Tracing day-zero and forecasting the COVID-19 outbreak in Lombardy, Italy: A compartmental modelling and numerical optimization approach

Factors associated with vaccine hesitancy against COVID-19 among adults in Europe: a descriptive study analysis applying socio-ecological framework

OBJECTIVE

This study aimed to explore the factors associated with COVID-19 vaccine hesitancy in Europe among adults by using the Socio-Ecological Model.

RESULTS

This cross-sectional study used secondary data collected from respondents residing in 27 EU countries at the time of May 2021. The outcome was vaccine hesitancy against COVID-19, and the total sample size of 23,606 was analysed by binary logistic regression, as well as McKelvey and Zavonoia's R2. After adding each level of variables, the model found the significant and increased association with vaccine hesitancy in younger age groups (21-39 years and 40-60 years vs. 65 years+), who left full-time education at a young age (16-19 years), those with manual jobs, those with children at home, individuals residing in small towns, and beliefs related to the vaccine. Together, the levels explained 49.5% of the variance associated with vaccine hesitancy, and the addition to each variable layer increased the variance. This highlights the need to consider broad factors at multiple levels to enhance vaccine acceptance and uptake.

Bayesian monitoring of COVID-19 in Sweden

In an effort to provide regional decision support for the public healthcare, we design a data-driven compartment-based model of COVID-19 in Sweden. From national hospital statistics we derive parameter priors, and we develop linear filtering techniques to drive the simulations given data in the form of daily healthcare demands. We additionally propose a posterior marginal estimator which provides for an improved temporal resolution of the reproduction number estimate as well as supports robustness checks via a parametric bootstrap procedure. From our computational approach we obtain a Bayesian model of predictive value which provides important insight into the progression of the disease, including estimates of the effective reproduction number, the infection fatality rate, and the regional-level immunity. We successfully validate our posterior model against several different sources, including outputs from extensive screening programs. Since our required data in comparison is easy and non-sensitive to collect, we argue that our approach is particularly promising as a tool to support monitoring and decisions within public health. Significance: Using public data from Swedish patient registries we develop a national-scale computational model of COVID-19. The parametrized model produces valuable weekly predictions of healthcare demands at the regional level and validates well against several different sources. We also obtain critical epidemiological insights into the disease progression, including, e.g., reproduction number, immunity and disease fatality estimates. The success of the model hinges on our novel use of filtering techniques which allows us to design an accurate data-driven procedure using data exclusively from healthcare demands, i.e., our approach does not rely on public testing and is therefore very cost-effective.

Source identification via contact tracing in the presence of asymptomatic patients

Inferring the source of a diffusion in a large network of agents is a difficult but feasible task, if a few agents act as sensors revealing the time at which they got hit by the diffusion. One of the main limitations of current source identification algorithms is that they assume full knowledge of the contact network, which is rarely the case, especially for epidemics, where the source is called patient zero. Inspired by recent implementations of contact tracing algorithms, we propose a new framework, which we call Source Identification via Contact Tracing Framework (SICTF). In the SICTF, the source identification task starts at the time of the first hospitalization, and initially we have no knowledge about the contact network other than the identity of the first hospitalized agent. We may then explore the network by contact queries, and obtain symptom onset times by test queries in an adaptive way, i.e., both contact and test queries can depend on the outcome of previous queries. We also assume that some of the agents may be asymptomatic, and therefore cannot reveal their symptom onset time. Our goal is to find patient zero with as few contact and test queries as possible. We implement two local search algorithms for the SICTF: the LS algorithm, which has recently been proposed by Waniek et al. in a similar framework, is more data-efficient, but can fail to find the true source if many asymptomatic agents are present, whereas the LS+ algorithm is more robust to asymptomatic agents. By simulations we show that both LS and LS+ outperform previously proposed adaptive and non-adaptive source identification algorithms adapted to the SICTF, even though these baseline algorithms have full access to the contact network. Extending the theory of random exponential trees, we analytically approximate the source identification probability of the LS/ LS+ algorithms, and we show that our analytic results match the simulations. Finally, we benchmark our algorithms on the Data-driven COVID-19 Simulator (DCS) developed by Lorch et al., which is the first time source identification algorithms are tested on such a complex dataset.

Using real-time ascertainment rate estimate from infection and hospitalization dataset for modeling the spread of infectious disease: COVID-19 case study in the Czech Republic

We present a novel approach to estimate the time-varying ascertainment rate in almost real-time, based on the surveillance of positively tested infectious and hospital admission data. We also address the age dependence of the estimate. The ascertainment rate estimation is based on the Bayes theorem. It can be easily calculated and used (i) as part of a mechanistic model of the disease spread or (ii) to estimate the unreported infections or changes in their proportion in almost real-time as one of the early-warning signals in case of undetected outbreak emergence. The paper also contains a case study of the COVID-19 epidemic in the Czech Republic. The case study demonstrates the usage of the ascertainment rate estimate in retrospective analysis, epidemic monitoring, explanations of differences between waves, usage in the national Anti-epidemic system, and monitoring of the effectiveness of non-pharmaceutical interventions on Czech nationwide surveillance datasets. The Czech data reveal that the probability of hospitalization due to SARS-CoV-2 infection for the senior population was 12 times higher than for the non-senior population in the monitored period from the beginning of March 2020 to the end of May 2021. In a mechanistic model of COVID-19 spread in the Czech Republic, the ascertainment rate enables us to explain the links between all basic compartments, including new cases, hospitalizations, and deaths.

