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On Using SIR Models to Model Disease Scenarios for COVID-19
... From (8) and (9), it follows that dS(t) dt From the last two equations, considering the speed of recovery dR(t) dt equal to the average of infected people to the moment of time t, defined in (4), we will get the differential equations system of model SIR of Kermack and McKendrick [9] that found the wide use; in particular, it was used for modeling of distribution of COVID-19 [2]: ...
... Also worth noting the presence of multicollinearity, which is an approximate linear dependence for the estimated parameters. It is expressed in the fact that in the neighborhood of the minimum of criterion (70) the surface F(a) is gently sloping that leads to the fact that for a (1) a (2) , it takes place that F(a (1) ) ≈ F(a (2) ). Multicollinearity was also noted for criterion (62). ...
... Also worth noting the presence of multicollinearity, which is an approximate linear dependence for the estimated parameters. It is expressed in the fact that in the neighborhood of the minimum of criterion (70) the surface F(a) is gently sloping that leads to the fact that for a (1) a (2) , it takes place that F(a (1) ) ≈ F(a (2) ). Multicollinearity was also noted for criterion (62). ...
Models of epidemic dynamics in the form of systems of differential equations of the type SIR and its generalizations, for example SEIR and SIRS, have become widespread in epidemiology. Their coefficients are averages of some epidemic indicators, for example the time when a person is contagious. Statistical data about spreading of the epidemic are known in discrete periods of time, for example twenty-four hours. Therefore, adjustment of the differential equations system under such data comes across cleanly calculable difficulties. They can be avoided, initially to build a model in discrete time as a system of difference equations. Such initial consideration allows, as it shown in the article, to get a general model. On its basis, the models of development of epidemics can be built taking into account their specific. There is another way to obtain a model in discrete time. It consists in discretizing the original model in continuous time. The model obtained in this way is inaccurate, and it is only an approximation to the original one, which makes it possible to simplify calculations and increase the stability of the calculation process. This model is inappropriate, for example, for fitting the model to statistical data. Another argument against the use of systems of differential equations is that the coefficients of such a model may not be the same during a day. For example, the number of contacts of an infected person with susceptible people during a day differs from that at night. However, there is no such difference for daily data. It is possible depending on the day of the week.
... Our paper also connects with recent work that enriches structural models from epidemiology, primarily the so-called Susceptible-Infected-Recovered (SIR) framework. The structural nature of the SIR model allows for the analysis of policy and counterfactual scenarios (e.g., Atkeson (2020), Fernández-Villaverde and Jones (2020), Hornstein (2020)). A hybrid approach is taken by Atkeson et al. (2020), who fit data on daily deaths to a mixture of Weibull functions to obtain a timevarying reproduction rate for an SIR model. ...
... However, the mapping between the different stages of the pandemic need not be fixed, as policies or individual decisions vary over time. Atkeson (2020) argues that statistical models without sufficient flexibility can face a similar problem by showing that the initial IHME model implicitly assumes a declining trend in the effective reproduction number of an SIR model. Our approach avoids such assumptions by decoupling the different phases of the pandemic through the various parameters. ...
We estimate a panel model with endogenously time-varying parameters for COVID-19 cases and deaths in U.S. states. The functional form for infections incorporates important features of epidemiological models but is flexibly parameterized to capture different trajectories of the pandemic. Daily deaths are modeled as a spike-and-slab regression on lagged cases. Our Bayesian estimation reveals that social distancing and testing have significant effects on the parameters. For example, a 10 percentage point increase in the positive test rate is associated with a 2 percentage point increase in the death rate among reported cases. The model forecasts perform well, even relative to models from epidemiology and statistics.
... In order to circumvent the parameter issue of classic SIR-derived methods while still allowing the mathematical model to cope with time-varying coefficients, the use of Machine Learning strategies has been a popular choice and a trend. Indeed, recent developments involving variable-parameter SIR variants to assess the course of Covid-19 can be found in [18][19][20][21][22][23][24][25][26][27][28], which include the use of effective Artificial Intelligence (AI) strategies, for example in [18,19,[29][30][31][32][33]. Following these recent efforts in modeling Covid-19 dynamics from epidemic models tuned with learning mechanisms, in this paper we propose an effective, data-driven SIR model whose parameters are fully calibrated by temporal functions, learned from individual regressors and trained on different data sources. ...
... The so-called effective reproduction number, R 0 (t) or R t , is an important epidemiological metric that quantifies the average number of new infections arising from a primary infected individual in the population [25,40]. In practice, R t measures the Covid-19 spread rate, and it changes as either the individuals gain immunity or die. ...
São Paulo is the most populous state in Brazil, home to around 22% of the country’s population. The total number of Covid-19-infected people in São Paulo has reached more than 1 million, while its total death toll stands at 25% of all the country’s fatalities. Joining the Brazilian academia efforts in the fight against Covid-19, in this paper we describe a unified framework for monitoring and forecasting the Covid-19 progress in the state of São Paulo. More specifically, a freely available, online platform to collect and exploit Covid-19 time-series data is presented, supporting decision-makers while still allowing the general public to interact with data from different regions of the state. Moreover, a novel forecasting data-driven method has also been proposed, by combining the so-called Susceptible-Infectious-Recovered-Deceased model with machine learning strategies to better fit the mathematical model’s coefficients for predicting Infections, Recoveries, Deaths, and Viral Reproduction Numbers. We show that the obtained predictor is capable of dealing with badly conditioned data samples while still delivering accurate 10-day predictions. Our integrated computational system can be used for guiding government actions mainly in two basic aspects: real-time data assessment and dynamic predictions of Covid-19 curves for different regions of the state. We extend our analysis and investigation to inspect the virus spreading in Brazil in its regions. Finally, experiments involving the Covid-19 advance in other countries are also given.
... Mathematical and computational models are key tools for understanding pandemic spread and designing intervention policies that help control a pandemic's spread (Atkeson 2020;Andraud et al. 2012). In particular, coupled ordinary and partial differential equations, as well as simpler growthcurve equations, are previously used to capture pandemic spread in general Kampmeijer and Zadoks 1997;Lazebnik 2023;Zhang et al. 2023;Asadi-Zeydabadi et al. 2021) and STD diseases spread, in particular (Liljeros et al. 2003;Galvin and Cohen 2004). ...
