato, and Vetro [88]. More precisely, to limit the spread of a…
We estimate the growth in demand for ICU beds in Chicago during the emerging COVID-19 epidemic, using state-of-the-art computer simulations calibrated for the SARS-CoV-2 virus. The questions we address are these: (1) Will the ICU capacity in Chicago be exceeded, and if so by how much? (2) Can strong mitigation strategies, such as lockdown or shelter in place order, prevent the overflow of capacity? (3) When should such strategies be implemented? Our answers are as follows: (1) The ICU capacity may be exceeded by a large amount, probably by a factor of ten. (2) Strong mitigation can avert this …
The COVID-19 pandemic led several countries to resort to social distancing, the only known way to slow down the spread of the virus and keep the health system under control. Here we use an individual based model (IBM) to study how the duration, start date and intensity of quarantine affect the height and position of the peak of the infection curve. We show that stochastic effects, inherent to the model dynamics, lead to variable outcomes for the same set of parameters, making it crucial to compute the probability of each result. To simplify the analysis we divide the outcomes in only two categ…
By characterising the time evolution of COVID-19 in term of its "velocity" (log of the new cases per day) and its rate of variation, or "acceleration", we show that in many countries there has been a deceleration even before lockdowns were issued. This feature, possibly due to the increase of social awareness, can be rationalised by a susceptible-hidden-infected-recovered (SHIR) model introduced by Barnes, in which a hidden (isolated from the virus) compartment $H$ is gradually populated by susceptible people, thus reducing the effectiveness of the virus spreading. By introducing a partial hid…
In all Countries the political decisions aim to achieve an almost stable configuration with a small number of new infected individuals per day due to Covid-19. When such a condition is reached, the containment effort is usually reduced in favor of a gradual reopening of the social life and of the various economical sectors. However, in this new phase, the infection spread restarts and a quantitative analysis of the regrowth is very useful. We discuss a macroscopic approach which, on the basis of the collected data in the first lockdown, after few days from the beginning of the new phase, outli…
COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in significantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health as well as the economical and social textures, France and Italy governments have partially released lockdown measures. Here we extrapolate the long-term behavior of the epidemics in both countries using a Susceptible-Exposed-Infected-Recovered (SEIR) model where parameters are stochastically perturbed to handle the un…
Imported COVID-19 cases, if unchecked, can jeopardize the effort of domestic containment. We aim to find out what sustainable border control options for different entities (e.g., countries, states) exist during the reopening phases, given their own choice of domestic control measures and new technologies such as contact tracing. We propose a SUIHR model, which represents an extension to the discrete time SIR models. The model focuses on studying the spreading of virus predominantly by asymptomatic and pre-symptomatic patients. Imported risk and (1-tier) contact tracing are both built into the …
The infectious coronavirus disease 2019 (COVID-19) has become a serious global pandemic. Different studies have shown that increasing temperature can play a crucial role in the spread of the virus. Most of these studies were limited to winter or moderate temperature levels and were conducted using conventional models. However, traditional models are too simplistic to investigate complex, non-linear relationships and suffer from some restrictions. Therefore, we employed copula models to examine the impact of high temperatures on virus transmission. The findings from the copula models showed tha…
We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitati…
A compartmental epidemic model is proposed to predict the Covid-19 virus spread. It considers: both detected and undetected infected populations, medical quarantine and social sequestration, release from sequestration, plus possible reinfection. The coefficients in the model are evaluated by fitting to empirical data for eight US states: Arizona, California, Florida, Illinois, Louisiana, New Jersey, New York State, and Texas. Together these states make up 43% of the US population; some of these states appear to have handled their initial outbreaks well, while others appear to be emerging hotsp…
HKUST (University of Science & Technology)（香港科技大学）；International Computer Science Institute（国际计算机科学研究所）；Ecole de Guerre Economique（经济战争学院）；University of Cambridge（剑桥大学）；Manifold Research；University College London（伦敦大学学院）；ELU AI Ltd（ELU AI有限公司）；Royal Free Hospital（皇家自由医院）；Population Research Institute, The Family Federation of Finland（芬兰家庭联合会人口研究所）
We present two models for the COVID-19 pandemic predicting the impact of universal face mask wearing upon the spread of the SARS-CoV-2 virus--one employing a stochastic dynamic network based compartmental SEIR (susceptible-exposed-infectious-recovered) approach, and the other employing individual ABM (agent-based modelling) Monte Carlo simulation--indicating (1) significant impact under (near) universal masking when at least 80% of a population is wearing masks, versus minimal impact when only 50% or less of the population is wearing masks, and (2) significant impact when universal masking is …
A reaction-diffusion model was developed describing the spread of the COVID-19 virus considering the mean daily movement of susceptible, exposed and asymptomatic individuals. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, R0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of un…