A model of behavioural response to risk accurately predicts the statistical distribution of COVID-19 infection and reproduction numbers

One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This homeostatic response is active until approximate herd immunity is reached: in this domain the model predicts that the reproduction rate R will be centred around a median of 1, that proportional change in infection numbers will follow the standard Cauchy distribution with location and scale parameters 0 and 1, and that high infection numbers will follow a power-law frequency distribution with exponent 2. To test these predictions we used worldwide COVID-19 data from 1st February 2020 to 30th June 2022 to calculate [Formula: see text] confidence interval estimates across countries for these R, location, scale and exponent parameters. The resulting median R estimate was [Formula: see text] (predicted value 1) the proportional change location estimate was [Formula: see text] (predicted value 0), the proportional change scale estimate was [Formula: see text] (predicted value 1), and the frequency distribution exponent estimate was [Formula: see text] (predicted value 2); in each case the observed estimate agreed with model predictions.

Mitigating the outbreak of an infectious disease over its life cycle: A diffusion-based approach

We first qualitatively divide the cycle of an infectious disease outbreak into five distinct stages by following the adoption categorization from the diffusion theory. Next, we apply a standard mechanistic model, the susceptible-infected-recovered model, to simulate a variety of transmission scenarios and to quantify the benefits of various countermeasures. In particular, we apply the specific values of the newly infected to quantitatively divide an outbreak cycle into stages. We therefore reveal diverging patterns of countermeasures in different stages. The stage is critical in determining the evolutionary characteristics of the diffusion process. Our results show that it is necessary to employ appropriate diverse strategies in different stages over the life cycle of an infectious disease outbreak. In the early stages, we need to focus on prevention, early detection, and strict countermeasure (e.g., isolation and lockdown) for controlling an epidemic. It is better safe (i.e., stricter countermeasures) than sorry (i.e., let the virus spread out). There are two reasons why we should implement responsive and strict countermeasures in the early stages. The countermeasures are very effective, and the earlier the more total infected reduction over the whole cycle. The economic and societal burden for implementing countermeasures is relatively small due to limited affected areas, and the earlier the less burden. Both reasons change to the opposite in the late stages. The strategic focuses in the late stages become more delicate and balanced for two reasons: the same countermeasures become much less effective, and the society bears a much heavier burden. Strict countermeasures may become unnecessary, and we need to think about how to live with the infectious disease.

The Wealth of Nations and the First Wave of COVID-19 Diffusion

A large debate has risen about the hypothesis that “COVID-19 is a disease for the rich ones” suggesting that both its diffusion and mortality rates are somehow linked with economic wealth. In this study we observe a sample of 138 countries during the first wave contagion period, namely the 5 weeks between 24 March and 21 April 2020. Using different data sources, our estimates show that both the early infection and the mortality rates of COVID-19 are higher in wealthier countries, more precisely in countries with a higher GDP per capita. As an explanation of this finding, we also find that both mortality and infection rates increase with a higher share of elderly population and with the international flows of imported goods or tourists. However, the death rate decreases in countries with higher endowments of health facilities. We also demonstrate that these results are robust to simultaneity, unobserved heterogeneity, the possible poor quality of the data on COVID-19 deaths, and the extension of the time frame.

Backcasting COVID-19: a physics-informed estimate for early case incidence

It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea and Brazil. We assume that the second wave was more accurately monitored, even though we acknowledge that behavioural changes occurred during the pandemic and region- (or country-) specific monitoring protocols evolved. We then construct a manifold diffeomorphic to that of the implied original dynamical system, using fatalities or hospitalizations only. Finally, we restrict the diffeomorphism to the reported cases coordinate of the dynamical system. Our main finding is that in the European countries studied, the actual cases are under-reported by as much as 50%. On the other hand, in South Korea-which had a proactive mitigation approach-a far smaller discrepancy between the actual and reported cases is predicted, with an approximately 18% predicted underestimation. We believe that our backcasting framework is applicable to other epidemic outbreaks where (due to limited or poor quality data) there is uncertainty around the actual cases.

Narrative Review of the COVID-19 Pandemic's First Two Years in Italy

Italy was the first country in the western world to be affected by the COVID-19 pandemic, arguably among the worst-affected ones, counting 12 million cases and 150 thousand deaths two years since the first case. Facing new challenges, Italy has enacted different strategies and policies to limit the spread of the SARS-CoV-2 virus and treat those affected by COVID-19. This narrative review provided an overview of factors, measures, and actions that shaped Italy's first two years of the COVID-19 pandemic by investigating epidemiological data and using a mixed-method approach. This narrative review aimed to summarize the most relevant aspects and measures and analyze available data to provide policymakers and healthcare providers with the instruments to learn from this pandemic and improve their preparedness for future pandemic events. The first two years of the pandemic differ in that, during the first year, significant necessary changes to the way health systems were organized were implemented, increasing healthcare spending and adopting social and physical distancing measures that were stricter than the ones adopted in the second year. However, as the pandemic progressed, increased knowledge of the virus and related variants, as well as the introduction of highly effective vaccines, which were not equally available to the whole population, resulted in a stratification of COVID-19 infections and deaths based on factors such as age, vaccination status, and individual susceptibility to the virus.

