The challenges of modeling and forecasting the spread of COVID-19

The impact of non-pharmaceutical interventions, demographic, social, and climatic factors on the initial growth rate of COVID-19: A cross-country study

On March 11, 2020 the World Health Organization announced that the COVID-19 disease developed into a global pandemic. In the present paper, we aimed at analysing how the implementation of Non-Pharmaceutical Interventions (NPI) as well as climatic, social, and demographic variables affected the initial growth rate of COVID-19. In more detail, we aimed at identifying and assessing all the predictors in a whole picture of the COVID-19 outbreak and the effectiveness of the response of the countries to the pandemic. It can be expected, indeed, that there is a subtle and complex interplay among the various parameters. As such, we estimated the initial growth rate of COVID-19 for countries across the globe, and used a multiple linear regression model to study the association between the initial growth rate and NPI as well as pre-existing country characteristics (climatic, social and demographic variables measured before the current epidemic began). We obtained a mean initial growth rate of 0.120 (SD 0.076), in the range 0.023-0.315. Ten (8 pre-existing country characteristics and 2 NPI) out of 29 factors considered (21 pre-existing country characteristics and 8 NPI) were associated with the initial growth of COVID-19. Population in urban agglomerations of more than 1 million, PM2.5 air pollution mean annual exposure, life expectancy, hospital beds available, urban population, Global Health Security detection index and restrictions on international movement had the most significant effects on the initial growth of COVID-19. Based on available data and the results we obtained, NPI put in place by governments around the world alone may not have had a significant impact on the initial growth of COVID-19. Only restrictions on international movements had a relative significance with respect to the initial growth rate, whereas demographic, climatic, and social variables seemed to play a greater role in the initial growth rate of COVID-19.

An epidemic model for non-first-order transmission kinetics

Compartmental models in epidemiology characterize the spread of an infectious disease by formulating ordinary differential equations to quantify the rate of disease progression through subpopulations defined by the Susceptible-Infectious-Removed (SIR) scheme. The classic rate law central to the SIR compartmental models assumes that the rate of transmission is first order regarding the infectious agent. The current study demonstrates that this assumption does not always hold and provides a theoretical rationale for a more general rate law, inspired by mixed-order chemical reaction kinetics, leading to a modified mathematical model for non-first-order kinetics. Using observed data from 127 countries during the initial phase of the COVID-19 pandemic, we demonstrated that the modified epidemic model is more realistic than the classic, first-order-kinetics based model. We discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n. While k finds utility in evaluating the effectiveness of control measures due to its responsiveness to external factors, n is more closely related to the intrinsic properties of the epidemic agent, including reproductive ability. The rate law for the modified compartmental SIR model is generally applicable to mixed-kinetics disease transmission with heterogeneous transmission mechanisms. By analyzing early-stage epidemic data, this modified epidemic model may be instrumental in providing timely insight into a new epidemic and developing control measures at the beginning of an outbreak.

The prediction of the lifetime of the new coronavirus in the USA using mathematical models

The World Health Organization (WHO) on December 31, 2019, was informed of several cases of respiratory diseases of unknown origin in the city of Wuhan in the Chinese Province of Hubei, the clinical manifestations of which were similar to those of viral pneumonia and manifested as fever, cough, and shortness of breath. And, the disease caused by the virus is named the new coronavirus disease 2019 and it will be abbreviated as 2019-nCoV and COVID-19. As of January 30, 2020, the WHO classified this epidemic as a global health emergency (Chung et al. in Radiology 295(1):202-207, 2020). It is an international real-life problem. Due to deaths, globally everyone is under fear. Now, it is the responsibility of researchers to give hope to the people. In this article, we aim to better protect people and general pandemic preparedness by predicting the lifetime of the disease-causing virus using three mathematical models. This article deals with a complex real-life problem people face all over the world, an international real-life problem. The main focus is on the USA due to large infection and death due to coronavirus and thereby the life of every individual is uncertain. The death counts of the USA from February 29 to April 22, 2020, are used in this article as a data set. The death counts of the USA are fitted by the solutions of three mathematical models and a solution to an international problem is achieved. Based on the death rate, the lifetime of the coronavirus COVID-19 is predicted as 1464.76 days from February 29, 2020. That is, after March 2024 there will be no death in the USA due to COVID-19 if everyone follows the guidelines of WHO and the advice of healthcare workers. People and government can get prepared for this situation and many lives can be saved. It is the contribution of soft computing. Finally, this article suggests several steps to control the spread and severity of the disease. The research work, the lifetime prediction presented in this article is entirely new and differs from all other articles in the literature.