Sexually transmitted diseases (STDs) are a group of pathogens infecting new hosts through sexual interactions. Due to its social and economic burden, multiple models have been proposed to study the spreading of pathogens. In parallel, in the ever-evolving landscape of digital social interactions, the pervasive utilization of dating apps has become a prominent facet of modern society. Despite the surge in popularity and the profound impact on relationship formation, a crucial gap in the literature persists regarding the potential ramifications of dating apps usage on the dynamics of STDs. In this paper, we address this gap by presenting a novel mathematical framework - an extended Susceptible-Infected-Susceptible (SIS) epidemiological model to elucidate the intricate interplay between dating apps engagement and the propagation of STDs. Namely, as dating apps are designed to make users revisit them and have mainly casual sexual interactions with other users, they increase the number of causal partners, which increases the overall spread of STDS. Using extensive simulation, based on real-world data, explore the effect of dating apps adoption and control on the STD spread. We show that an increased adoption of dating apps can result in an STD outbreak if not handled appropriately.
... It would be also interesting to extend the model to analyze the joint dynamics of infection and economy-as done in the economics literature using macro-SIR models-and examine the effects of various policy interventions on both infection and economy. See, for example, [16,[28][29][30][31][32][33], among many others. We leave these interesting extensions for future research. ...
Many countries have experienced multiple waves of infection during the COVID-19 pandemic. We propose a novel but parsimonious extension of the SIR model, a CSIR model, that can endogenously generate waves. In the model, cautious individuals take appropriate prevention measures against the virus and are not exposed to infection risk. Incautious individuals do not take any measures and are susceptible to the risk of infection. Depending on the size of incautious and susceptible population, some cautious people lower their guard and become incautious—thus susceptible to the virus. When the virus spreads sufficiently, the population reaches “temporary” herd immunity and infection subsides thereafter. Yet, the inflow from the cautious to the susceptible eventually expands the susceptible population and leads to the next wave. We also show that the CSIR model is isomorphic to the SIR model with time-varying parameters.
... Various studies have been carried out to form a model for the spread of Covid-19, such as the SIR model. However, the dissemination medium taken in the previous SIR model such as in [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], and [22] still focuses on human-to-human interactions and has not considered the possibility of Coronavirus infection through inanimate objects . Thus, in this study we construct a new mathematical model in the form of a three-dimensional differential equation system that considers those two facts, i.e. the Coronavirus-to-human besides human-to-human interactions and the existence of Coronavirus in inanimate objects which can infect humans. ...
Covid-19 is a dangerous disease that is easily transmitted, both through living media in the form of interactions with infected human, as well as through inanimate objects in the form of surfaces contaminated with the Coronavirus. Various preventive and repressive efforts have been made to prevent the spread of this disease, such as isolating and recovering the infected human. In this study, the authors construct and analyze a new mathematical model in the form of a three-dimensional differential equations system that represent the interactions between subpopulations of coronavirus living on inanimate objects, susceptible human, and infected human within a population. The purpose of this study is to investigate the criteria that must be met in order to create a population free from Covid-19 by considering inanimate objects as a medium for its spread besides living objects. The model solution that represents the number of each subpopulation is non-negative and bounded, so it is in accordance with the biological condition that the number of subpopulations cannot be negative and there is always a limit for its value. The eradication rate of Coronavirus living on inanimate objects, the recovery rate of infected human, and the interaction rate between susceptible human and infected human such that the population is free from Covid-19 for any initial conditions of each subpopulation were investigated in this study through global stability analysis of the disease-free equilibrium point of the model.
... The most commonly used simple compartment models divide the population into compartments representing different states. These compartments are often assigned to Susceptible, Infected, and Recovered (SIR) statistics, while dynamics between them are modeled using differential equations [19]. Despite the use of compartment models to simulate epidemics initiated with [20], they have evolved significantly through the introduction of more detailed compartments and conditions used to analyze the dynamics more comprehensively [21]. ...
It is crucial to immediately curb the spread of a disease once an outbreak is identified in a pandemic. An agent-based simulator will enable policymakers to evaluate the effectiveness of different hypothetical strategies and policies with a higher level of granularity. This will allow them to identify vulnerabilities and asses the threat level more effectively, which in turn can be used to build resilience within the community against a pandemic. This study proposes a PanDemic SIMulator (PDSIM), which is capable of modeling complex environments while simulating realistic human motion patterns. The ability of the PDSIM to track the infection propagation patterns, contact paths, places visited, characteristics of people, vaccination, and testing information of the population allows the user to check the efficacy of different containment strategies and testing protocols. The results obtained based on the case studies of COVID-19 are used to validate the proposed model. However, they are highly extendable to all pandemics in general, enabling robust planning for more sustainable communities.
... We developed a combined epidemiological and economic model that can be optimized by adjusting control variables representing physical distancing and random testing with self-isolation policies. As with similar compartment-based models used in previous studies, the model used here is as parsimonious as possible while including enough detail to address our main research questions 41,42 . Descriptions of all parameters and the primary and low and high values used in our epi-econ model are provided in Table 3. ...
Two distinct strategies for controlling an emerging epidemic are physical distancing and regular testing with self-isolation. These strategies are especially important before effective vaccines or treatments become widely available. The testing strategy has been promoted frequently but used less often than physical distancing to mitigate COVID-19. We compared the performance of these strategies in an integrated epidemiological and economic model that includes a simple representation of transmission by “superspreading,” wherein a relatively small fraction of infected individuals cause a large share of infections. We examined the economic benefits of distancing and testing over a wide range of conditions, including variations in the transmissibility and lethality of the disease meant to encompass the most prominent variants of COVID-19 encountered so far. In a head-to-head comparison using our primary parameter values, both with and without superspreading and a declining marginal value of mortality risk reductions, an optimized testing strategy outperformed an optimized distancing strategy. In a Monte Carlo uncertainty analysis, an optimized policy that combined the two strategies performed better than either one alone in more than 25% of random parameter draws. Insofar as diagnostic tests are sensitive to viral loads, and individuals with high viral loads are more likely to contribute to superspreading events, superspreading enhances the relative performance of testing over distancing in our model. Both strategies performed best at moderate levels of transmissibility, somewhat lower than the transmissibility of the ancestral strain of SARS-CoV-2.
... The emerging empirical literature on the economic impact of the COVID-19 pandemic curtailment measures (national lockdown) has 7 THE IMPACT OF COVID-19 ON HOUSEHOLD WELFARE … 145 relied heavily on aggregated macro-level models and data. Atkeson (2020) evaluates the use of the SIR model to determine the lockdown measures associated with a less severe economic downturn and low contagion of the virus. The author's application of the model to the United States predicts social distancing of 12-18 months (in the absence of a vaccine) as the best measure, compared to a strict national lockdown. ...