Combining and comparing regional SARS-CoV-2 epidemic dynamics in Italy: Bayesian meta-analysis of compartmental models and global sensitivity analysis

During autumn 2020, Italy faced a second important SARS-CoV-2 epidemic wave. We explored the time pattern of the instantaneous reproductive number, R ₀(t), and estimated the prevalence of infections by region from August to December calibrating SIRD models on COVID-19-related deaths, fixing at values from literature Infection Fatality Rate (IFR) and average infection duration. A Global Sensitivity Analysis (GSA) was performed on the regional SIRD models. Then, we used Bayesian meta-analysis and meta-regression to combine and compare the regional results and investigate their heterogeneity. The meta-analytic R ₀(t) curves were similar in the Northern and Central regions, while a less peaked curve was estimated for the South. The maximum R ₀(t) ranged from 2.15 (South) to 2.61 (North) with an increase following school reopening and a decline at the end of October. The predictive performance of the regional models, assessed through cross validation, was good, with a Mean Absolute Percentage Error of 7.2% and 10.9% when considering prediction horizons of 7 and 14 days, respectively. Average temperature, urbanization, characteristics of family medicine and healthcare system, economic dynamism, and use of public transport could partly explain the regional heterogeneity. The GSA indicated the robustness of the regional R ₀(t) curves to different assumptions on IFR. The infectious period turned out to have a key role in determining the model results, but without compromising between-region comparisons.

EKF-SIRD model algorithm for predicting the coronavirus (COVID-19) spreading dynamics

In this paper, we study the Covid 19 disease profile in the Algerian territory since February 25, 2020 to February 13, 2021. The idea is to develop a decision support system allowing public health decision and policy-makers to have future statistics (the daily prediction of parameters) of the pandemic; and also encourage citizens for conducting health protocols. Many studies applied traditional epidemic models or machine learning models to forecast the evolution of coronavirus epidemic, but the use of such models alone to make the prediction will be less precise. For this purpose, we assume that the spread of the coronavirus is a moving target described by an epidemic model. On the basis of a SIRD model (Susceptible-Infection-Recovery- Death), we applied the EKF algorithm to predict daily all parameters. These predicted parameters will be much beneficial to hospital managers for updating the available means of hospitalization (beds, oxygen concentrator, etc.) in order to reduce the mortality rate and the infected. Simulations carried out reveal that the EKF seems to be more efficient according to the obtained results.

Optimal vaccine roll-out strategies including social distancing for pandemics

Non-pharmacological interventions (NPIs), principally social distancing, in combination with effective vaccines, aspire to develop a protective immunity shield against pandemics and particularly against the COVID-19 pandemic. In this study, an agent-based network model with small-world topology is employed to find optimal policies against pandemics, including social distancing and vaccination strategies. The agents' states are characterized by a variation of the SEIR model (susceptible, exposed, infected, recovered). To explore optimal policies, an equation-free method is proposed to solve the inverse problem of calibrating an agent's infection rate with respect to the vaccination efficacy. The results show that prioritizing the first vaccine dose in combination with mild social restrictions, is sufficient to control the pandemic, with respect to the number of deaths. Moreover, for the same mild number of social contacts, we find an optimal vaccination ratio of 0.85 between older people of ages > 65 compared to younger ones.

Designing social distancing policies for the COVID-19 pandemic: A probabilistic model predictive control approach

The effective control of the COVID-19 pandemic is one the most challenging issues of recent years. The design of optimal control policies is challenging due to a variety of social, political, economical and epidemiological factors. Here, based on epidemiological data reported in recent studies for the Italian region of Lombardy, which experienced one of the largest and most devastating outbreaks in Europe during the first wave of the pandemic, we present a probabilistic model predictive control (PMPC) approach for the systematic study of what if scenarios of social distancing in a retrospective analysis for the first wave of the pandemic in Lombardy. The performance of the proposed PMPC was assessed based on simulations of a compartmental model that was developed to quantify the uncertainty in the level of the asymptomatic cases in the population, and the synergistic effect of social distancing during various activities, and public awareness campaign prompting people to adopt cautious behaviors to reduce the risk of disease transmission. The PMPC takes into account the social mixing effect, i.e. the effect of the various activities in the potential transmission of the disease. The proposed approach demonstrates the utility of a PMPC approach in addressing COVID-19 transmission and implementing public relaxation policies.