An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

A model of COVID-19 propagation based on a gamma subordinated negative binomial branching process

We build a parsimonious Crump-Mode-Jagers continuous time branching process of COVID-19 propagation based on a negative binomial process subordinated by a gamma subordinator. By focusing on the stochastic nature of the process in small populations, our model provides decision making insight into mitigation strategies as an outbreak begins. Our model accommodates contact tracing and isolation, allowing for comparisons between different types of intervention. We emphasize a physical interpretation of the disease propagation throughout which affords analytical results for comparison to simulations. Our model provides a basis for decision makers to understand the likely trade-offs and consequences between alternative outbreak mitigation strategies particularly in office environments and confined work-spaces. Combining the asymptotic limit of our model with Bayesian hierarchical techniques, we provide US county level inferences for the reproduction number from cumulative case count data over July and August of this year.

Control strategies for COVID-19 epidemic with vaccination, shield immunity and quarantine: A metric temporal logic approach

Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can specify the expected control outcomes such as "the deaths from the infection should never exceed one thousand per day within the next three months" or "the population immune from the disease should eventually exceed 200 thousand within the next 100 to 120 days". We then develop methods for synthesizing control strategies with MTL specifications. To the best of our knowledge, this is the first paper to systematically synthesize control strategies based on the COVID-19 epidemic models with formal specifications. We provide simulation results in three different case studies: vaccination control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; shield immunity control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; and quarantine control for the COVID-19 epidemic with model parameters estimated from data in Wuhan, China. The results show that the proposed synthesis approach can generate control inputs such that the time-varying numbers of individuals in each category (e.g., infectious, immune) satisfy the MTL specifications. The results also show that early intervention is essential in mitigating the spread of COVID-19, and more control effort is needed for more stringent MTL specifications. For example, based on the model in Lombardy, Italy, achieving less than 100 deaths per day and 10000 total deaths within 100 days requires 441.7% more vaccination control effort than achieving less than 1000 deaths per day and 50000 total deaths within 100 days.

Public perceptions, individual characteristics, and preventive behaviors for COVID-19 in six countries: a cross-sectional study

Background

Public perceptions and personal characteristics are heterogeneous between countries and subgroups, which may have different impacts on health-protective behaviors during the coronavirus disease 2019 (COVID-19) pandemic. To assess whether self-reported perceptions of COVID-19 and personal characteristics are associated with protective behaviors among general adults and to compare patterns in six different countries.

Methods

This cross-sectional study uses the secondary data collected through an online survey between 15 and 23 April 2020 across six countries (China, Italy, Japan, Korea, the UK, and the USA). A total of 5945 adults aged 18 years or older were eligible for our analysis. A logistic regression model was used to estimate odds ratios (OR) and 95% confidence intervals (95%CI) of three recommended behaviors (wearing a mask, handwashing, and avoiding social gatherings).

Results

In most countries except for China, the participants who perceived wearing a mask as being extremely effective to curtail the pandemic were more likely to wear a mask (OR, 95%CI: Italy: 4.14, 2.08–8.02; Japan: 3.59, 1.75–7.30; Korea: 7.89, 1.91–31.63: UK: 9.23, 5.14–17.31; USA: 4.81, 2.61–8.92). Those who perceived that handwashing was extremely effective had higher ORs of this preventive behavior (OR, 95%CI: Italy: 16.39, 3.56–70.18; Japan: 12.24, 4.03–37.35; Korea: 12.41, 2.02–76.39; UK: 18.04, 2.60–152.78; USA: 10.56, 2.21–44.32). The participants who perceived avoiding social gathering as being extremely effective to curtail the pandemic were more likely to take this type of preventive behavior (OR, 95%CI: China: 3.79, 1.28–10.23; Korea: 6.18, 1.77–20.60; UK: 4.45, 1.63–11.63; USA: 4.34, 1.84–9.95). The associations between personal characteristics, living environment, psychological status, and preventive behaviors varied across different countries. Individuals who changed their behavior because of recommendations from doctors/public health officials were more likely to take preventive behaviors in many countries.