Italy was the first European country to be hard hit by the SARS-CoV-2 virus pandemic. The country has a long history of disparities in wealth, health and socio-economic development between the Northern and the Central/Southern regions. The COVID-19 outbreak was higher in the richest areas of Italy, but the whole country suffered from increasing socio-economic and health inequalities. Existing health inequalities were exascerbated: mortality rates were higher for men than for women, widening the gender-based life expectancy gap. They were also higher among the elderly, particularly those living in care homes. However, the incidence of mental health conditions, and the demand for mental health care, is increasing, particularly among the younger generations.We find that the pandemic had a negative impact on access to healthcare, especially for some types of services. Regions with a higher per capita income and lower income inequality experienced lower reductions in access to specialized services. We find evidence of worsening inequalities in health and access to healthcare for some fragile population groups, the elderly and the migrants.We conclude that the pandemic highlighted the urgent need to address both pre-existing and newly emerging forms of socioeconomic inequaliy. The next generation European Union funds and the linked national recovery and resilience public investment are targeted to foster economic growth and overcome the structural, geographic, socio-economic and health divide in Italy. The success of this will depend on the effectiveness of the National Recovery and Resilience Plan, on the capacity to improve public investment governance, and on the post-pandemic growth the country will experience.
... Thus, one should show that the proposed Spatio-temporal epidemiological sub-model (see Sections 2.1 and 2.2) and the economic sub-model are well representing the epidemiological and economic dynamics in the discussed case. Indeed, a large body of work conducted supports these claims [41][42][43][44][45][46][47][48][49][50][51]. Hence, one can treat the following results as a good approximation while taking caution due to stochastic nature of the dynamics. ...
During a global epidemiological crisis, lockdowns and border closures substantially disrupt international supply chains, underscoring the importance of choosing an intervention policy that accounts for the unique structure of input-output linkages among domestic industries. This study develops a pioneering mathematical model to quantify the role of pandemic-related intervention policies in the economic impact of a pandemic outbreak in an economy where sectors are complements throughout input-output networks. Our approach is based on three pillars - epidemiological, social, and economic sub-models. Moreover, we present in silico computer simulations to examine the influence of work capsules, work-from-home, vaccination, and industry closure on the damage a pandemic could inflict on output at the industry level. A comparison between work capsules and work-from-home policies shows that the latter decreases economic loss much more than the former. Compared to a state without interventions, a work-from-home policy affecting 12% of the workforce will decrease output loss by 1.4 percentage points during an epidemiological crisis following a COVID-19-like outbreak. Under the constraint of choosing one intervention policy, vaccination significantly reduces the loss of output, particularly in industries that require close customer-seller contacts. In the analysis of scenarios of integrating intervention policies, it is found that, using direct marginal contribution as the measure, the vaccination intervention is approximately 4.5 times more effective in reducing output loss than the work-from-home intervention.
... Recovered state consists of individuals who have immunity from a vaccine or acquired immunity and died people. Several investigating of COVID-19 SIR model are studied in [10][11][12]. The models are in the form of system of three nonlinear ordinary differential equations (ODEs). ...
In this paper, we propose a COVID-19 epidemic model with quarantine class. The model contains 6 sub-populations, namely the susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and death (D) sub-populations. For the proposed model, we show the existence, uniqueness, non-negativity, and boundedness of solution. We obtain two equilibrium points, namely the disease-free equilibrium (DFE) point and the endemic equilibrium (EE) point. Applying the next generation matrix, we get the basic reproduction number (R 0). It is found that R 0 is inversely proportional to the quarantine rate as well as to the recovery rate of infected sub-population. The DFE point always exists and if R 0 < 1 then the DFE point is asymptotically stable, both locally and globally. On the other hand, if R 0 > 1 then there exists an EE point, which is globally asymptotically stable. Here, there occurs a forward bifurcation driven by R 0. The dynamical properties of the proposed model have been verified our numerical simulations.
... With the recent COVID-19 pandemic, attempts have also been made to explain the structure of the underlying virus, how it spreads, prevention measures, containment and diagnostic protocols, vaccines and the global impact [11][12][13]. The vast majority of papers have employed the SIR model to predict the spread of the pandemic or the number of COVID-19 cases [14][15][16][17][18]. Other papers employed the SEIR model [19][20][21], and others were also found that refer to the SI [22,23] or SIS model [24,25]. ...
Mathematical modeling has served as an epidemiological tool to enhance the modeling efforts of the social and economic impacts of the pandemic. This article reviews epidemiological network models, which are conceived as a flexible way of representing objects and their relationships. Many studies have used these models over the years, and they have also been used to explain COVID-19. Based on the information provided by the Web of Science database, exploratory, descriptive research based on the techniques and tools of bibliometric analysis of scientific production on epidemiological network models was carried out. The epidemiological models used in the papers are diverse, highlighting those using the SIS (Susceptible-Infected-Susceptible), SIR (Susceptible-Infected-Recovered) and SEIR (Susceptible-Exposed-Infected-Removed) models. No model can perfectly predict the future, but they provide a sufficiently accurate approximation for policy makers to determine the actions needed to curb the pandemic. This review will allow any researcher or specialist in epidemiological modeling to know the evolution and development of related work on this topic.
... Andrew G. Atkeson has introduced a simple SIR model of the progression of COVID-19 to aid understanding of how such a model might be incorporated into more standard macroeconomic models. He allows quantitative statements regarding the tradeoff between the severity and timing of suppression of the disease through social distancing and the progression of the disease in the population (Atkeson, 2020). ...
Due to the recent threatening pandemic COVID-19, the research area of this disease is increasing. This paper tries to establish COVID-19 infection transmission by Susceptible-Infectious-Recovered (SIR) compartmental model for epidemic prediction and prevention. The model is built based on the secondary data of the infected persons and discharged patients. It is considered as a valuable tool in public health sector, as it can provide suggestions about the fatality of pandemic to take necessary actions for preventing the infections. COVID-19 is spreading worldwide extremely, and at present it becomes both local and global concern. This model can show the fatality of COVID-19 with time and can predict whether the disease will further spread or abolish completely. This study stresses on vaccination to reduce the infection of the disease. It can provide how many people are needed to be vaccinated to create herd immunity against COVID-19. Overtime the immunity due to vaccination may decrease and after a fixed period the immunity of COVID-19 due to vaccination may extinct completely. The article attempts to give a mathematical presentation to aware the immunity loss individuals with other susceptible. It also tries to alert the people about the re-infection of the previous COVID-19 infected persons. The aim of this study is to minimize both global economic losses and deaths due to COVID-19.