The State of the Art of Data Mining Algorithms for Predicting the COVID-19 Pandemic

Current computer systems are accumulating huge amounts of information in several application domains. The outbreak of COVID-19 has increased rekindled interest in the use of data mining techniques for the analysis of factors that are related to the emergence of an epidemic. Data mining techniques are being used in the analysis and interpretation of information, which helps in the discovery of patterns, planning of isolation policies, and even predicting the speed of proliferation of contagion in a viral disease such as COVID-19. This research provides a comprehensive study of various data mining algorithms that are used in conjunction with epidemiological prediction models. The document considers that there is an opportunity to improve or develop tools that offer an accurate prognosis in the management of viral diseases through the use of data mining tools, based on a comparative study of 35 research papers.

Planning as Inference in Epidemiological Dynamics Models

In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policy-making could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.

The world trade network: country centrality and the COVID-19 pandemic

International trade is based on a set of complex relationships between different countries that can be modelled as an extremely dense network of interconnected agents. On the one hand, this network might favour the economic growth of countries, but on the other, it can also favour the diffusion of diseases, such as COVID-19. In this paper, we study whether, and to what extent, the topology of the trade network can explain the rate of COVID-19 diffusion and mortality across countries. We compute the countries' centrality measures and we apply the community detection methodology based on communicability distance. We then use these measures as focal regressors in a negative binomial regression framework. In doing so, we also compare the effects of different measures of centrality. Our results show that the numbers of infections and fatalities are larger in countries with a higher centrality in the global trade network.

Simulation of the impact of people mobility, vaccination rate, and virus variants on the evolution of Covid-19 outbreak in Italy

We have further extended our compartmental model describing the spread of the infection in Italy. As in our previous work, the model assumes that the time evolution of the observable quantities (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depends on average parameters, namely people diffusion coefficient, infection cross-section, and population density. The model provides information on the tight relationship between the variation of the reported infection cases and a well-defined observable physical quantity: the average number of people that lie within the daily displacement area of any single person. With respect to our previous paper, we have extended the analyses to several regions in Italy, characterized by different levels of restrictions and we have correlated them to the diffusion coefficient. Furthermore, the model now includes self-consistent evaluation of the reproduction index, effect of immunization due to vaccination, and potential impact of virus variants on the dynamical evolution of the outbreak. The model fits the epidemic data in Italy, and allows us to strictly relate the time evolution of the number of hospitalized cases and fatalities to the change of people mobility, vaccination rate, and appearance of an initial concentration of people positives for new variants of the virus.

Optimization in the Context of COVID-19 Prediction and Control: A Literature Review

This paper presents an overview of some key results from a body of optimization studies that are specifically related to COVID-19, as reported in the literature during 2020-2021. As shown in this paper, optimization studies in the context of COVID-19 have been used for many aspects of the pandemic. From these studies, it is observed that since COVID-19 is a multifaceted problem, it cannot be studied from a single perspective or framework, and neither can the related optimization models. Four new and different frameworks are proposed that capture the essence of analyzing COVID-19 (or any pandemic for that matter) and the relevant optimization models. These are: (i) microscale vs. macroscale perspective; (ii) early stages vs. later stages perspective; (iii) aspects with direct vs. indirect relationship to COVID-19; and (iv) compartmentalized perspective. To limit the scope of the review, only optimization studies related to the prediction and control of COVID-19 are considered (public health focused), and which utilize formal optimization techniques or machine learning approaches. In this context and to the best of our knowledge, this survey paper is the first in the literature with a focus on the prediction and control related optimization studies. These studies include optimization of screening testing strategies, prediction, prevention and control, resource management, vaccination prioritization, and decision support tools. Upon reviewing the literature, this paper identifies current gaps and major challenges that hinder the closure of these gaps and provides some insights into future research directions.

Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples

We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a zero-dimensional (0D; ordinary-differential-equation-level) compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations (SEAIHR model). We emphasize the importance of the viral latent period (reflected in the exposed population) and the key role of an asymptomatic population. We optimize model parameters for both regions by comparing predictions to the cumulative number of infected and total number of deaths, the reported data we found to be most reliable, via minimizing the ℓ^{2} norm of the difference between predictions and observed data. We consider the sensitivity of model predictions on reasonable variations of model parameters and initial conditions, and we address issues of parameter identifiability. We model both the prequarantine and postquarantine evolution of the epidemic by a time-dependent change of the viral transmission rates that arises in response to containment measures. Subsequently, a spatially distributed version of the 0D model in the form of reaction-diffusion equations is developed. We consider that, after an initial localized seeding of the infection, its spread is governed by the diffusion (and 0D model "reactions") of the asymptomatic and symptomatically infected populations, which decrease with the imposed restrictive measures. We inserted the maps of the two regions, and we imported population-density data into the finite-element software package COMSOL Multiphysics®, which was subsequently used to numerically solve the model partial differential equations. Upon discussing how to adapt the 0D model to this spatial setting, we show that these models bear significant potential towards capturing both the well-mixed, zero-dimensional description and the spatial expansion of the pandemic in the two regions. Veins of potential refinement of the model assumptions towards future work are also explored.

SUIHTER: a new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy

The COVID-19 epidemic is the latest in a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated infected (I), hospitalized (H), threatened (T), extinct (E) and recovered (R). A suitable parameter calibration that is based on the combined use of the least-squares method and the Markov chain Monte Carlo method is proposed with the aim of reproducing the past history of the epidemic in Italy, which surfaced in late February and is still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are made available daily by the Italian Civil Protection Department. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak, which emerged in autumn 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at a national level.