Conclusions

These findings suggest that higher perceived effectiveness may be a common factor to encourage preventive behaviors in response to the COVID-19 pandemic. These results may provide a better understanding of the homogeneity and heterogeneity of factors related to preventive behaviors and improve public health policies in various countries and groups.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12199-021-00952-2.

Mortality containment vs. Economics Opening: Optimal policies in a SEIARD model

We extend the classic approach (SIR) to a SEAIRD model with policy controls. A social planner's objective reflects the trade-off between mortality reduction and GDP, featuring its perception of the value of statistical life (PVSL). We introduce realistic and drastic limitations to the control available to it. Within this setup, we explore the results of various control policies. We notably describe the joint dynamics of infection and economy in different contexts with unique or multiple confinement episodes. Compared to other approaches, our contributions are: (i) to restrict the class of functions accessible to the social planner, and in particular to impose that they remain constant over some fixed periods; (ii) to impose implementation frictions, e.g. a lag in their implementation; (iii) to prove the existence of optimal strategies within this set of possible controls; iv) to exhibit a sudden change in optimal policy as the statistical value of life is raised, from laissez-faire to a sizeable lockdown level, indicating a possible reason for conflicting policy proposals.

Effects of containment and closure policies on controlling the COVID-19 pandemic in East Asia

Growing efforts have been made to pool coronavirus data and control measures from countries and regions to compare the effectiveness of government policies. We examine whether these strategies can explain East Asia's effective control of the COVID-19 pandemic based on time-series data with cross-correlations between the Stringency Index and number of confirmed cases during the early period of outbreaks. We suggest that multidisciplinary empirical research in healthcare and social sciences, personality, and social psychology is needed for a clear understanding of how cultural values, social norms, and individual predispositions interact with policy to affect life-saving behavioural changes in different societies.

Modelling and predicting the effect of social distancing and travel restrictions on COVID-19 spreading

To date, the only effective means to respond to the spreading of the COVID-19 pandemic are non-pharmaceutical interventions (NPIs), which entail policies to reduce social activity and mobility restrictions. Quantifying their effect is difficult, but it is key to reducing their social and economic consequences. Here, we introduce a meta-population model based on temporal networks, calibrated on the COVID-19 outbreak data in Italy and applied to evaluate the outcomes of these two types of NPIs. Our approach combines the advantages of granular spatial modelling of meta-population models with the ability to realistically describe social contacts via activity-driven networks. We focus on disentangling the impact of these two different types of NPIs: those aiming at reducing individuals' social activity, for instance through lockdowns, and those that enforce mobility restrictions. We provide a valuable framework to assess the effectiveness of different NPIs, varying with respect to their timing and severity. Results suggest that the effects of mobility restrictions largely depend on the possibility of implementing timely NPIs in the early phases of the outbreak, whereas activity reduction policies should be prioritized afterwards.

The impact of non-pharmaceutical interventions on SARS-CoV-2 transmission across 130 countries and territories

BACKGROUND

Non-pharmaceutical interventions (NPIs) are used to reduce transmission of SARS coronavirus 2 (SARS-CoV-2) that causes coronavirus disease 2019 (COVID-19). However, empirical evidence of the effectiveness of specific NPIs has been inconsistent. We assessed the effectiveness of NPIs around internal containment and closure, international travel restrictions, economic measures, and health system actions on SARS-CoV-2 transmission in 130 countries and territories.

METHODS

We used panel (longitudinal) regression to estimate the effectiveness of 13 categories of NPIs in reducing SARS-CoV-2 transmission using data from January to June 2020. First, we examined the temporal association between NPIs using hierarchical cluster analyses. We then regressed the time-varying reproduction number (Rt) of COVID-19 against different NPIs. We examined different model specifications to account for the temporal lag between NPIs and changes in Rt, levels of NPI intensity, time-varying changes in NPI effect, and variable selection criteria. Results were interpreted taking into account both the range of model specifications and temporal clustering of NPIs.