... We set the infection fatality rate π D / (π R + π D ) to 0 . 032% as reported in table 2 for Bogotá and impose π R + π D = 7 / 18 , following Atkeson (2020) . This gives us two equations that pin down π D and π R . ...
We document the heterogeneous effect of covid-19 on health and economic outcomes across socioeconomic strata in Bogotá. We assess its distributional impact and evaluate policy counterfactuals in an heterogeneous agent quantitative dynamic general equilibrium model intertwined with a behavioral epidemiological model.
... Pandeminin makroekonomik sonuçlarını araştıran ve değişik senaryolarda sürecin ilerleyişi hakkında tahminde bulunan küresel, bölgesel veya ülke bazında bir çok çalışma yapılmıştır (Almeida vd., 2021;Atkeson, 2020;Fornaro ve Wolf, 2020;Malliet, Reynès, Landa, Hamdi-Cherif ve Saussay, 2020). Fernandes (2020) (2021) çalışmalarında, Dünya'nın 8 büyük ekonomisi (Amerika Birleşik Devletleri, Meksika, Almanya, İtalya, İspanya, Fransa, Hindistan ve Japonya) üzerine 2020 yılı GSYİH'ları için yaptıkları tahminler şu şekildedir; Amerika Birleşik Devletleri (%-10.53), ...
... SeeAtkeson (2020) andMoll (2020) for the exposition of SIR models. ...
We build a tractable SIR-macro-model with time-varying parameters and use it to explore various policy questions such as when to lift the state of emergency (SOE). An earlier departure from the SOE results in smaller output loss and more deaths in the short run. However, if the SOE is lifted too early, the number of new cases will surge and another SOE may need to be issued in the future, possibly resulting in both larger output loss and more deaths. That is, the tradeoff between output and infection that exists in the short run does not necessarily exist in the long run. Our model-based analysis—updated weekly since January 2021, frequently reported by media, and presented to policymakers on many occasions—has played a unique role in the policy response to the COVID-19 crisis in Japan.
... Many tools and methods were used by researchers in these scenarios, including predictions based on the Bayesian model [52,53], SIR models [54,55], an agent-based model and a deterministic compartmental model [56], fractional models [57], and a modified SEIR compartmental model [58]. ...
The article presents a prediction regarding the development of passenger transport services, considering random factors related to the COVID-19 pandemic situation, based on scenario methods. The SARS-CoV-2 coronavirus pandemic has significantly affected the way passenger transport services are provided, mainly due to sanitary restrictions imposed by epidemiological services. At the same time, the communication behaviour of travellers has also changed, which in turn has influenced the demand for these services. The following study investigates transport service future development issues from multiple perspectives, including demand analysis, the selection of major factors influencing the development of passenger transport for individual Polish passengers using an online questionnaire, and scenario designs. The main purpose of this article is to build various scenarios for the development of passenger transport, considering changes in the demand for these services and factors related to their perception by the users of the means of transport. The main factors influencing the future development of passenger transport and the possible scenarios can support public transport service providers in planning their services in the post-shutdown phase as well as in their respective modelling development requirements. This can support the planning process with decision-making based on future behavioural trends.
... AA writer Peterson Ozili's paper called "Spillover of COVID-19: Impact on the Global Economy" explains the economic progress with financial strategies, safety measures, and travel rules and regulations [13]. The author known as Andrew Atkeson wrote a paper called "What will be the Economic Impact of Covid-19 in the US? Rough Estimates of Disease Scenarios" which uses the SIR model for predicting the future of this disastrous pandemic [14]. Nevertheless, the relationship between increasing cases of Covid and the economic loss is not discussed. ...
The pandemic of Covid-19 which started in the year 2019 did not just cause an effect on the living of millions of people but in the economic and social sectors of every part of the world as well. It is a challenging task to determine the interrelation between COVID-19 cases with respect to the economy in the top affected countries. This paper explores; how severe Impact of COVID-19 1st wave on the economic facets of Pakistan as compared to the Top Fifteen affected countries. Moreover, this paper uses COVID-19 well-known dataset provided by John Hopkins and Stock Market Datasets collectively to carry out the critical analysis successfully. We found a relationship between the cumulative numbers of confirmed cases in each country with a declining state of countries' economies: the higher decline in the stock market indicates a higher number of confirmed cases.
... 17 In addition, the SEIR model relies on the fact that there is no power to stop epidemics other than community acquisition of herd immunity. 18 Henceforward, it can be said that in order to deal with the disease, a suitable and reliable vaccine must be available, which has begun to emerge now, where a set of vaccines have been distributed in many countries to limit the spread of the disease in the long run. This result is consistent with the findings of Uzma 19 through a follow-up of the behavior of the MERS-CoV virus, which is of the same strain as Covid-19. ...
Saudi Arabia, like any other part of the earthly globe, has been exposed to the Covid-19 pandemic. The first case appeared on March 3, 2020, followed by an increase in the number of infections until it reached thousands with the numbers on the rise. Therefore, adopting clear strategies to deal with the pandemic according to specific data on its size is necessary. In this study, the time series of the number of infections and deaths were analyzed to study the behavior of the pandemic over time. The cumulative curve of the phenomenon was analyzed to show the extent of the pandemic's decline or spread. On the other hand, the time curve of the number of cases of the pandemic was fitted based on a set of mathematical and statistical models, which were divided into three sections [nonlinear growth model, Susceptible, Exposed, Infectious, Recovered (SEIR) model, regression model] to attain the best possible fitting of the relationship curve. The results show that the Weibull model and Polynomial model at (n = 4) are the best models for fitting the relationship at short run and the SEIR model gives better relationship fitting at long run. In conclusion, there is a tendency for the disease to decline during the short period, while expecting other waves of the epidemic that will recede in the long term with the emergence of a suitable vaccine.
... While we do not impose the specific relationships that are implied by theoretical models drawn from epidemiology (e.g. Atkeson, 2020;Eichenbaum, Rebelo, and Trabandt, 2020;Fernández-Villaverde and Jones, 2020), we let our choice of functional forms be guided by the typical behavior of an infectious disease over time. This allows us to gain flexibility in modeling the epidemic and thereby avoid the potential pitfalls of imposing strict behavior of the contagion. ...
We estimate a statistical model for COVID-19 cases and deaths in New Zealand. New Zealand is an important test case for statistical and theoretical research into the dynamics of the global pandemic since it went through a full cycle of infections. We choose functional forms for infections and deaths that incorporate important features of epidemiological models but allow for flexible parameterization to capture different trajectories of the pandemic. Our Bayesian estimation reveals that the simple statistical framework we employ fits the data well and allows for a transparent characterization of the uncertainty surrounding the trajectories of infections and deaths.