Could the new coronavirus have infected humans prior November 2019?

The pandemic caused by the SARS-CoV-2 virus is believed to originate in China from where it spread to other parts of the world. The first cluster of diseased individuals was reported in China as early as in December 2019. It has also been well established that the virus stroke Italy later in January or in February 2020, hence distinctly after the outbreak in China. The work by Apolone et al. published in the Italian Medical Journal in November 2020 and retracted upon expression of concern on 22 March 2021, however propose that the virus could have stroke people already in September 2019, possibly following even earlier outbreak in China. By fitting an early part of the epidemic curve with the exponential and extrapolating it backwards, we could estimate the day-zero of the epidemic and calculated its confidence intervals in Italy and China. We also calculated how probable it is that Italy encountered the virus prior 1 January 2020. We determined an early portion of the epidemic curve representing unhindered exponential growth which fit the exponential model with high determination >0.97 in both countries. We conservatively suggest that the day-zero in China and Italy was 8 December 2019 (95% CI: 3 Dec., 20 Dec.) and 22 January 2020 (95% CI: 16 Jan., 29 Jan.), respectively. Given the uncertainty of the very early data in China and adjusting hence our model to fit the exponentially behaved data only, we can even admit that the pandemic originated through November 2019 (95% CI: 31 Oct., 22 Dec.). With high confidence (p <0.01) China encountered the virus prior Italy. We generally view any pre-pandemic presence of the virus in humans before November 2019 as very unlikely. The later established dynamics of the epidemics data suggests that the country of the origin was China.

Propagation Analysis of COVID-19: An SIR Model-Based Investigation of the Pandemic

The paper investigates the spread pattern and dynamics of Covid-19 propagation based on SIR model. Using the model dynamics, an analytical estimation has been obtained for virus span, its longevity, growing pattern, etc. Experimental simulations are carried out on the data of four regions of India over a period of two months of country-wide lockdown. The analysis illustrates the effect of lockdown on the contact rate and its implication. Simulation results illustrate that there is a cut-down in effective contact rate by a considerable factor ranging from 2 to 4 for the selected regions. Further, the estimates for the vaccines to be developed, maximum range and span of the disease can be also estimated. Results portray that the SIR model is a significant tool to cast the dynamics and predictions of Covid-19 outbreak in comparison to other epidemic models. The study demonstrates the progression of real time data in accordance with the SIR model with high accuracy.

Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

Early assessments of the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries, more robust inferences could be made. Using multiple countries, data streams and methods, we estimated that, when unconstrained, European COVID-19 confirmed cases doubled on average every 3 days (range 2.2-4.3 days) and Italian hospital and intensive care unit admissions every 2-3 days; values that are significantly lower than the 5-7 days dominating the early published literature. Furthermore, we showed that the impact of physical distancing interventions was typically not seen until at least 9 days after implementation, during which time confirmed cases could grow eightfold. We argue that such temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number R0 for initiating interventions, and that the combination of fast growth and long detection delays explains the struggle in countries' outbreak response better than large values of R0 alone. One year on from first reporting these results, reproduction numbers continue to dominate the media and public discourse, but robust estimates of unconstrained growth remain essential for planning worst-case scenarios, and detection delays are still key in informing the relaxation and re-implementation of interventions. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Covasim: An agent-based model of COVID-19 dynamics and interventions

The COVID-19 pandemic has created an urgent need for models that can project epidemic trends, explore intervention scenarios, and estimate resource needs. Here we describe the methodology of Covasim (COVID-19 Agent-based Simulator), an open-source model developed to help address these questions. Covasim includes country-specific demographic information on age structure and population size; realistic transmission networks in different social layers, including households, schools, workplaces, long-term care facilities, and communities; age-specific disease outcomes; and intrahost viral dynamics, including viral-load-based transmissibility. Covasim also supports an extensive set of interventions, including non-pharmaceutical interventions, such as physical distancing and protective equipment; pharmaceutical interventions, including vaccination; and testing interventions, such as symptomatic and asymptomatic testing, isolation, contact tracing, and quarantine. These interventions can incorporate the effects of delays, loss-to-follow-up, micro-targeting, and other factors. Implemented in pure Python, Covasim has been designed with equal emphasis on performance, ease of use, and flexibility: realistic and highly customized scenarios can be run on a standard laptop in under a minute. In collaboration with local health agencies and policymakers, Covasim has already been applied to examine epidemic dynamics and inform policy decisions in more than a dozen countries in Africa, Asia-Pacific, Europe, and North America.

