How and When to End the COVID-19 Lockdown: An Optimization Approach

Model analysis and data validation of structured prevention and control interruptions of emerging infectious diseases

The design of optimized non-pharmaceutical interventions (NPIs) is critical to the effective control of emergent outbreaks of infectious diseases such as SARS, A/H1N1 and COVID-19 and to ensure that numbers of hospitalized cases do not exceed the carrying capacity of medical resources. To address this issue, we formulated a classic SIR model to include a close contact tracing strategy and structured prevention and control interruptions (SPCIs). The impact of the timing of SPCIs on the maximum number of non-isolated infected individuals and on the duration of an infectious disease outside quarantined areas (i.e. implementing a dynamic zero-case policy) were analyzed numerically and theoretically. These analyses revealed that to minimize the maximum number of non-isolated infected individuals, the optimal time to initiate SPCIs is when they can control the peak value of a second rebound of the epidemic to be equal to the first peak value. More individuals may be infected at the peak of the second wave with a stronger intervention during SPCIs. The longer the duration of the intervention and the stronger the contact tracing intensity during SPCIs, the more effective they are in shortening the duration of an infectious disease outside quarantined areas. The dynamic evolution of the number of isolated and non-isolated individuals, including two peaks and long tail patterns, have been confirmed by various real data sets of multiple-wave COVID-19 epidemics in China. Our results provide important theoretical support for the adjustment of NPI strategies in relation to a given carrying capacity of medical resources.

Dynamically adjustable SVEIR(MH) model of multiwave epidemics: Estimating the effects of public health measures against COVID-19

The COVID-19 pandemic was characterized by multiple subsequent, overlapping outbreaks, as well as extremely rapid changes in viral genomes. The information about local epidemics spread and the epidemic control measures was shared on a daily basis (number of cases and deaths) via centralized repositories. The vaccines were developed within the first year of the pandemic. New modes of monitoring and sharing of epidemic data were implemented using Internet resources. We modified the basic SEIR compartmental model to include public health measures, multiwave scenarios, and the variation of viral infectivity and transmissibility reflected by the basic reproduction number R0 of emerging viral variants. SVEIR(MH) model considers the capacity of the medical system, lockdowns, vaccination, and changes in viral reproduction rate on the epidemic spread. The developed model uses daily infection reports for assessing the epidemic dynamics, and daily changes of mobility data from mobile phone networks to assess the lockdown effectiveness. This model was deployed to six European regions Baden-Württemberg (Germany), Belgium, Czechia, Lombardy (Italy), Sweden, and Switzerland for the first 2 years of the pandemic. The correlation coefficients between observed and reported infection data showed good concordance for both years of the pandemic (ρ = 0.84-0.94 for the raw data and ρ = 0.91-0.98 for smoothed 7-day averages). The results show stability across the regions and the different epidemic waves. Optimal control of epidemic waves can be achieved by dynamically adjusting epidemic control measures in real-time. SVEIR(MH) model can simulate different scenarios and inform adjustments to the public health policies to achieve the target outcomes. Because this model is highly representative of actual epidemic situations, it can be used to assess both the public health and socioeconomic effects of the public health measures within the first 7 days of the outbreak.

Analysis of the COVID-19 pandemic using a compartmental model with time-varying parameters fitted by a genetic algorithm

Analyzing the COVID-19 pandemic is a critical factor in developing effective policies to deal with similar challenges in the future. However, many parameters (e.g., the actual number of infected people, the effectiveness of vaccination) are still subject to considerable debate because they are unobservable. To model a pandemic and estimate unobserved parameters, researchers use compartmental models. Most often, in such models, the transition rates are considered as constants, which allows simulating only one epidemiological wave. However, multiple waves have been reported for COVID-19 caused by different strains of the virus. This paper presents an approach based on the reconstruction of real distributions of transition rates using genetic algorithms, which makes it possible to create a model that describes several pandemic peaks. The model is fitted on registered COVID-19 cases in four countries with different pandemic control strategies (Germany, Sweden, UK, and US). Mean absolute percentage error (MAPE) was chosen as the objective function, the MAPE values of 2.168%, 2.096%, 1.208% and 1.703% were achieved for the listed countries, respectively. Simulation results are consistent with the empirical statistics of medical studies, which confirms the quality of the model. In addition to observables such as registered infected, the output of the model contains variables that cannot be measured directly. Among them are the proportion of the population protected by vaccines, the size of the exposed compartment, and the number of unregistered cases of COVID-19. According to the results, at the peak of the pandemic, between 14% (Sweden) and 25% (the UK) of the population were infected. At the same time, the number of unregistered cases exceeds the number of registered cases by 17 and 3.4 times, respectively. The average duration of the vaccine induced immune period is shorter than claimed by vaccine manufacturers, and the effectiveness of vaccination has declined sharply since the appearance of the Delta and Omicron strains. However, on average, vaccination reduces the risk of infection by about 65-70%.

Design of effective outpatient sentinel surveillance for COVID-19 decision-making: a modeling study

BACKGROUND

Decision-makers impose COVID-19 mitigations based on public health indicators such as reported cases, which are sensitive to fluctuations in supply and demand for diagnostic testing, and hospital admissions, which lag infections by up to two weeks. Imposing mitigations too early has unnecessary economic costs while imposing too late leads to uncontrolled epidemics with unnecessary cases and deaths. Sentinel surveillance of recently-symptomatic individuals in outpatient testing sites may overcome biases and lags in conventional indicators, but the minimal outpatient sentinel surveillance system needed for reliable trend estimation remains unknown.