... All these models and estimations aim to help the public and decision-makers derive strategies to prevent the disease's harmful effects. Atkeson (2020) and Atkeson et al. (2020), intended to introduce economists to a simple SIR model of the progression of COVID-19 in the United States over the one / one and a half years' perspective and tried to answer the question that how countrybased mitigation measures influence the course of the COVID-19 epidemic. Moreover, Anderson et. ...
... The projected number of closed cases at the end of the epidemic is around 3.7 million. 26 For the other three countries, the sensitivity of the out-of sample projections to the value of κ is much lower because θ T is already close to 1.0 (China and Brazil) or because the number of infections is well past the peak (Italy Atkeson (2020c) provides a simplified example of IHME's pre-May 4 forecasting approach. He shows that when mapped into the daily number of deaths predicted by a simple SIRD model, the IHME's approach implies an effective reproduction number that falls linearly over time, possibly resulting in an optimistic forecast if the declining time trend does not materialize in practice. ...
We study the impact of socioeconomic factors on two key parameters of epidemic dynamics. Specifically, we investigate a parameter capturing the rate of deceleration at the very start of an epidemic, and a parameter that reflects the pre-peak and post-peak dynamics at the turning point of an epidemic like coronavirus disease 2019 (COVID-19). We find two important results. The policies to fight COVID-19 (such as social distancing and containment) have been effective in reducing the overall number of new infections, because they influence not only the epidemic peaks, but also the speed of spread of the disease in its early stages. The second important result of our research concerns the role of healthcare infrastructure. They are just as effective as anti-COVID policies, not only in preventing an epidemic from spreading too quickly at the outset, but also in creating the desired dynamic around peaks: slow spreading, then rapid disappearance.
We investigate the contagion of US COVID-19 panic news, measured by the sentiment-based RavenPack US Panic Index, on the local stock market returns of 48 countries. Local stock market returns are found to be more significantly negatively associated with the US panic news than local panic news. Our results show that a 1% increase in the US Panic Index reduces local stock returns by 1.44%. The result holds for regional and subregional groupings and are robust to alternative measures of COVID-19 information. Furthermore, our contagion channel analysis shows that the differences of opinion channel is the key contagion transmission channel from the US to local markets. This alludes to the investor behavior contagion view, and not the fundamental contagion view, being the main driver of global contagion during the pandemic.
This study examines the relationship between the COVID-19 pandemic and stock returns. We find that pandemic risk is a significant determinant of cross-sectional stock returns. The time-varying effective reproduction number from the susceptible-infectious-recovered epidemic model is introduced as a proxy measure for COVID-19 risk. The two-step generalized method of moments estimation results indicate that the COVID-19 factor commands a significant positive risk premium. The results are robust to different test assets, serial interval parameters, portfolio construction methods and alternative proxy measures, providing strong empirical evidence that the COVID-19 factor is a priced risk factor during the COVID-19 pandemic.
We develop a Bayesian method for estimating the dynamics of COVID‐19 deaths and discover four key findings that expose the limitations of current structural epidemiological models. (1) Death growth rates declined rapidly from high levels during the initial 30 days of the epidemic worldwide. (2) After this initial period, these rates fluctuated substantially around zero percent. (3) The cross‐location standard deviation of death growth rates decreased rapidly in the first 10 days but remained high afterwards. (4) These insights apply to both effective reproduction numbers and their cross‐location variability through epidemiological models. Our method is applicable to studying other epidemics.
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This paper studies containment policies for combating a pandemic in an open-economy context. It does so via quantitative analyses using a model that incorporates a standard epidemiological compartmental model in a general equilibrium multi-country, multi-sector Ricardian model of international trade with input–output linkages. We quantitatively evaluate the long-run welfare and real-income losses due to the short-run pandemic shocks, and we study the role of trade in these effects. We devise a novel approach to computing national optimal policies. We find that (1) the long-run welfare and real-income losses due to just two years of pandemic shocks are substantial; (2) international trade helps buffer both the welfare and real-income losses, and it also saves lives; (3) the computed optimal policies indicate that most countries should have tightened their containment measures relative to what was done; and (4) compared to the case of autarky, the optimal policy under trade is generally more stringent.
It is crucial to immediately curb the spread of a disease once an outbreak is identified in a pandemic. An agent based simulator will enable the policymakers to evaluate the effectiveness of different hypothetical strategies and policies with a higher level of granularity. This will allow them to identify the vulnerabilities and asses the threat level more effectively, which in turn can be used to build resilience within the community against a pandemic. This study proposes a PanDemic SIMulator (PDSIM ) which is capable of modeling complex environments while simulating realistic human motion patterns. The ability of PDSIM to track the infection propagation patterns, contact paths, places visited, characteristics of people, vaccination, and testing information of the population, allows the user to check the efficacy of different containment strategies and testing protocols. The results obtained based on the case studies of Covid-19 are used to validate the proposed model. However, it is highly extendable to all pandemics in general, enabling robust planning for more sustainable communities.
This chapter investigates the impact of COVID-19 on the Comoros’s household welfare, poverty, and labor market outcomes. The lockdown policy coincided with data collection for the 2020 Harmonized Survey on Living Conditions of Households, lending itself to a quasi-natural experiment in which households that were interviewed before the lockdown fall into the control group, while those that were interviewed after the lockdown fall into the treated group. The chapter uses matching techniques and finds a reduction in household expenditure, increased poverty, and lower likelihood of employment. Impacts are larger at the top of the distribution suggesting COVID-19 may have reduced inequality, although the poor were also negatively affected. Additionally, the ability of households to use assets as a coping mechanism was limited. In a context of limited safety nets and government interventions, stringent lockdown policies appear to increase the vulnerability of the existing poor and push others into poverty.
We introduce a model of the diffusion of an epidemic with demographically heterogeneous agents interacting socially on a spatially structured network. Contagion-risk averse agents respond behaviorally to the diffusion of the infections by limiting their social interactions. Schools and workplaces also respond by allowing students and employees to attend and work remotely. The spatial structure induces local herd immunities along socio-demographic dimensions, which significantly affect the dynamics of infections. We study several non-pharmaceutical interventions; e.g., i) lockdown rules, which set thresholds on the spread of the infection for the closing and reopening of economic activities; ii) neighborhood lockdowns, leveraging granular (neighborhood-level) information to improve the effectiveness public health policies; iii) selective lockdowns, which restrict social interactions by location (in the network) and by the demographic characteristics of the agents. Substantiating a “Lucas critique” argument, we assess the cost of naive discretionary policies ignoring agents and firms’ behavioral responses.