Covasim: An agent-based model of COVID-19 dynamics and interventions

The COVID-19 pandemic has created an urgent need for models that can project epidemic trends, explore intervention scenarios, and estimate resource needs. Here we describe the methodology of Covasim (COVID-19 Agent-based Simulator), an open-source model developed to help address these questions. Covasim includes country-specific demographic information on age structure and population size; realistic transmission networks in different social layers, including households, schools, workplaces, long-term care facilities, and communities; age-specific disease outcomes; and intrahost viral dynamics, including viral-load-based transmissibility. Covasim also supports an extensive set of interventions, including non-pharmaceutical interventions, such as physical distancing and protective equipment; pharmaceutical interventions, including vaccination; and testing interventions, such as symptomatic and asymptomatic testing, isolation, contact tracing, and quarantine. These interventions can incorporate the effects of delays, loss-to-follow-up, micro-targeting, and other factors. Implemented in pure Python, Covasim has been designed with equal emphasis on performance, ease of use, and flexibility: realistic and highly customized scenarios can be run on a standard laptop in under a minute. In collaboration with local health agencies and policymakers, Covasim has already been applied to examine epidemic dynamics and inform policy decisions in more than a dozen countries in Africa, Asia-Pacific, Europe, and North America.

Estimation of novel coronavirus (COVID-19) reproduction number and case fatality rate: A systematic review and meta-analysis

BACKGROUND AND AIMS

Realizing the transmission potential and the magnitude of the coronavirus disease 2019 (COVID-19) aids public health monitoring, strategies, and preparation. Two fundamental parameters, the basic reproduction number (R 0) and case fatality rate (CFR) of COVID-19, help in this understanding process. The objective of this study was to estimate the R 0 and CFR of COVID-19 and assess whether the parameters vary in different regions of the world.

METHODS

We carried out a systematic review to find the reported estimates of the R 0 and the CFR in articles from international databases between January 1 and August 31, 2020. Random-effect models and Forest plots were implemented to evaluate the mean effect size of R 0 and the CFR. Furthermore, R 0 and CFR of the studies were quantified based on geographic location, the tests/thousand population, and the median population age of the countries where the studies were conducted. To assess statistical heterogeneity among the selected articles, the I 2 statistic and the Cochran's Q test were used.

RESULTS

Forty-five studies involving R 0 and 34 studies involving CFR were included. The pooled estimation of R 0 was 2.69 (95% CI: 2.40, 2.98), and that of the CFR was 2.67 (2.25, 3.13). The CFR in different regions of the world varied significantly, from 2.49 (2.08, 2.94) in Asia to 3.40 (2.81, 4.04) in North America. We observed higher mean CFR values for the countries with lower tests (3.15 vs 2.16) and greater median population age (3.13 vs 2.27). However, R 0 did not vary significantly in different regions of the world.

CONCLUSIONS

An R 0 of 2.69 and a CFR of 2.67 indicate the severity of the COVID-19. Although R 0 and CFR may vary over time, space, and demographics, we recommend considering these figures in control and prevention measures.

Mathematical modelling for decision making of lockdown during COVID-19

Due to the recent worldwide outbreak of COVID-19, there has been an enormous change in our lifestyle and it has a severe impact in different fields like finance, education, business, travel, tourism, economy, etc., in all the affected countries. In this scenario, people must be careful and cautious about the symptoms and should act accordingly. Accurate predictions of different factors, like the end date of the pandemic, duration of lockdown and spreading trend can guide us through the pandemic and precautions can be taken accordingly. Multiple attempts have been made to model the virus transmission, but none of them has investigated it at a global level. The novelty of the proposed work lies here. In this paper, first, authors have analysed spreading of the said disease using data collected from various platforms and then, have presented a predictive mathematical model for fifteen countries from first, second and third world for probable future projections of this pandemic. The prediction can be used by planning commission, healthcare organizations and the government agencies as well for creating suitable arrangements against this pandemic.

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period

In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can also be used for determining the time evolution of the associated number of deaths: for the epidemics in Spain, Germany, Italy and the UK, the parameters defining these formulae were computed using data up to 1 May 2020, a period of lockdown for these countries; then, the predictions of the formulae were compared with the data for the following 122 days, namely until 1 September. These comparisons, in addition to demonstrating the remarkable predictive capacity of our simple formulae, also show that for a rather long time the easing of the lockdown measures did not affect the number of deaths. The importance of these results regarding predictions of the number of Covid-19 deaths during the post-lockdown period is discussed.

The first wave of the SARS-CoV-2 epidemic in Tuscany (Italy): A SI2R2D compartmental model with uncertainty evaluation

With the aim of studying the spread of the SARS-CoV-2 infection in the Tuscany region of Italy during the first epidemic wave (February-June 2020), we define a compartmental model that accounts for both detected and undetected infections and assumes that only notified cases can die. We estimate the infection fatality rate, the case fatality rate, and the basic reproduction number, modeled as a time-varying function, by calibrating on the cumulative daily number of observed deaths and notified infected, after fixing to plausible values the other model parameters to assure identifiability. The confidence intervals are estimated by a parametric bootstrap procedure and a Global Sensitivity Analysis is performed to assess the sensitivity of the estimates to changes in the values of the fixed parameters. According to our results, the basic reproduction number drops from an initial value of 6.055 to 0 at the end of the national lockdown, then it grows again, but remaining under 1. At the beginning of the epidemic, the case and the infection fatality rates are estimated to be 13.1% and 2.3%, respectively. Among the parameters considered as fixed, the average time from infection to recovery for the not notified infected appears to be the most impacting one on the model estimates. The probability for an infected to be notified has a relevant impact on the infection fatality rate and on the shape of the epidemic curve. This stresses the need of collecting information on these parameters to better understand the phenomenon and get reliable predictions.