RESULTS

There was strong evidence for an association between two NPIs (school closure, internal movement restrictions) and reduced Rt. Another three NPIs (workplace closure, income support, and debt/contract relief) had strong evidence of effectiveness when ignoring their level of intensity, while two NPIs (public events cancellation, restriction on gatherings) had strong evidence of their effectiveness only when evaluating their implementation at maximum capacity (e.g. restrictions on 1000+ people gathering were not effective, restrictions on < 10 people gathering were). Evidence about the effectiveness of the remaining NPIs (stay-at-home requirements, public information campaigns, public transport closure, international travel controls, testing, contact tracing) was inconsistent and inconclusive. We found temporal clustering between many of the NPIs. Effect sizes varied depending on whether or not we included data after peak NPI intensity.

CONCLUSION

Understanding the impact that specific NPIs have had on SARS-CoV-2 transmission is complicated by temporal clustering, time-dependent variation in effects, and differences in NPI intensity. However, the effectiveness of school closure and internal movement restrictions appears robust across different model specifications, with some evidence that other NPIs may also be effective under particular conditions. This provides empirical evidence for the potential effectiveness of many, although not all, actions policy-makers are taking to respond to the COVID-19 pandemic.

The impact of non-pharmaceutical interventions on SARS-CoV-2 transmission across 130 countries and territories

BACKGROUND

Non-pharmaceutical interventions (NPIs) are used to reduce transmission of SARS coronavirus 2 (SARS-CoV-2) that causes coronavirus disease 2019 (COVID-19). However, empirical evidence of the effectiveness of specific NPIs has been inconsistent. We assessed the effectiveness of NPIs around internal containment and closure, international travel restrictions, economic measures, and health system actions on SARS-CoV-2 transmission in 130 countries and territories.

METHODS

We used panel (longitudinal) regression to estimate the effectiveness of 13 categories of NPIs in reducing SARS-CoV-2 transmission using data from January to June 2020. First, we examined the temporal association between NPIs using hierarchical cluster analyses. We then regressed the time-varying reproduction number (R_t) of COVID-19 against different NPIs. We examined different model specifications to account for the temporal lag between NPIs and changes in R_t, levels of NPI intensity, time-varying changes in NPI effect, and variable selection criteria. Results were interpreted taking into account both the range of model specifications and temporal clustering of NPIs.

RESULTS

There was strong evidence for an association between two NPIs (school closure, internal movement restrictions) and reduced R_t. Another three NPIs (workplace closure, income support, and debt/contract relief) had strong evidence of effectiveness when ignoring their level of intensity, while two NPIs (public events cancellation, restriction on gatherings) had strong evidence of their effectiveness only when evaluating their implementation at maximum capacity (e.g. restrictions on 1000+ people gathering were not effective, restrictions on < 10 people gathering were). Evidence about the effectiveness of the remaining NPIs (stay-at-home requirements, public information campaigns, public transport closure, international travel controls, testing, contact tracing) was inconsistent and inconclusive. We found temporal clustering between many of the NPIs. Effect sizes varied depending on whether or not we included data after peak NPI intensity.

CONCLUSION

Understanding the impact that specific NPIs have had on SARS-CoV-2 transmission is complicated by temporal clustering, time-dependent variation in effects, and differences in NPI intensity. However, the effectiveness of school closure and internal movement restrictions appears robust across different model specifications, with some evidence that other NPIs may also be effective under particular conditions. This provides empirical evidence for the potential effectiveness of many, although not all, actions policy-makers are taking to respond to the COVID-19 pandemic.

Challenge of forecasting demand of medical resources and supplies during a pandemic: A comparative evaluation of three surge calculators for COVID-19

Ever since the World Health Organization (WHO) declared the new coronavirus disease 2019 (COVID-19) as a pandemic, there has been a public health debate concerning medical resources and supplies including hospital beds, intensive care units (ICU), ventilators and protective personal equipment (PPE). Forecasting COVID-19 dissemination has played a key role in informing healthcare professionals and governments on how to manage overburdened healthcare systems. However, forecasting during the pandemic remained challenging and sometimes highly controversial. Here, we highlight this challenge by performing a comparative evaluation for the estimations obtained from three COVID-19 surge calculators under different social distancing approaches, taking Lebanon as a case study. Despite discrepancies in estimations, the three surge calculators used herein agree that there will be a relative shortage in the capacity of medical resources and a significant surge in PPE demand if the social distancing policy is removed. Our results underscore the importance of implementing containment interventions including social distancing in alleviating the demand for medical care during the COVID-19 pandemic in the absence of any medication or vaccine. The paper also highlights the value of employing several models in surge planning.

COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling

Epidemiological models are widely used to analyze the spread of diseases such as the global COVID-19 pandemic caused by SARS-CoV-2. However, all models are based on simplifying assumptions and often on sparse data. This limits the reliability of parameter estimates and predictions. In this manuscript, we demonstrate the relevance of these limitations and the pitfalls associated with the use of overly simplistic models. We considered the data for the early phase of the COVID-19 outbreak in Wuhan, China, as an example, and perform parameter estimation, uncertainty analysis and model selection for a range of established epidemiological models. Amongst others, we employ Markov chain Monte Carlo sampling, parameter and prediction profile calculation algorithms. Our results show that parameter estimates and predictions obtained for several established models on the basis of reported case numbers can be subject to substantial uncertainty. More importantly, estimates were often unrealistic and the confidence/credibility intervals did not cover plausible values of critical parameters obtained using different approaches. These findings suggest, amongst others, that standard compartmental models can be overly simplistic and that the reported case numbers provide often insufficient information for obtaining reliable and realistic parameter values, and for forecasting the evolution of epidemics.

A Synergetic R-Shiny Portal for Modeling and Tracking of COVID-19 Data

The purpose of this paper is to introduce a useful online interactive dashboard (https://mahdisalehi.shinyapps.io/Covid19Dashboard/) that visualize and follow confirmed cases of COVID-19 in real-time. The dashboard was made publicly available on 6 April 2020 to illustrate the counts of confirmed cases, deaths, and recoveries of COVID-19 at the level of country or continent. This dashboard is intended as a user-friendly dashboard for researchers as well as the general public to track the COVID-19 pandemic, and is generated from trusted data sources and built in open-source R software (Shiny in particular); ensuring a high sense of transparency and reproducibility. The R Shiny framework serves as a platform for visualization and analysis of the data, as well as an advance to capitalize on existing data curation to support and enable open science. Coded analysis here includes logistic and Gompertz growth models, as two mathematical tools for predicting the future of the COVID-19 pandemic, as well as the Moran's index metric, which gives a spatial perspective via heat maps that may assist in the identification of latent responses and behavioral patterns. This analysis provides real-time statistical application aiming to make sense to academic- and public consumers of the large amount of data that is being accumulated due to the COVID-19 pandemic.

The between-farm transmission dynamics of porcine epidemic diarrhoea virus: A short-term forecast modelling comparison and the effectiveness of control strategies

A limited understanding of the transmission dynamics of swine disease is a significant obstacle to prevent and control disease spread. Therefore, understanding between-farm transmission dynamics is crucial to developing disease forecasting systems to predict outbreaks that would allow the swine industry to tailor control strategies. Our objective was to forecast weekly porcine epidemic diarrhoea virus (PEDV) outbreaks by generating maps to identify current and future PEDV high-risk areas, and simulating the impact of control measures. Three epidemiological transmission models were developed and compared: a novel epidemiological modelling framework was developed specifically to model disease spread in swine populations, PigSpread, and two models built on previously developed ecosystems, SimInf (a stochastic disease spread simulations) and PoPS (Pest or Pathogen Spread). The models were calibrated on true weekly PEDV outbreaks from three spatially related swine production companies. Prediction accuracy across models was compared using the receiver operating characteristic area under the curve (AUC). Model outputs had a general agreement with observed outbreaks throughout the study period. PoPS had an AUC of 0.80, followed by PigSpread with 0.71, and SimInf had the lowest at 0.59. Our analysis estimates that the combined strategies of herd closure, controlled exposure of gilts to live viruses (feedback) and on-farm biosecurity reinforcement reduced the number of outbreaks. On average, 76% to 89% reduction was seen in sow farms, while in gilt development units (GDU) was between 33% to 61% when deployed to sow and GDU farms located in probabilistic high-risk areas. Our multi-model forecasting approach can be used to prioritize surveillance and intervention strategies for PEDV and other diseases potentially leading to more resilient and healthier pig production systems.