METHODS

We used a stochastic, compartmental transmission model to evaluate the performance of various surveillance indicators at reliably triggering an alarm in response to, but not before, a step increase in transmission of SARS-CoV-2. The surveillance indicators included hospital admissions, hospital occupancy, and sentinel cases with varying levels of sampling effort capturing 5, 10, 20, 50, or 100% of incident mild cases. We tested 3 levels of transmission increase, 3 population sizes, and conditions of either simultaneous transmission increase or lagged increase in the older population. We compared the indicators' performance at triggering alarm soon after, but not prior, to the transmission increase.

RESULTS

Compared to surveillance based on hospital admissions, outpatient sentinel surveillance that captured at least 20% of incident mild cases could trigger an alarm 2 to 5 days earlier for a mild increase in transmission and 6 days earlier for a moderate or strong increase. Sentinel surveillance triggered fewer false alarms and averted more deaths per day spent in mitigation. When transmission increase in older populations lagged the increase in younger populations by 14 days, sentinel surveillance extended its lead time over hospital admissions by an additional 2 days.

CONCLUSIONS

Sentinel surveillance of mild symptomatic cases can provide more timely and reliable information on changes in transmission to inform decision-makers in an epidemic like COVID-19.

Adverse Reactions of COVID-19 Vaccines: A Scoping Review of Observational Studies

The COVID-19 pandemic had a severe global impact. A range of campaigns and activities, including vaccines, are being implemented to counteract this pandemic. Using observational data, the goal of this scoping review is to identify adverse events connected with COVID-19 vaccinations. We conduct a scoping study and searched three databases from the start of the COVID-19 pandemic in 2020 through June 2022. Based on our criteria and searched keywords, the review included eleven papers in total, with the majority of the studies being conducted in developed countries. The study populations varied and included general community populations, healthcare professionals, military forces, and patients with systemic lupus and cancer. This study includes vaccines from Pfizer-BioNTech, Oxford-AstraZeneca, Sinopharm, and Moderna. The COVID-19 vaccine-related adverse events were classified into three types: local side effects, systemic side effects, and other side effects such as allergies. The adverse reactions to COVID-19 vaccines are mild to moderate in severity, with no significant influence or interference in individual daily activities and no unique patterns in cause of death among vaccine-related deaths. According to the findings of these investigations, the COVID-19 vaccine is safe to administer and induces protection. It is vital to convey accurate information to the public about vaccination side effects, potential adverse responses, and the safety level of the vaccines supplied. Multiple strategies must be implemented at the individual, organizational, and population levels to eliminate vaccine hesitance. Future studies could investigate the vaccine's effect on people of various ages and medical conditions.

Can infectious modelling be applicable globally - lessons from COVID 19

Contagious diseases are needed to be monitored to prevent spreading within communities. Timely advice and predictions are necessary to overcome the consequences of those epidemics. Currently, emphasis has been placed on computer modelling to achieve the needed forecasts, the best example being the COVID-19 pandemic. Scientists used various models to determine how diverse sociodemographic factors correlated and influenced COVID-19 Global transmission and demonstrated the utility of computer models as tools in disease management. However, as modelling is done with assumptions with set rules, calculating uncertainty quantification is essential in infectious modelling when reporting the results and trustfully describing the limitations. This article summarizes the infectious disease modelling strategies, challenges, and global applicability by focusing on the COVID-19 pandemic.

COVID-19 exit strategy during vaccine implementation: a balance between social distancing and herd immunity

Currently, health authorities around the world are struggling to limit the spread of COVID-19. Since the beginning of the pandemic, social distancing has been the most important strategy used by most countries to control disease spread by flattening and elongating the epidemic curve. Another strategy, herd immunity, was also applied by some countries through relaxed control measures that allow the free spread of natural infection to build up solid immunity within the population. In 2021, COVID-19 vaccination was introduced with tremendous effort as a promising strategy for limiting the spread of disease. Therefore, in this review, we present the current knowledge about social distancing, herd immunity strategies, and aspects of their implementation to control the COVID-19 pandemic in the presence of the newly developed vaccines. Finally, we suggest a short-term option for controlling the pandemic during vaccine application.

On the economic growth equilibria during the Covid-19 pandemic

The aim of this paper is to study the effects of the Covid-19 pandemic suppression policies (i.e. containment measures or lockdowns) on labor supply, capital accumulation, and so the economic growth. We merge an epidemic SIS population model and a Solow's type growth model, i.e. we propose a fusion between economics and epidemiology. We show the creation and the destruction of economic growth equilibria driven by the suppression policies and by the severity of the disease. The dynamic stability properties of the equilibria are mainly determined by (i) the stringency of the suppression policies, (ii) the proportion of infected workers, (iii) the recovery rate of workers, and (iv) the economy's saving rate. Thus, economies can fall into the stable equilibrium of the poverty trap if the propensity to save is low and the economic policies that reduce the spread of infection are severe enough with high levels of infection and low rates of illness recovery. Otherwise, with high savings rates and if the suppression policies perform in such a way that infection levels are low and recovery rates are high, then the economies converge towards the equilibrium of high economic growth with capital accumulation. The scenario is rather complex since there is a multiplicity of equilibria such that economies can be in one scenario or another, characterized by stability or (structural) instability, i.e. bifurcation paths. Numerical simulations corroborate our results.

Rapid Antigen Diagnostics as Frontline Testing in the COVID‐19 Pandemic

The ongoing global COVID‐19 pandemic, caused by the SARS‐CoV‐2 virus, has resulted in significant loss of life since December 2019. Timely and precise virus detection has been proven as an effective solution to reduce the spread of the virus and to track the epidemic. Rapid antigen diagnostics has played a significant role in the frontline of COVID‐19 testing because of its convenience, low cost, and high accuracy. Herein, different types of recently innovated in‐lab and commercial antigen diagnostic technologies with emphasis on the strengths and limitations of these technologies including the limit of detection, sensitivity, specificity, affordability, and usability are systematically reviewed. The perspectives of assay development are looked into.