We here propose to model active and cumulative cases data from COVID-19 by a continuous effective model based on a modified diffusion equation under Lifshitz scaling with a dynamic diffusion coefficient. The proposed model is rich enough to capture different aspects of a complex virus diffusion as humanity has been recently facing. The model being continuous it is bound to be solved analytically and/or numerically. So, we investigate two possible models where the diffusion coefficient associated with possible types of contamination are captured by some specific profiles. The active cases curve…
The COVID-19 pandemic has been a great catastrophe that upended human lives and caused millions of deaths all over the world. The rapid spread of the virus, with its early-stage exponential growth and subsequent 'waves', caught many medical professionals and decision-makers unprepared. Even though epidemiological models have been known for almost a century (since the 'Spanish Influenza' pandemic of 1918-20), the real-life spread of the SARS-CoV-2 virus often confounded the modelers. While the general framework of epidemiological models like SEIR (susceptible-exposed-infected-recovered) or SIR …
Analyzing the SARS-CoV-2 pandemic outbreak based on actual data while reflecting the characteristics of the real city provides beneficial information for taking reasonable infection control measures in the future. We demonstrate agent-based modeling for Tokyo based on GPS information and official national statistics and perform a spatiotemporal analysis of the infection situation in Tokyo. As a result of the simulation during the first wave of SARS-CoV-2 in Tokyo using real GPS data, the infection occurred in the service industry, such as restaurants, in the city center, and then the infected …
The last leg of the year 2019 gave rise to a virus named COVID-19 (Corona Virus Disease 2019). Since the beginning of this infection in India, the government implemented several policies and restrictions to curtail its spread among the population. As the time passed, these restrictions were relaxed and people were advised to follow precautionary measures by themselves. These timely decisions taken by the Indian government helped in decelerating the spread of COVID-19 to a large extent. Despite these decisions, the pandemic continues to spread and hence, there is an urgent need to plan and cont…
The spread of COVID-19 caused by the recently discovered SARS-CoV-2 virus has become a worldwide problem with devastating consequences. To slow down the spread of the pandemic, mass quarantines have been implemented globally, provoking further social and economic disruptions. Here, we implement a comprehensive contact tracing network analysis to find an optimized quarantine protocol to dismantle the chain of transmission of coronavirus with minimal disruptions to society. We track billions of anonymized GPS human mobility datapoints from a compilation of hundreds of mobile apps deployed in Lat…
A recent work (DOI 10.1101/2020.05.06.20093310) indicated that temporarily splitting larger populations into smaller groups can efficiently mitigate the spread of SARS-CoV-2 virus. The fact that, soon afterwards, on May 15, 2020, the two million people Slovenia was the first European country proclaiming the end of COVID-19 epidemic within national borders may be relevant from this perspective. Motivated by this evolution, in this paper we investigate the time dynamics of coronavirus cases in Slovenia with emphasis on how efficient various containment measures act to diminish the number of COVI…
This work provides an overview on deterministic and stochastic models that have previously been proposed by us to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Europe and USA. Briefly, we describe realistic deterministic and stochastic models for the evolution of the COVID-19 pandemic, subject to the lockdown and quarantine measures, which take into account the time-delay for recovery or death processes. Realistic dynamic equations for the entire process have been derived by adopting the so-called "kinetic-type reactions approach". The lockdown and the quarantin…
The COVID-19 has caused more than three million infections and over two hundred thousand deaths by April 20201. Limiting socioeconomic activities (SA) is among the most adopted governmental mitigating efforts to combat the transmission of the virus, though the degree varies dramatically among different regimes2. This study aims to quantify the contribution from the SA and weather conditions to the transmission of COVID-19 at global scale. Ruling out the unobservable factors including medical facilities and other control policies (MOC) through region-by-time fixed effects3,4, we show that the l…
Coronavirus disease (COVID-19) which is caused by SARS-COV2 has become a pandemic. This disease is highly infectious and potentially fatal, causing a global public health concern. To contain the spread of COVID-19, governments are adopting nationwide interventions, like lockdown, containment and quarantine, restrictions on travel, cancelling social events and extensive testing. To understand the effects of these measures on the control of the epidemic in a data-driven manner, we propose a probabilistic cellular automata (PCA) based modified SEIQR model. The transitions associated with the mode…
The very first case of corona-virus illness was recorded on 30 January 2020, in India and the number of infected cases, including the death toll, continues to rise. In this paper, we present short-term forecasts of COVID-19 for 28 Indian states and five union territories using real-time data from 30 January to 21 April 2020. Applying Holt's second-order exponential smoothing method and autoregressive integrated moving average (ARIMA) model, we generate 10-day ahead forecasts of the likely number of infected cases and deaths in India for 22 April to 1 May 2020. Our results show that the number …
As of November 2020, the number of COVID-19 cases is increasing rapidly in many countries. In Europe, the virus spread slowed considerably in the late spring due to strict lockdown, but a second wave of the pandemic grew throughout the fall. In this study, we first reconstruct the time evolution of the effective reproduction numbers ${\cal R}(t)$ for each country by integrating the equations of the classic SIR model. We cluster countries based on the estimated ${\cal R}(t)$ through a suitable time series dissimilarity. The result suggests that simple dynamical mechanisms determine how countrie…