We analyze how poverty and a country’s fiscal space impact policy and welfare in times of a pandemic. We introduce a subsistence level of consumption into a tractable heterogeneous agent framework, and use this framework to characterize optimal joint policies of a lockdown and transfer payments. In our model, a more stringent lockdown helps fighting the pandemic, but it also deepens the recession, which implies that poorer parts of society find it harder to subsist. This reduces their compliance with the lockdown, and may cause deprivation of the very poor, giving rise to an excruciating trade-off between saving lives from the pandemic and from deprivation. Transfer payments help mitigate this trade-off. We show that, ceteris paribus, the optimal lockdown is stricter in richer countries and the aggregate death burden and welfare losses smaller. We then consider a government borrowing constraint and show that limited fiscal space lowers the optimal lockdown and welfare, and increases the aggregate death burden during the pandemic. This is particularly true in societies where a larger fraction of the population is in poverty. We discuss evidence from the literature and provide reduced-form regressions that support the relevance of our main mechanisms. We finally discuss distributional consequences and the political economy of fighting a pandemic.
We analyze lending by traditional as well as fintech lenders during COVID-19. Comparing samples of fintech and bank loan records across the outbreak, we find that fintech companies are more likely to expand credit access to new and financially constrained borrowers after the start of the pandemic. However, this increased credit provision may not be sustainable; the delinquency rate of fintech loans triples after the outbreak, but there is no significant change in the delinquency of bank loans. Borrowers holding both loan types prioritize the payment of bank loans. These results shed light on the benefits provided by shadow banking in a crisis and hint at the potential fragility of such institutions when delinquency rates spike.
This work is concerned with the spatiotemporal dynamics of the coronavirus disease 2019 (COVID-19) in Germany. Our goal is twofold: first, we propose a novel spatial econometric model of the epidemic spread across NUTS-3 regions to identify the role played by commuting-to-work patterns for spatial disease transmission. Second, we explore if the imposed containment (lockdown) measures during the first pandemic wave in spring 2020 have affected the strength of this transmission channel. Our results from a spatial panel error correction model indicate that, without containment measures in place, commuting-to-work patterns were the first factor to significantly determine the spatial dynamics of daily COVID-19 cases in Germany. This indicates that job commuting, particularly during the initial phase of a pandemic wave, should be regarded and accordingly monitored as a relevant spatial transmission channel of COVID-19 in a system of economically interconnected regions. Our estimation results also provide evidence for the triggering role of local hot spots in disease transmission and point to the effectiveness of containment measures in mitigating the spread of the virus across German regions through reduced job commuting and other forms of mobility.
Supplementary information:
The online version contains supplementary material available at 10.1007/s10109-021-00349-3.
This paper studies optimal containment policy for combating a pandemic in an open- economy context. It does so via quantitative analyses using a model that incorporates a standard epidemiological compartmental model in a multi-country, multi-sector Ricardian model of international trade with full-fledged input-output linkages. We devise a novel approach in computing optimal national policies in the long run, and contrast these policies with a baseline in which countries maintain their current policies until vaccine availability. The welfare gains under optimal policies are asymmetric as the gains for the set of countries which should tighten up the containment measures are much larger than those which should relax. We also find that the welfare implications of optimal policies in open economies differ significantly from those in closed ones.
Many of the models used to track, forecast, and inform the response to epidemics such as COVID-19 assume that everyone has an equal chance of encountering those who are infected with a disease. But this assumption does not reflect the fact that individuals interact mostly within much narrower groups. We argue that incorporating a network perspective, which accounts for patterns of real-world interactions, into epidemiological models provides useful insights into the spread of infectious diseases.
We demonstrate a methodology for replicating and projecting the path of COVID-19 using a simple epidemiology model. We fit the model to daily data on the number of infected cases in China, Italy, the United States, and Brazil. These four countries can be viewed as representing different stages, from later to earlier, of a COVID-19 epidemic cycle. We solve for a model-implied effective reproduction number
R
t
each day so that the model closely replicates the daily number of currently infected cases in each country. For out-of-sample projections, we fit a behavioral function to the in-sample data that allows for the endogenous response of
R
t
to movements in the lagged number of infected cases. We show that declines in measures of population mobility tend to precede declines in the model-implied reproduction numbers for each country. This pattern suggests that mandatory and voluntary stay-at-home behavior and social distancing during the early stages of the epidemic worked to reduce the effective reproduction number and mitigate the spread of COVID-19.
This paper considers a modification of the standard Susceptible-Infected-Recovered (SIR) model of epidemic that allows for different degrees of compulsory as well as voluntary social distancing. It is shown that the fraction of population that self-isolates varies with the perceived probability of contracting the disease. Implications of social distancing both on the epidemic and recession curves are investigated and their trade off is simulated under a number of different social distancing and economic participation scenarios. We show that mandating social distancing is very effective at flattening the epidemic curve, but is costly in terms of employment loss. However, if targeted towards individuals most likely to spread the infection, the employment loss can be somewhat reduced. We also show that voluntary self-isolation driven by individual's perceived
risk of becoming infected kicks in only towards the peak of the epidemic and has little or no impact on flattening the epidemic curve. Using available statistics and correcting for measurement errors, we estimate the rate of exposure to COVID-19 for 21 Chinese provinces and a selected number of countries. The exposure rates are generally small, but vary considerably between Hubei and other Chinese provinces as well as across countries. Strikingly, the exposure rate in Hubei province is around 40 times larger than the rates for other Chinese provinces, with the exposure rates for some European countries being 3-5 times larger than Hubei (the epicenter of the epidemic). The paper also provides country-specific estimates of the recovery rate, showing it to be about 21 days (a week longer than the 14 days typically assumed), and relatively homogeneous across Chinese provinces and for a selected number of countries.
What happens next?
Four months into the severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2) outbreak, we still do not know enough about postrecovery immune protection and environmental and seasonal influences on transmission to predict transmission dynamics accurately. However, we do know that humans are seasonally afflicted by other, less severe coronaviruses. Kissler et al. used existing data to build a deterministic model of multiyear interactions between existing coronaviruses, with a focus on the United States, and used this to project the potential epidemic dynamics and pressures on critical care capacity over the next 5 years. The long-term dynamics of SARS-CoV-2 strongly depends on immune responses and immune cross-reactions between the coronaviruses, as well as the timing of introduction of the new virus into a population. One scenario is that a resurgence in SARS-CoV-2 could occur as far into the future as 2025.