Perceived Changes of Attitudes and Behaviors of Seventh-Day Adventists During the COVID-19 Pandemic: Findings from a Cross-Sectional Survey in Germany

To analyze which pandemic related changes of attitudes and behaviors were perceived by Seventh-day Adventists (SDA) and how these relate to wellbeing, a cross-sectional survey with standardized questionnaires was performed. Participants (n = 1,494) stated changes for Relationships, Digital media usage and Nature/Silence/Contemplation, but not for Spirituality or Reflection of life. Best predictors of psychological wellbeing (WHO-5) were Spiritual wellbeing, perceived Restrictions and Awe/Gratitude (R² = .32). Mediation analyses (R² = 0.51) revealed a mediation effect of Awe/Gratitude between spiritual to psychological wellbeing (β = 0.11, p < 0.0001). Perceived changes were less relevant to buffer the negative effects of the pandemic; instead, they were related to fears of future. More relevant to stabilize SDAs´ wellbeing was their spirituality.

Loss of Faith and Decrease in Trust in a Higher Source During COVID-19 in Germany

Many people relied on their faith as one resource in order to cope during the COVID-19 pandemic. In Germany, between the eighteen months from June 2020 to November 2021, different participants at different times were assessed during different phases of the COVID-19 pandemic. The total sample of this continuous cross-sectional survey consisted of 4,693 participants. Analyses revealed that with the 2nd wave of the infection and its 2nd lockdown, trust in a Higher Source, along with praying and meditation decreased. Also, the sharp increase in corona-related stressors was associated with a decline of wellbeing and a continuing loss of faith. These developments were observed in both Catholics and Protestants, and in both younger and older persons. In addition, the long phases of insecurity and social isolation lacking the significant support usually given by religious communities may have likewise challenged the religious-coping capacities of religious/spiritual people themselves.

Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

SUPPLEMENTARY INFORMATION

The online version supplementary material available at 10.1007/s11071-022-07235-7.

Modeling the dynamics of COVID-19 pandemic with implementation of intervention strategies

The ongoing COVID-19 epidemic spread rapidly throughout India, with 34,587,822 confirmed cases and 468,980 deaths as of November 30, 2021. Major behavioral, clinical, and state interventions have implemented to mitigate the outbreak and prevent the persistence of the COVID-19 in human-to-human transmission in India and worldwide. Hence, the mathematical study of the disease transmission becomes essential to illuminate the real nature of the transmission behavior and control of the diseases. We proposed a compartmental model that stratify into nine stages of infection. The incidence data of the SRAS-CoV-2 outbreak in India was analyzed for the best fit to the epidemic curve and we estimated the parameters from the best fitted curve. Based on the estimated model parameters, we performed a short-term prediction of our model. We performed sensitivity analysis with respect to R 0 and obtained that the disease transmission rate has an impact in reducing the spread of diseases. Furthermore, considering the non-pharmaceutical and pharmaceutical intervention policies as control functions, an optimal control problem is implemented to reduce the disease fatality. To mitigate the infected individuals and to minimize the cost of the controls, an objective functional has been formulated and solved with the aid of Pontryagin's maximum principle. This study suggest that the implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Our numerical simulations exhibit that the combination of two controls is more effective when compared with the combination of single control as well as no control.

How political choices shaped Covid connectivity: The Italian case study

The importance of implementing new methodologies to study the ever-increasing amount of Covid-19 data is apparent. The aftermath analysis of these data could inform us on how specific political decisions influenced the dynamics of the pandemic outbreak. In this paper we use the Italian outbreak as a case study, to study six different Covid indicators collected in twenty Italian regions. We define a new object, the Covidome, to investigate the network of functional Covid interactions between regions. We analyzed the Italian Covidome over the course of 2020, and found that Covid connectivity between regions follows a sharp North-South community gradient. Furthermore, we explored the Covidome dynamics and individuated differences in regional Covid connectivity between the first and second waves of the pandemic. These differences can be associated to the two different lockdown strategies adopted for the first and the second wave from the Italian government. Finally, we explored to what extent Covid connectivity was associated with the Italian geographical network, and found that Central regions were more tied to the structural constraints than Northern or Southern regions in the spread of the virus. We hope that this approach will be useful in gaining new insights on how political choices shaped Covid dynamics across nations.

A Review of COVID-19 Modelling Strategies in Three Countries to Develop a Research Framework for Regional Areas

At the end of December 2019, an outbreak of COVID-19 occurred in Wuhan city, China. Modelling plays a crucial role in developing a strategy to prevent a disease outbreak from spreading around the globe. Models have contributed to the perspicacity of epidemiological variations between and within nations and the planning of desired control strategies. In this paper, a literature review was conducted to summarise knowledge about COVID-19 disease modelling in three countries-China, the UK and Australia-to develop a robust research framework for the regional areas that are urban and rural health districts of New South Wales, Australia. In different aspects of modelling, summarising disease and intervention strategies can help policymakers control the outbreak of COVID-19 and may motivate modelling disease-related research at a finer level of regional geospatial scales in the future.

Mechanistic modelling of COVID-19 and the impact of lockdowns on a short-time scale

BACKGROUND

To mitigate the spread of the COVID-19 coronavirus, some countries have adopted more stringent non-pharmaceutical interventions in contrast to those widely used. In addition to standard practices such as enforcing curfews, social distancing, and closure of non-essential service industries, other non-conventional policies also have been implemented, such as the total lockdown of fragmented regions, which are composed of sparsely and highly populated areas.