A Retrospective Analysis of the COVID-19 Pandemic Evolution in Italy

Simple Summary

Given the progress of the COVID-19 pandemic, it has become crucial to retrace the past epidemic trajectories to grasp non-trivial, qualitative features of viral dynamics that could contribute to the design of general guidelines for future outbreaks or epidemics. In this regard, we used a refinement of the SIDARTHE (Susceptible, Infected, Diagnosed, Ailing, Recognized, Threatened, Healed, Extinct) model to develop a retrospective computational analysis focused on an Italian case study. Our work aimed at evaluating the efficacy of adopted countermeasures (inferred from the resulting model parameters), and additionally providing an estimate of the undetected viral circulation as well as the day zero of the COVID-19 outbreak in Italy, which are not directly inferable from the data.

Abstract

Late 2019 saw the outbreak of COVID-19, a respiratory disease caused by the new coronavirus SARS-CoV-2, which rapidly turned into a pandemic, killing more than 2.77 million people and infecting more than 126 million as of late March 2021. Daily collected data on infection cases and hospitalizations informed decision makers on the ongoing pandemic emergency, enabling the design of diversified countermeasures, from behavioral policies to full lockdowns, to curb the virus spread. In this context, mechanistic models could represent valuable tools to optimize the timing and stringency of interventions, and to reveal non-trivial properties of the pandemic dynamics that could improve the design of suitable guidelines for future epidemics. We performed a retrospective analysis of the Italian epidemic evolution up to mid-December 2020 to gain insight into the main characteristics of the original strain of SARS-CoV-2, prior to the emergence of new mutations and the vaccination campaign. We defined a time-varying optimization procedure to calibrate a refined version of the SIDARTHE (Susceptible, Infected, Diagnosed, Ailing, Recognized, Threatened, Healed, Extinct) model and hence accurately reconstruct the epidemic trajectory. We then derived additional features of the COVID-19 pandemic in Italy not directly retrievable from reported data, such as the estimate of the day zero of infection in late November 2019 and the estimate of the spread of undetected infection. The present analysis contributes to a better understanding of the past pandemic waves, confirming the importance of epidemiological modeling to support an informed policy design against epidemics to come.

Easing COVID-19 lockdown measures while protecting the older restricts the deaths to the level of the full lockdown

Guided by a rigorous mathematical result, we have earlier introduced a numerical algorithm, which using as input the cumulative number of deaths caused by COVID-19, can estimate the effect of easing of the lockdown conditions. Applying this algorithm to data from Greece, we extend it to the case of two subpopulations, namely, those consisting of individuals below and above 40 years of age. After supplementing the Greek data for deaths with the data for the number of individuals reported to be infected by SARS-CoV-2, we estimated the effect on deaths and infections in the case that the easing of the lockdown measures is different for these two subpopulations. We found that if the lockdown measures are partially eased only for the young subpopulation, then the effect on deaths and infections is small. However, if the easing is substantial for the older population, this effect may be catastrophic.

Lessons from the devastating impact of the first COVID-19 wave in Italy

Herein, we are critically examining the chain of events and discussing previously unrecognized factors that led to the 'perfect COVID-19 storm' in northern Italy during the first epidemic wave in spring 2020. SARS-CoV-2 was circulating uncontrollably at least for five weeks before the adoption of containment measures, and the role of exponential growth in the spread of the virus, conveyed by a high R₀, was likely underestimated. An understanding of this failure's causes and contexts will help us to control the strong second wave of the pandemic we are now facing in Europe, and to be better prepared for future outbreaks.

Modeling and forecasting of COVID-19 using a hybrid dynamic model based on SEIRD with ARIMA corrections

The outbreak of novel coronavirus (COVID-19) attracted worldwide attention. It has posed a significant challenge for the global economies, especially the healthcare sector. Even with a robust healthcare system, countries were not prepared for the ramifications of COVID-19. Several statistical, dynamic, and mathematical models of the COVID-19 outbreak including the SEIR model have been developed to analyze the infection its transmission dynamics. The objective of this research is to use public data to study the properties associated with the COVID-19 pandemic to develop a dynamic hybrid model based on SEIRD and ascertainment rate with automatically selected parameters. The proposed model consists of two parts: the modified SEIRD dynamic model and ARIMA models. We fit SEIRD model parameters against historical values of infected, recovered and deceased population divided by ascertainment rate, which, in turn, is also a parameter of the model. Residuals of the first model for infected, recovered, and deceased populations are then corrected using ARIMA models. The model can analyze the input data in real-time and provide long- and short-term forecasts with confidence intervals. The model was tested and validated on the US COVID statistics dataset from the COVID Tracking Project. For validation, we use unseen recent statistical data. We use five common measures to estimate model prediction ability: MAE, MSE, MLSE, Normalized MAE, and Normalized MSE. We proved a great model ability to make accurate predictions of infected, recovered, and deceased patients. The output of the model can be used by the government, private sectors, and policymakers to reduce health and economic risks significantly improved consumer credit scoring.