Science , this issue p. 860
The outbreak of coronavirus named COVID-19 has disrupted the Chinese economy and is spreading globally. The evolution of the disease and its economic impact is highly uncertain which makes it difficult for policymakers to formulate an appropriate macroeconomic policy response. In order to better understand possible economic outcomes, this paper explores seven different scenarios of how COVID-19 might evolve in the coming year using a modelling technique developed by Lee and McKibbin (2003) and extended by McKibbin and Sidorenko (2006). It examines the impacts of different scenarios on macroeconomic outcomes and financial markets in a global hybrid DSGE/CGE general equilibrium model.
The scenarios in this paper demonstrate that even a contained outbreak could significantly impact the global economy in the short run. These scenarios demonstrate the scale of costs that might be avoided by greater investment in public health systems in all economies but particularly in less developed economies where health care systems are less developed and population density is high.
In a simple susceptible-infected-recovered (SIR) model, the initial speed at which infected cases increase is indicative of the long-term trajectory of the outbreak. Yet during real-world outbreaks, individuals may modify their behavior and take preventative steps to reduce infection risk. As a consequence, the relationship between the initial rate of spread and the final case count may become tenuous. Here, we evaluate this hypothesis by comparing the dynamics arising from a simple SIR epidemic model with those from a modified SIR model in which individuals reduce contacts as a function of the current or cumulative number of cases. Dynamics with behavior change exhibit significantly reduced final case counts even though the initial speed of disease spread is nearly identical for both of the models. We show that this difference in final size projections depends critically in the behavior change of individuals. These results also provide a rationale for integrating behavior change into iterative forecast models. Hence, we propose to use a Kalman filter to update models with and without behavior change as part of iterative forecasts. When the ground truth outbreak includes behavior change, sequential predictions using a simple SIR model perform poorly despite repeated observations while predictions using the modified SIR model are able to correct for initial forecast errors. These findings highlight the value of incorporating behavior change into baseline epidemic and dynamic forecast models.
In this paper, the exact analytical solution of the
Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric
form. By using the exact solution we investigate some explicit models
corresponding to fixed values of the parameters, and show that the numerical
solution reproduces exactly the analytical solution. We also show that the
generalization of the SIR model, including births and deaths, described by a
nonlinear system of differential equations, can be reduced to an Abel type
equation. The reduction of the complex SIR model with vital dynamics to an Abel
type equation can greatly simplify the analysis of its properties. The general
solution of the Abel equation is obtained by using a perturbative approach, in
a power series form, and it is shown that the general solution of the SIR model
with vital dynamics can be represented in an exact parametric form.
This paper fully characterizes the optimal control of a recurrent infectious disease through the use of (non-vaccine) prevention and treatment. The dynamic system may admit multiple steady states and the optimal policy may be path dependent. We find that an optimal path cannot end at a point with maximal prevention; it is necessarily zero or at an intermediate level. In contrast, an optimal path must end at a point at which treatment is either maximal or minimal. We find that the comparative statics of the model may radically differ across steady states, which has important policy implications. Last, we consider the model with decentralized decision making and compare the equilibrium outcomes with the socially optimal outcomes. We find that steady state prevalence levels in decentralized equilibrium must be equal to or higher than the socially optimal levels. While steady state treatment levels under decentralization are typically socially optimal, steady state prevention (if used) is socially suboptimal.
Severe acute respiratory syndrome (SARS) has been the first severe contagious disease to emerge in the 21st century. The available epidemic curves for SARS show marked differences between the affected regions with respect to the total number of cases and epidemic duration, even for those regions in which outbreaks started almost simultaneously and similar control measures were implemented at the same time. The authors developed a likelihood-based estimation procedure that infers the temporal pattern of effective reproduction numbers from an observed epidemic curve. Precise estimates for the effective reproduction numbers were obtained by applying this estimation procedure to available data for SARS outbreaks that occurred in Hong Kong, Vietnam, Singapore, and Canada in 2003. The effective reproduction numbers revealed that epidemics in the various affected regions were characterized by markedly similar disease transmission potentials and similar levels of effectiveness of control measures. In controlling SARS outbreaks, timely alerts have been essential: Delaying the institution of control measures by 1 week would have nearly tripled the epidemic size and would have increased the expected epidemic duration by 4 weeks.
The reproduction number, R, defined as the average number of secondary cases generated by a primary case, is a crucial quantity for identifying the intensity of interventions required to control an epidemic. Current estimates of the reproduction number for seasonal influenza show wide variation and, in particular, uncertainty bounds for R for the pandemic strain from 1918 to 1919 have been obtained only in a few recent studies and are yet to be fully clarified. Here, we estimate R using daily case notifications during the autumn wave of the influenza pandemic (Spanish flu) in the city of San Francisco, California, from 1918 to 1919. In order to elucidate the effects from adopting different estimation approaches, four different methods are used: estimation of R using the early exponential-growth rate (Method 1), a simple susceptible-exposed-infectious-recovered (SEIR) model (Method 2), a more complex SEIR-type model that accounts for asymptomatic and hospitalized cases (Method 3), and a stochastic susceptible-infectious-removed (SIR) with Bayesian estimation (Method 4) that determines the effective reproduction number Rt at a given time t. The first three methods fit the initial exponential-growth phase of the epidemic, which was explicitly determined by the goodness-of-fit test. Moreover, Method 3 was also fitted to the whole epidemic curve. Whereas the values of R obtained using the first three methods based on the initial growth phase were estimated to be 2.98 (95% confidence interval (CI): 2.73, 3.25), 2.38 (2.16, 2.60) and 2.20 (1.55, 2.84), the third method with the entire epidemic curve yielded a value of 3.53 (3.45, 3.62). This larger value could be an overestimate since the goodness-of-fit to the initial exponential phase worsened when we fitted the model to the entire epidemic curve, and because the model is established as an autonomous system without time-varying assumptions. These estimates were shown to be robust to parameter uncertainties, but the theoretical exponential-growth approximation (Method 1) shows wide uncertainty. Method 4 provided a maximum-likelihood effective reproduction number 2.10 (1.21, 2.95) using the first 17 epidemic days, which is consistent with estimates obtained from the other methods and an estimate of 2.36 (2.07, 2.65) for the entire autumn wave. We conclude that the reproduction number for pandemic influenza (Spanish flu) at the city level can be robustly assessed to lie in the range of 2.0-3.0, in broad agreement with previous estimates using distinct data.