METHODS

In this paper, we model the movement of a host population using a mechanistic approach based on random walks, which are either diffusive or super-diffusive. Infections are realised through a contact process, whereby a susceptible host is infected if in close spatial proximity of the infectious host with an assigned transmission probability. Our focus is on a short-time scale (∼ 3 days), which is the average time lag time before an infected individual becomes infectious.

RESULTS

We find that the level of infection remains approximately constant with an increase in population diffusion, and also in the case of faster population dispersal (super-diffusion). Moreover, we demonstrate how the efficacy of imposing a lockdown depends heavily on how susceptible and infectious individuals are distributed over space.

CONCLUSION

Our results indicate that on a short-time scale, the type of movement behaviour does not play an important role in rising infection levels. Also, lock-down restrictions are ineffective if the population distribution is homogeneous. However, in the case of a heterogeneous population, lockdowns are effective if a large proportion of infectious carriers are distributed in sparsely populated sub-regions.

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.

Modelling and optimal control of multi strain epidemics, with application to COVID-19

Reinfection and multiple viral strains are among the latest challenges in the current COVID-19 pandemic. In contrast, epidemic models often consider a single strain and perennial immunity. To bridge this gap, we present a new epidemic model that simultaneously considers multiple viral strains and reinfection due to waning immunity. The model is general, applies to any viral disease and includes an optimal control formulation to seek a trade-off between the societal and economic costs of mitigation. We validate the model, with and without mitigation, in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil. The model can derive optimal mitigation strategies for any number of viral strains, whilst also evaluating the effect of distinct mitigation costs on the infection levels. The results show that relaxations in the mitigation measures cause a rapid increase in the number of cases, and therefore demand more restrictive measures in the future.

De-escalation strategies for non-pharmaceutical interventions following infectious disease outbreaks: a rapid review and a proposed dynamic de-escalation framework

BACKGROUND

The severity of COVID-19, as well as the speed and scale of its spread, has posed a global challenge. Countries around the world have implemented stringent non-pharmaceutical interventions (NPI) to control transmission and prevent health systems from being overwhelmed. These NPI have had profound negative social and economic impacts. With the timeline to worldwide vaccine roll-out being uncertain, governments need to consider to what extent they need to implement and how to de-escalate these NPI. This rapid review collates de-escalation criteria reported in the literature to provide a guide to criteria that could be used as part of de-escalation strategies globally.

METHODS

We reviewed literature published since 2000 relating to pandemics and infectious disease outbreaks. The searches included Embase.com (includes Embase and Medline), LitCovid, grey literature searching, reference harvesting and citation tracking. Over 1,700 documents were reviewed, with 39 documents reporting de-escalation criteria included in the final analysis. Concepts retrieved through a thematic analysis of the included documents were interlinked to build a conceptual dynamic de-escalation framework.

RESULTS

We identified 52 de-escalation criteria, the most common of which were clustered under surveillance (cited by 43 documents, 10 criteria e.g. ability to actively monitor confirmed cases and contact tracing), health system capacity (cited by 30 documents, 11 criteria, e.g. ability to treat all patients within normal capacity) and epidemiology (cited by 28 documents, 7 criteria, e.g. number or changes in case numbers). De-escalation is a gradual and bi-directional process, and resurgence of infections or emergence of variants of concerns can lead to partial or full re-escalation(s) of response and control measures in place. Hence, it is crucial to rely on a robust public health surveillance system.

CONCLUSIONS

This rapid review focusing on de-escalation within the context of COVID-19 provides a conceptual framework and a guide to criteria that countries can use to formulate de-escalation plans.

Is Curfew Effective in Limiting SARS-CoV-2 Progression? An Evaluation in France Based on Epidemiokinetic Analyses

BACKGROUND

Since late summer 2020, the French authorities implemented a curfew/lightened lockdown-alternating strategy instead of strict lockdown, to improve acceptability and limit socioeconomic consequences. However, data on curfew-related efficacy to control the epidemic are scarce.

OBJECTIVE

To investigate the effects on COVID-19 spread in France of curfew combined to local and/or nationwide restrictions from late summer 2020 to mid-February 2021.

DESIGN

We conducted a comparative evaluation using a susceptible-infected-recovered (SIR)-based model completed with epidemiokinetic tools.

MAIN MEASURES

We analyzed the time-course of epidemic progression rate under curfew in French Guyana and five metropolitan regions where additional restrictions were implemented at different times. Using linear regressions of the decay/increase rates in daily contaminations, we calculated the epidemic regression half-lives (t_1/2β) for each identified period.

KEY RESULTS

In French Guyana, two decay periods with rapid regression (t_1/2β of ~10 days) were observed under curfew, with slowing (t_1/2β of ~43 days) when curfew was lightened. During the 2-week pre-lockdown curfew (2020/10/17-2020/11/02) in Provence-Alpes-Côte-d'Azur, Auvergne-Rhône-Alpes, and Ile-de-France, the epidemic progression was unchanged. During the post-lockdown curfew (2020/12/15-2020/02/14), the epidemic slowly regressed in Grand-Est (t_1/2β of ~37 days), whereas its progression rate plateaued in Auvergne-Rhône-Alpes and increased immediately in Provence-Alpes-Côte-d'Azur, Ile-de-France, and Nouvelle-Aquitaine, whatever the curfew starting time was (06:00 or 08:00 pm). Interestingly, a delayed slow decay (17 days < t_1/2β < 64 days) occurred under curfew in all regions except Ile-de-France.