A country comparison of place-based activity response to COVID-19 policies

The emergence of the novel Coronavirus Disease in late 2019 (COVID-19) and subsequent pandemic led to an immense disruption in the daily lives of almost everyone on the planet. Faced with the consequences of inaction, most national governments responded with policies that restricted the activities conducted by their inhabitants. As schools and businesses shuttered, the mobility of these people decreased. This reduction in mobility, and related activities, was recorded through ubiquitous location-enabled personal mobile devices. Patterns emerged that varied by place-based activity. In this work the differences in these place-based activity patterns are investigated across nations, specifically by focusing on the relationship between government enacted policies and changes in community activity patterns. By addressing five research questions, we show that people's activity response to government action varies widely both across nations as well as regionally within them. Three assessment measures, namely cosine similarity, lag response, and subregional variation, are devised and the results correlate with a number of global indices. We discuss these findings and the relationship between government action and residents' response.

Tracing day-zero and forecasting the COVID-19 outbreak in Lombardy, Italy: A compartmental modelling and numerical optimization approach

INTRODUCTION

Italy became the second epicenter of the novel coronavirus disease 2019 (COVID-19) pandemic after China, surpassing by far China's death toll. The disease swept through Lombardy, which remained in lockdown for about two months, starting from the 8th of March. As of that day, the isolation measures taken in Lombardy were extended to the entire country. Here, assuming that effectively there was one case "zero" that introduced the virus to the region, we provide estimates for: (a) the day-zero of the outbreak in Lombardy, Italy; (b) the actual number of asymptomatic infected cases in the total population until March 8; (c) the basic (R0)and the effective reproduction number (Re) based on the estimation of the actual number of infected cases. To demonstrate the efficiency of the model and approach, we also provide a tentative forecast two months ahead of time, i.e. until May 4, the date on which relaxation of the measures commenced, on the basis of the COVID-19 Community Mobility Reports released by Google on March 29.

METHODS

To deal with the uncertainty in the number of the actual asymptomatic infected cases in the total population Volpert et al. (2020), we address a modified compartmental Susceptible/ Exposed/ Infectious Asymptomatic/ Infected Symptomatic/ Recovered/ Dead (SEIIRD) model with two compartments of infectious persons: one modelling the cases in the population that are asymptomatic or experience very mild symptoms and another modelling the infected cases with mild to severe symptoms. The parameters of the model corresponding to the recovery period, the time from the onset of symptoms to death and the time from exposure to the time that an individual starts to be infectious, have been set as reported from clinical studies on COVID-19. For the estimation of the day-zero of the outbreak in Lombardy, as well as of the "effective" per-day transmission rate for which no clinical data are available, we have used the proposed SEIIRD simulator to fit the numbers of new daily cases from February 21 to the 8th of March. This was accomplished by solving a mixed-integer optimization problem. Based on the computed parameters, we also provide an estimation of the basic reproduction number R0 and the evolution of the effective reproduction number Re. To examine the efficiency of the model and approach, we ran the simulator to "forecast" the epidemic two months ahead of time, i.e. from March 8 to May 4. For this purpose, we considered the reduction in mobility in Lombardy as released on March 29 by Google COVID-19 Community Mobility Reports, and the effects of social distancing and of the very strict measures taken by the government on March 20 and March 21, 2020.

RESULTS

Based on the proposed methodological procedure, we estimated that the expected day-zero was January 14 (min-max rage: January 5 to January 23, interquartile range: January 11 to January 18). The actual cumulative number of asymptomatic infected cases in the total population in Lombardy on March 8 was of the order of 15 times the confirmed cumulative number of infected cases, while the expected value of the basic reproduction number R0 was found to be 4.53 (min-max range: 4.40- 4.65). On May 4, the date on which relaxation of the measures commenced the effective reproduction number was found to be 0.987 (interquartiles: 0.857, 1.133). The model approximated adequately two months ahead of time the evolution of reported cases of infected until May 4, the day on which the phase I of the relaxation of measures was implemented over all of Italy. Furthermore the model predicted that until May 4, around 20% of the population in Lombardy has recovered (interquartile range: ∼10% to ∼30%).

State-level needs for social distancing and contact tracing to contain COVID-19 in the United States

Starting in mid-May 2020, many US states began relaxing social distancing measures that were put in place to mitigate the spread of COVID-19. To evaluate the impact of relaxation of restrictions on COVID-19 dynamics and control, we developed a transmission dynamic model and calibrated it to US state-level COVID-19 cases and deaths. We used this model to evaluate the impact of social distancing, testing and contact tracing on the COVID-19 epidemic in each state. As of July 22, 2020, we found only three states were on track to curtail their epidemic curve. Thirty-nine states and the District of Columbia may have to double their testing and/or tracing rates and/or rolling back reopening by 25%, while eight states require an even greater measure of combined testing, tracing, and distancing. Increased testing and contact tracing capacity is paramount for mitigating the recent large-scale increases in U.S. cases and deaths.