We use data on deaths in New York City, Madrid, Stockholm, and other world cities as well as in various U.S. states and other regions and countries to estimate, quickly and with limited data, a standard epidemiological model of COVID-19. We allow for a time-varying contact rate in order to capture behavioral and policy-induced changes associated with social distancing. We simulate the model forward to consider possible scenarios for various countries, states, and cities, including the potential impact of herd immunity on re-opening.
We carry out some analysis of the daily data on the number of new cases and the number of new deaths by (191) countries as reported to the European Centre for Disease Prevention and Control (ECDC). Our benchmark model is a quadratic time trend model applied to the log of new cases for each country. We use our model to predict when the peak of the epidemic will arise in terms of new cases or new deaths in each country and the peak level. We also predict how long the number of new daily cases in each country will fall by an order of magnitude. Finally, we also forecast the total number of cases and deaths for each country. We consider two models that link the joint evolution of new cases and new deaths.
The spread of the coronavirus SARS-CoV-2 has predictable features
Policies of isolating infectives in the general stochastic epidemic are considered. With costs assigned to the infection and isolation of individuals, an optimal policy is found, which at any stage minimises the expected future cost. An optimal policy is also found for the general deterministic epidemic and the two policies are compared. Finally, some numerical examples are provided.
The threat of an influenza pandemic has alarmed countries around the globe and given rise to an intense interest in disease mitigation measures. This article reviews what is known about the effectiveness and practical feasibility of a range of actions that might be taken in attempts to lessen the number of cases and deaths resulting from an influenza pandemic. The article also discusses potential adverse second- and third-order effects of mitigation actions that decision makers must take into account. Finally, the article summarizes the authors' judgments of the likely effectiveness and likely adverse consequences of the range of disease mitigation measures and suggests priorities and practical actions to be taken.
Rachel 2020, and Toda 2020. See Abakuks 1972 for an early application of optimal control to the study of epidemics. See also Farboodi
- See
- Argente Alvarez
See, for example, Alvarez, Argente, and Lippi 2020, Rachel 2020, and Toda 2020. See Abakuks
1972 for an early application of optimal control to the study of epidemics. See also Farboodi, Jarosch,
and Shimer 2020 and Kruse and Strack 2020.
for discussions of how to estimate the effective reproduction number from case data. 28. In the United States, during April, the number of diagnostic tests being conducted every day is growing, at best, at a linear rather than exponential rate
- Nishiura Chowell
- Bettencourt
See Wallinga and Teunis 2004 and Chowell, Nishiura, and Bettencourt 2007 for discussions of
how to estimate the effective reproduction number from case data.
28. In the United States, during April, the number of diagnostic tests being conducted every day
is growing, at best, at a linear rather than exponential rate. Time series data on tests performed are
available here: https://covidtracking.com/data/us-daily.
29. See https://www.economist.com/graphic-detail/2020/04/16/trackingcovid-19-excess-deaths-across-countries for a discussion of the extent to which
data on deaths due to COVID-19 are accurately measured. Also see https://www.cdc.gov/
nchs/nvss/vsrr/covid19/tech_notes.htm for provisional estimates of excess mortality
in the United States.
30. Thanks to James Stock for pointing out this calculation.
31. This discussion substantially extends Atkeson 2020a.
countries for plots of the pattern of active case counts across many countries. 35. The specific procedures implemented in the IMHE model are described here
See, for example the description of the Columbia University Mailman School of Public Health
Model at https://www.medrxiv.org/content/10.1101/2020.03.21.20040303v2, or
the model used by COVIDActNow described at https://data.covidactnow.org/Covid_
Act_Now_Model_References_and_Assumptions.pdf.
34. See https://www.endcoronavirus.org/countries for plots of the pattern of active
case counts across many countries.
35. The specific procedures implemented in the IMHE model are described here: https://
www.medrxiv.org/content/medrxiv/suppl/2020/04/25/2020.04.21.20074732.DC1/
2020.04.21.20074732-2.pdf.
2020 and Chudik, Pesaran, and Rebucci 2020 for useful studies on which forecasts of future transmission of the disease might be based. 39. Data on the level of deaths at various dates used in the exercise
- See Gupta
See Gupta et al. 2020 and Chudik, Pesaran, and Rebucci 2020 for useful studies on which
forecasts of future transmission of the disease might be based.
39. Data on the level of deaths at various dates used in the exercise are taken from https:
//www.worldometers.info/coronavirus/country/us/.
this discussion of the patterns of infections for COVID-19 that might be based on analogies
- See
See, for example, this discussion of the patterns of infections for COVID-19 that might be based
on analogies to influenza pandemics: https://www.cidrap.umn.edu/sites/default/
files/public/downloads/cidrap-covid19-viewpoint-part1_0.pdf.
What Will be the Economic Impact of COVID-19 in the U.S.? Rough Estimates of Disease Scenarios
- Andrew Atkeson
Atkeson, Andrew. 2020a. "How Deadly is COVID-19? Understanding the Difficulties with Estimation
of its Fatality Rate." Staff Report 598, Federal Reserve Bank of Minneapolis, March.
. 2020b. "What Will be the Economic Impact of COVID-19 in the U.S.? Rough Estimates of
Disease Scenarios." Staff Report 595, Federal Reserve Bank of Minneapolis.
Estimating and Forecasting Disease Scenarios for COVID-19 with an SIR Model
- Andrew Atkeson
- Karen Kopecky
- Tao Zha
Atkeson, Andrew, Karen Kopecky, and Tao Zha. 2020. "Estimating and Forecasting Disease Scenarios
for COVID-19 with an SIR Model." June.
The Macroeconomics of Epidemics
- Martin S Eichenbaum
- Sergio Rebelo
- Mathias Trabant
Eichenbaum, Martin S., Sergio Rebelo, and Mathias Trabant. 2020. "The Macroeconomics of
Epidemics." Working Paper 26882, NBER, April.
Fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the SARS-COV-2 epidemic
- Jose Lourenco
- Robert Paton
- Mahan Ghafari
- Moritz Kraemer
- Craig Thompson
- Peter Simmonds
- Paul Klenerman
- Sunetra Gupta
Lourenco, Jose, Robert Paton, Mahan Ghafari, Moritz Kraemer, Craig Thompson, Peter Simmonds,
Paul Klenerman, and Sunetra Gupta. 2020. "Fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the SARS-COV-2 epidemic." Cold Spring Harbor Laboratory Press (March).
An Analytical Model of COVID-19 Lockdowns
- Lucasz Rachel
Rachel, Lucasz. 2020. "An Analytical Model of COVID-19 Lockdowns." May.
Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact
- Alexis Toda
- Akira
Toda, Alexis Akira. 2020. "Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and
Economic Impact." Technical report. Cornell University, March.