CONCLUSIONS

Curfew allowed the temporary control of SARS-CoV-2 epidemic, however variably in the French regions, without preventing lockdown necessity. To accelerate the epidemic regression such as observed in French Guyana, curfew should be implemented timely with additional restrictions.

Optimal COVID-19 Vaccine Sharing Between Two Nations That Also Have Extensive Travel Exchanges

Countries around the world have observed reduced infections from the SARS-CoV-2 virus, that causes COVID-19 illness, primarily due to non-pharmaceutical interventions (NPIs) such as lockdowns and social distancing measures designed to limit physical proximity between people. However, economies and societal interactions require restarting, and so lockdowns cannot continue indefinitely. Therefore, much hope is placed in using newly developed vaccines as a route back to normality, but this raises key questions about how they are shared. There are also emerging questions regarding travel. For instance, international business and trade necessitates at least some in-person exchanges, alongside restarting travel also for tourist purposes. By utilising a Susceptible-Infected-Recovered-Vaccinated (SIRV) mathematical model, we simulate the populations of two nations in parallel, where the first nation produces a vaccine and decides the extent to which it is shared with the second. Overlaying our mathematical structure is the virus-related effects of travel between the two nations. We find that even with extensive travel, nation one minimises its total number of deaths by simply retaining vaccines, aiming for full inoculation as fast as possible, suggesting that the risks posed by travel can be mitigated by rapidly vaccinating its own population. If instead we consider the total deaths i.e., sum of deaths of both nations, then such a policy of not sharing by nation one until full vaccination is highly sub-optimal. A policy of low initial sharing causes many more deaths in nation two than lives saved in nation one, raising important ethical issues. This imbalance in the health impact of vaccination provision must be considered as some countries begin to approach the point of extensive vaccination, while others lack the resources to do so.

Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic

A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with realistic reduced mobility values to inform public policy making, and we exemplify the applicability of the methodology using datasets from England and France.

In many countries, the COVID-19 pandemic has revealed a gap between public policy making and the use of advanced technological tools to inform such a process. In the big data era, decisions concerning the implementation of quarantines and travel restrictions are still being taken based on incomplete public health data, despite the myriad of information our society provides in real time, such as mobility data, commuting network structures, and financial patterns, to name a few. To advance towards an effective data-driven, quantitative policy making, we propose a computational framework where a predictive epidemiological model is fitted by feeding both public health and Google mobility data. The resulting model is then used as a basis for designing mobility reduction strategies which are optimised taking into account both the healthcare system capacity, and the economic impact of an extended lockdown. For the COVID-19 pandemic in England and France, we show that it is possible to design lockdown policies allowing a partial return to workplaces and schools, while maintaining the epidemic under control.

Optimizing time-limited non-pharmaceutical interventions for COVID-19 outbreak control

Retrospective analyses of the non-pharmaceutical interventions (NPIs) used to combat the ongoing COVID-19 outbreak have highlighted the potential of optimizing interventions. These optimal interventions allow policymakers to manage NPIs to minimize the epidemiological and human health impacts of both COVID-19 and the intervention itself. Here, we use a susceptible-infectious-recovered (SIR) mathematical model to explore the feasibility of optimizing the duration, magnitude and trigger point of five different NPI scenarios to minimize the peak prevalence or the attack rate of a simulated UK COVID-19 outbreak. An optimal parameter space to minimize the peak prevalence or the attack rate was identified for each intervention scenario, with each scenario differing with regard to how reductions to transmission were modelled. However, we show that these optimal interventions are fragile, sensitive to epidemiological uncertainty and prone to implementation error. We highlight the use of robust, but suboptimal interventions as an alternative, with these interventions capable of mitigating the peak prevalence or the attack rate over a broader, more achievable parameter space, but being less efficacious than theoretically optimal interventions. This work provides an illustrative example of the concept of intervention optimization across a range of different NPI strategies. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

One Year of Coronavirus Disease 2019 (COVID-19) in Brazil: A Political and Social Overview

Background

Coronavirus Disease 2019 (COVID-19) became the deadliest pandemic of the new millennium. One year after it became a pandemic, the current COVID-19 situation in Brazil is an example of how the impacts of a pandemic are beyond health outcomes and how health, social, and political actions are intertwined.

Objectives

We aimed to provide an overview of the first year of the COVID-19 pandemic in Brazil, from a social and political point of view, and to discuss the perspectives from now on.

Methods

This is a narrative review using official, scientific (PubMed, Medline, and SciELO databases) and publicly available data. Press articles were also used that contain important information not found in these databases.

Findings

We address the impacts of COVID-19 in different regions of Brazil, on indigenous populations, health care workers, and how internal social contrasts impacted the pandemics advance across the country. We also discuss key points that culminated in the countrys failed management of the COVID-19 spread, such as poor management of the public health care system, disparities between public and private health care infrastructure, lack of mass testing and viral spread tracking, lack of preparedness and planning to implement strict isolation and social distancing measures, and, most importantly, political instability, a deteriorating Health Ministry and sabotaging attitudes of the countrys president, including anti-scientific actions, underplaying COVID-19 severity, spreading and powering fake news about the pandemic, promoting knowingly inefficient medications for COVID-19 treatment, and interference in collective health policies, including the countrys vaccination plan.

Conclusions

After one year of COVID-19 and a disastrous management of the disease, Brazil has more than 11 million cases, 270,000 deaths, and the highest number of daily deaths due to COVID-19 in the world, most of which could have been avoided and can be credited to negligence of municipal, state, and federal authorities, especially President Jair Messias Bolsonaro. Unfortunately, the country is an example of what not to do in a pandemic setting.