28 Models Later: Model Competition and the Zombie Apocalypse

Between Fall 2011 and Fall 2012 students at Utah State University played several rounds of Humans versus Zombies (HvZ), a role-playing variant of tag popular on college campuses. The goal of the game is for the zombies to tag humans, converting them into more zombies. Based on portrayals of 'zombieism' in popular culture, one might treat HvZ as a disease system. However, a traditional SIR model with mass-action dynamics does a poor job of modeling HvZ, leading to the natural question: What mechanisms drive the dynamics of the HvZ system? We use model competition, with Bayesian Information Criterion as arbiter, to answer this question. First, we develop a suite of models with a variety of transmission mechanisms and fit to data from fall 2011. We use model competition to determine which model(s) have the most support from the data, thereby offering insight into driving mechanisms for HvZ. Bootstrapping is used to both assess the significance of individual mechanisms and to determine confidence in the performance of our models. Finally, we test predictions of the best models with data from fall 2012. Results indicate that through both years of the game humans tend to cluster defensively, zombies tend to hunt in groups, some zombies are more proficient hunters, and some humans leave the game.

Estimating density limits for walking pedestrians keeping a safe interpersonal distancing

With people trying to keep a safe distance from others due to the COVID-19 outbreak, the way in which pedestrians walk has completely changed since the pandemic broke out1,2. In this work, laboratory experiments demonstrate the effect of several variables-such as the pedestrian density, the walking speed and the prescribed safety distance-on the interpersonal distance established when people move within relatively dense crowds. Notably, we observe that the density should not be higher than 0.16 pedestrians per square meter (around 6 m2 per pedestrian) in order to guarantee an interpersonal distance of 1 m. Although the extrapolation of our findings to other more realistic scenarios is not straightforward, they can be used as a first approach to establish density restrictions in urban and architectonic spaces based on scientific evidence.

Panel forecasts of country-level Covid-19 infections

We use a dynamic panel data model to generate density forecasts for daily active Covid-19 infections for a panel of countries/regions. Our specification that assumes the growth rate of active infections can be represented by autoregressive fluctuations around a downward sloping deterministic trend function with a break. Our fully Bayesian approach allows us to flexibly estimate the cross-sectional distribution of slopes and then implicitly use this distribution as prior to construct Bayes forecasts for the individual time series. We find some evidence that information from locations with an early outbreak can sharpen forecast accuracy for late locations. There is generally a lot of uncertainty about the evolution of active infection, due to parameter and shock uncertainty, in particular before and around the peak of the infection path. Over a one-week horizon, the empirical coverage frequency of our interval forecasts is close to the nominal credible level. Weekly forecasts from our model are published at https://laurayuliu.com/covid19-panel-forecast/.

A simple, SIR-like but individual-based epidemic model: Application in comparison of COVID-19 in New York City and Wuhan

In this study, an individual-based epidemic model, considering latent-infectious-recovery periods, is presented. The analytic solution of the model in the form of recursive formulae with a time-dependent transmission coefficient is derived and implanted in Excel. The simulated epidemic curves from the model fit very well with the daily reported cases of COVID-19 in Wuhan, China and New York City (NYC), USA. These simulations show that the transmission rate of NYC's COVID-19 is nearly 30% greater than the transmission rate of Wuhan's COVID-19, and that the actual number of cumulative infected people in NYC is around 9 times the reported number of cumulative COVID-19 cases in NYC. Results from this study also provide important information about latent period, infectious period and lockdown efficiency.