Key Points

One year after COVID-19 was declared a pandemic, Brazil had the second higher number of cases and deaths, and the highest number of daily deaths due to the disease. Lack of massive testing, non-stringent and ineffective collective health policies, poor management of the public health care system, and political instability were the main drivers of the countrys flawed management of the COVID-19 advancement. Anti-science and sabotaging actions by government had a pivotal role in the countrys current situation. Brazil has a large territory and is marked by social contrasts among different regions and states, which showed contrasting data regarding the impact caused by COVID-19. COVID-19 databases and data sharing are important to provide an overview of epidemiological aspects of the disease; however, Brazil lacks standardization in these datasets.

Fleeing lockdown and its impact on the size of epidemic outbreaks in the source and target regions - a COVID-19 lesson

The COVID-19 pandemic forced authorities worldwide to implement moderate to severe restrictions in order to slow down or suppress the spread of the disease. It has been observed in several countries that a significant number of people fled a city or a region just before strict lockdown measures were implemented. This behavior carries the risk of seeding a large number of infections all at once in regions with otherwise small number of cases. In this work, we investigate the effect of fleeing on the size of an epidemic outbreak in the region under lockdown, and also in the region of destination. We propose a mathematical model that is suitable to describe the spread of an infectious disease over multiple geographic regions. Our approach is flexible to characterize the transmission of different viruses. As an example, we consider the COVID-19 outbreak in Italy. Projection of different scenarios shows that (i) timely and stricter intervention could have significantly lowered the number of cumulative cases in Italy, and (ii) fleeing at the time of lockdown possibly played a minor role in the spread of the disease in the country.

Estimating asymptomatic SARS-CoV-2 infections in a geographic area of low disease incidence

Background

The SARS-CoV-2 infection has emerged as a rapidly spreading infection. Today it is relatively easy to isolate Covid-19 symptomatic cases, while remains problematic to control the disease spread by infected but symptom-free individuals. The control of this possible path of contagion requires drastic measures of social distancing, which imply the suspension of most activities and generate economic and social issues. This study is aimed at estimating the percentage of asymptomatic SARS-CoV-2 infection in a geographic area with relatively low incidence of Covid-19.

Methods

Blood serum samples from 388 healthy volunteers were analyzed for the presence of anti-SARS-CoV-2 IgG by using an ELISA assay based on recombinant viral nucleocapsid protein.

Results

We found that 7 out of 388 healthy volunteers, who declared no symptoms of Covid-19, like fever, cough, fatigue etc., in the preceding 5 months, have bona fide serum anti-SARS-CoV-2 IgG, that is 1.8% of the asymptomatic population (95% confidence interval: 0.69–2.91%).

Conclusions

The estimated range of asymptomatic individuals with anti-SARS-CoV-2 IgG should be between 26,565 and 112, 350. In the same geographic area, there are 4665 symptomatic diagnosed cases.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-021-06054-2.

The future of sustainability in the context of COVID-19

The COVID-19 pandemic is a global crisis emanating both from a virus (SARS-CoV-2) and from the drastic actions to contain it. Here, we reflect on the immediate responses of most world powers amid the pandemic chaos: totalitarian surveillance and nationalist isolation. Drawing on published literature, we consider measures such as wildlife-use bans, lockdowns and travel restrictions, along with their reverberations for people, economies and the planet. Our synthesis highlights significant shortfalls of applying command-and-control tactics in emergencies. For one, heavy-handed bans risk enormous unintended consequences and tend to fail if they lack legitimacy or clash with people's values. Furthermore, reactive and myopic strategies typically view the pandemic as a stand-alone crisis, rather than unravelling the complex interplay of nature-society interactions through which zoonotic diseases originate. A return to adaptive management approaches that recognise root causes and foster socio-ecological resilience will be essential to improve human and planetary health and mitigate future pandemics.

Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between ‘spatial' and ‘non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

Modelling COVID-19 contagion: risk assessment and targeted mitigation policies

We use a spatial epidemic model with demographic and geographical heterogeneity to study the regional dynamics of COVID-19 across 133 regions in England. Our model emphasizes the role of variability of regional outcomes and heterogeneity across age groups and geographical locations, and provides a framework for assessing the impact of policies targeted towards subpopulations or regions. We define a concept of efficiency for comparative analysis of epidemic control policies and show targeted mitigation policies based on local monitoring to be more efficient than country-level or non-targeted measures. In particular, our results emphasize the importance of shielding vulnerable subpopulations and show that targeted policies based on local monitoring can considerably lower fatality forecasts and, in many cases, prevent the emergence of second waves which may occur under centralized policies.

Hypercoagulability in COVID-19: A review of the potential mechanisms underlying clotting disorders

Severe acute respiratory syndrome coronavirus-2 has emerged as a new viral pandemic, causing Coronavirus disease 2019 (COVID-19) leading to a wide array of symptoms ranging from asymptomatic to severe respiratory failure. However, coagulation disorders have been found in some patients infected with SARS-CoV-2, leading to either a clotting disorder or hemorrhage. Several mechanisms attempt to explain the mechanism behind the pro-coagulant state seen with COVID-19 patients, including different receptor binding, cytokine storm, and direct viral endothelial damage. SARS-CoV-2 has also been recently found to bind to CLEC4M receptor, a receptor that participates in the clearance of von Willebrand Factor and Factor VIII. The competitive binding of SARS-CoV-2 to CLEC4M could lead to decreased clearance, and therefore a promotion of a pro-coagulative state; however, an experimental study needs to be done to prove such an association.

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.

Analysis of the Tradeoff Between Health and Economic Impacts of the Covid-19 Epidemic

Various measures have been taken in different countries to mitigate the Covid-19 epidemic. But, throughout the world, many citizens don't understand well how these measures are taken and even question the decisions taken by their government. Should the measures be more (or less) restrictive? Are they taken for a too long (or too short) period of time? To provide some quantitative elements of response to these questions, we consider the well-known SEIR model for the Covid-19 epidemic propagation and propose a pragmatic model of the government decision-making operation. Although simple and obviously improvable, the proposed model allows us to study the tradeoff between health and economic aspects in a pragmatic and insightful way. Assuming a given number of phases for the epidemic (namely, 4 in this paper) and a desired tradeoff between health and economic aspects, it is then possible to determine the optimal duration of each phase and the optimal severity level (i.e., the target transmission rate) for each of them. The numerical analysis is performed for the case of France but the adopted approach can be applied to any country. One of the takeaway messages of this analysis is that being able to implement the optimal 4-phase epidemic management strategy in France would have led to 1.05 million of infected people and a GDP loss of 231 billions € instead of 6.88 millions of infected and a loss of 241 billions €. This indicates that, seen from the proposed model perspective, the effectively implemented epidemic management strategy is good economically, whereas substantial improvements might have been obtained in terms of health impact. Our analysis indicates that the lockdown/severe phase should have been more severe but shorter, and the adjustment phase occurred earlier. Due to the natural tendency of people to deviate from the official rules, updating measures every month over the whole epidemic episode seems to be more appropriate.

Evaluating Social Distancing Measures and Their Association with the Covid-19 Pandemic in South America

Social distancing is a powerful non-pharmaceutical intervention used as a way to slow the spread of the SARS-CoV-2 virus around the world since the end of 2019 in China. Taking that into account, this work aimed to identify variations on population mobility in South America during the pandemic (15 February to 27 October 2020). We used a data-driven approach to create a community mobility index from the Google Covid-19 Community Mobility and relate it to the Covid stringency index from Oxford Covid-19 Government Response Tracker (OxCGRT). Two hypotheses were established: countries which have adopted stricter social distancing measures have also a lower level of circulation (H1), and mobility is occurring randomly in space (H2). Considering a transient period, a low capacity of governments to respond to the pandemic with more stringent measures of social distancing was observed at the beginning of the crisis. In turn, considering a steady-state period, the results showed an inverse relationship between the Covid stringency index and the community mobility index for at least three countries (H1 rejected). Regarding the spatial analysis, global and local Moran indices revealed regional mobility patterns for Argentina, Brazil, and Chile (H1 rejected). In Brazil, the absence of coordinated policies between the federal government and states regarding social distancing may have played an important role for several and extensive clusters formation. On the other hand, the results for Argentina and Chile could be signals for the difficulties of governments in keeping their population under control, and for long periods, even under stricter decrees.

Mathematical modeling of COVID-19 transmission dynamics in Uganda: Implications of complacency and early easing of lockdown

BACKGROUND

Uganda has a unique set up comprised of resource-constrained economy, social-economic challenges, politically diverse regional neighborhood and home to long-standing refuge crisis that comes from long and protracted conflicts of the great lakes. The devastation of the on-going global pandemic outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is likely to be escalated by these circumstances with expectations of the impact of the disease being severe.

MATERIALS AND METHODS

In this study, we formulate a mathematical model that incorporates the currently known disease characteristics and tracks various intervention measures that the government of Uganda has implemented since the reporting of the first case in March 2020. We then evaluate these measures to understand levels of responsiveness and adherence to standard operating procedures and quantify their impact on the disease burden. Novel in this model was the unique aspect of modeling the trace-and-isolate protocol in which some of the latently infected individuals tested positive while in strict isolation centers thereby reducing their infectious period.

RESULTS

The study findings show that even with elimination of all imported cases at any given time it would take up to nine months to rid Uganda of the disease. The findings also show that the optimal timing of easing of lockdowns while mitigating the possibility of re-emergence of a second epidemic wave requires avoiding the scenario of releasing too-many-too-soon. It is even more worrying that enhancing contact tracing would only affect the magnitude and timing of the second wave but cannot prevent it altogether.

CONCLUSION

We conclude that, given the prevailing circumstances, a phased-out lifting of lockdown measures, minimization of COVID-19 transmissibility within hospital settings, elimination of recruitment of infected individuals as well as enhanced contact tracing would be key to preventing overwhelming of the healthcare system that would come with dire consequences.

Facilitating Understanding, Modeling and Simulation of Infectious Disease Epidemics in the Age of COVID-19

Interest in the mathematical modeling of infectious diseases has increased due to the COVID-19 pandemic. However, many medical students do not have the required background in coding or mathematics to engage optimally in this approach. System dynamics is a methodology for implementing mathematical models as easy-to-understand stock-flow diagrams. Remarkably, creating stock-flow diagrams is the same process as creating the equivalent differential equations. Yet, its visual nature makes the process simple and intuitive. We demonstrate the simplicity of system dynamics by applying it to epidemic models including a model of COVID-19 mutation. We then discuss the ease with which far more complex models can be produced by implementing a model comprising eight differential equations of a Chikungunya epidemic from the literature. Finally, we discuss the learning environment in which the teaching of the epidemic modeling occurs. We advocate the widespread use of system dynamics to empower those who are engaged in infectious disease epidemiology, regardless of their mathematical background.

Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal

The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to "normal life" and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.

Strategies to exiting the COVID-19 lockdown for workplace and school: A scoping review

In an attempt to curb the COVID-19 pandemic, several countries have implemented various social restrictions, such as closing schools and asking people to work from home. Nevertheless, after months of strict quarantine, a reopening of society is required. Many countries are planning exit strategies to progressively lift the lockdown without leading to an increase in the number of COVID-19 cases. Identifying exit strategies for a safe reopening of schools and places of work is critical in informing decision-makers on the management of the COVID-19 health crisis. This scoping review describes multiple population-wide strategies, including social distancing, testing, and contact tracing. It highlights how each strategy needs to be based on both the epidemiological situation and contextualize at local circumstances to anticipate the possibility of COVID-19 resurgence. However, the retrieved evidence lacks operational solutions and are mainly based on mathematical models and derived from grey literature. There is a need to report the impact of the implementation of country-tailored strategies and assess their effectiveness through high-quality experimental studies.

Flattening the curves: on-off lock-down strategies for COVID-19 with an application to Brazil

The current COVID-19 pandemic is affecting different countries in different ways. The assortment of reporting techniques alongside other issues, such as underreporting and budgetary constraints, makes predicting the spread and lethality of the virus a challenging task. This work attempts to gain a better understanding of how COVID-19 will affect one of the least studied countries, namely Brazil. Currently, several Brazilian states are in a state of lock-down. However, there is political pressure for this type of measures to be lifted. This work considers the impact that such a termination would have on how the virus evolves locally. This was done by extending the SEIR model with an on / off strategy. Given the simplicity of SEIR we also attempted to gain more insight by developing a neural regressor. We chose to employ features that current clinical studies have pinpointed has having a connection to the lethality of COVID-19. We discuss how this data can be processed in order to obtain a robust assessment.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1186/s13362-020-00098-w.

A simulation–optimization framework for optimizing response strategies to epidemics☆

Epidemics require dynamic response strategies that encompass a multitude of policy alternatives and that balance health, economic and societal considerations. We propose a simulation–optimization framework to aid policymakers select closure, protection and travel policies to minimize the total number of infections under a limited budget. The proposed framework combines a modified, age-stratified SEIR compartmental model to evaluate the health impact of response strategies and a Genetic Algorithm to effectively search for better strategies. We implemented our framework on a real case study in Nova Scotia to devise optimized response strategies to COVID-19 under different budget scenarios and found a clear trade-off between health and economic considerations. Closure policies seem to be the most sensitive to policy restrictions, followed by travel policies. On the other hand, results suggest that practising social distancing and wearing masks are necessary whenever their economic impacts are bearable. The framework is generic and can be extended to encompass vaccination policies and to use different epidemiological models and optimization methods.

Improved glycemic control amongst people with long-standing diabetes during COVID-19 lockdown: a prospective, observational, nested cohort study

Background and aims

COVID-19 is likely to affect the lives of individuals with type 2 diabetes. However, the effect of COVID-19 lockdown on physical activity and glycemic control in such individuals is not known. We studied the physical activity and glycemic control during lockdown in comparison to pre-lockdown parameters in individuals with long-standing type 2 diabetes.

Methods

This prospective, observational study includes 2240 people with T2DM regularly attending diabetes clinic prior to lockdown. Glycemic record, HbA1c, and physical activity assessed with Global Physical Activity Questionnaire (GPAQ) as metabolic equivalents (MetS min/week) were obtained during lockdown (minimum duration of 3 months).

Results

A total of 422 out of 750 participants (nest) responded. The median (IQR) for age was 58 (52 to 64) years, duration of diabetes 11 (6 to 16) years, prevalent foot complications in 59.7%, and atherosclerotic cardiovascular disease in 21.3% of participants. There was a decrease in HbA1c from 7.8% (6.9 to 9.4) prior lockdown to 7.4% (6.6 to8.7) during lockdown [ΔHbA1c − 0.41 ± 0.27% (p = 0.005)] and postprandial blood glucose 200.0 mg/dl (152.0 to 252.0) to 158.0 (140.0 to 200.0) mg/dl (p < 0.001). The physical activity increased during lockdown from a GPAQ score 140 (0.0 to 1260) MetS to 840 (0.0 to 1680) MetS (p = 0.014). The improvement of glycemic control was observed in either gender and independent of the presence of foot complications or increase in physical activity.

Conclusions

There is an overall improvement of glycemic control during COVID-19 lockdown independent of increase in physical activity in people with long duration of diabetes.

Forecast predictions for the COVID-19 pandemic in Brazil by statistical modeling using the Weibull distribution for daily new cases and deaths

COVID-19 has killed more than 500,000 people worldwide and more than 60,000 in Brazil. Since there are no specific drugs or vaccines, the available tools against COVID-19 are preventive, such as the use of personal protective equipment, social distancing, lockdowns, and mass testing. Such measures are hindered in Brazil due to a restrict budget, low educational level of the population, and misleading attitudes from the federal authorities. Predictions for COVID-19 are of pivotal importance to subsidize and mobilize health authorities' efforts in applying the necessary preventive strategies. The Weibull distribution was used to model the forecast prediction of COVID-19, in four scenarios, based on the curve of daily new deaths as a function of time. The date in which the number of daily new deaths will fall below the rate of 3 deaths per million - the average level in which some countries start to relax the stay-at-home measures - was estimated. If the daily new deaths curve was bending today (i.e., about 1250 deaths per day), the predicted date would be on July 5. Forecast predictions allowed the estimation of overall death toll at the end of the outbreak. Our results suggest that each additional day that lasts to bend the daily new deaths curve may correspond to additional 1685 deaths at the end of COVID-19 outbreak in Brazil (R2 = 0.9890). Predictions of the outbreak can be used to guide Brazilian health authorities in the decision-making to properly fight COVID-19 pandemic.

Key questions for modelling COVID-19 exit strategies

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.