COVID-19 epidemiology in Canada from January to December 2020: the pre-vaccine era

This paper summarizes COVID-19 disease epidemiology in Canada in the pre-vaccine era—from January through to December 2020. Canadian case numbers, risk factors, disease presentations (including severe and critical disease), and outcomes are described. Differences between provinces and territories in geography, population size and density, health demographics, and pandemic impact are highlighted. Key concepts in public health response and mitigation are reviewed, including masking, physical distancing, hand washing, and the promotion of outdoor interactions. Adequate investment in public health infrastructure is stressed, and regional differences in screening and testing strategies are highlighted. The spread of COVID-19 in Canadian workplaces, long-term care homes, and schools is described and lessons learned emphasized. The impact of COVID-19 on vulnerable populations in Canada—including Indigenous Peoples, ethnic minorities and newcomers, people who use drugs, people who are homeless, people who are incarcerated, and people with disabilities—is described. Sex and gender disparities are also highlighted. Author recommendations include strategies to reduce transmission (such as test–trace–isolate), the establishment of nationally standardized definitions and public reporting, the protection of high risk and vulnerable populations, and the development of a national strategy on vaccine allocation.

A time-modulated Hawkes process to model the spread of COVID-19 and the impact of countermeasures

Motivated by the recent outbreak of coronavirus (COVID-19), we propose a stochastic model of epidemic temporal growth and mitigation based on a time-modulated Hawkes process. The model is sufficiently rich to incorporate specific characteristics of the novel coronavirus, to capture the impact of undetected, asymptomatic and super-diffusive individuals, and especially to take into account time-varying counter-measures and detection efforts. Yet, it is simple enough to allow scalable and efficient computation of the temporal evolution of the epidemic, and exploration of what-if scenarios. Compared to traditional compartmental models, our approach allows a more faithful description of virus specific features, such as distributions for the time spent in stages, which is crucial when the time-scale of control (e.g., mobility restrictions) is comparable to the lifetime of a single infection. We apply the model to the first and second wave of COVID-19 in Italy, shedding light onto several effects related to mobility restrictions introduced by the government, and to the effectiveness of contact tracing and mass testing performed by the national health service.

Optimal design of lock-down and reopening policies for early-stage epidemics through SIR-D models

The diffusion of COVID-19 represents a real threat for the health and economic system of a country. Therefore the governments have to adopt fast containment measures in order to stop its spread and to prevent the related devastating consequences. In this paper, a technique is proposed to optimally design the lock-down and reopening policies so as to minimize an aggregate cost function accounting for the number of individuals that decease due to the spread of COVID-19. A constraint on the maximal number of concomitant infected patients is also taken into account in order to prevent the collapse of the health system. The optimal procedure is built on the basis of a simple SIR model that describes the outbreak of a generic disease, without attempting to accurately reproduce all the COVID-19 epidemic features. This modeling choice is motivated by the fact that the containing measurements are actuated during the very first period of the outbreak, when the characteristics of the new emergent disease are not known but timely containment actions are required. In fact, as a consequence of dealing with poor preliminary data, the simplest modeling choice is able to reduce unidentifiability problems. Further, the relative simplicity of this model allows to compute explicitly its solutions and to derive closed-form expressions for the maximum number of infected and for the steady-state value of deceased individuals. These expressions can be then used to design static optimization problems so to determine the (open-loop) optimal lock-down and reopening policies for early-stage epidemics accounting for both the health and economic costs.

The coSIR model predicts effective strategies to limit the spread of SARS-CoV-2 variants with low severity and high transmissibility

Multiple new variants of SARS-CoV-2 have been identified as the COVID-19 pandemic spreads across the globe. However, most epidemic models view the virus as static and unchanging and thus fail to address the consequences of the potential evolution of the virus. Here, we built a competitive susceptible-infected-removed (coSIR) model to simulate the competition between virus strains of differing severities or transmissibility under various virus control policies. The coSIR model predicts that although the virus is extremely unlikely to evolve into a "super virus" that causes an increased fatality rate, virus variants with less severe symptoms can lead to potential new outbreaks and can cost more lives over time. The present model also demonstrates that the protocols restricting the transmission of the virus, such as wearing masks and social distancing, are the most effective strategy in reducing total mortality. A combination of adequate testing and strict quarantine is a powerful alternative to policies such as mandatory stay-at-home orders, which may have an enormous negative impact on the economy. In addition, building Mobile Cabin Hospitals can be effective and efficient in reducing the mortality rate of highly infectious virus strains.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11071-021-06705-8.

P systems in the time of COVID-19

In this paper, we present LOIMOS, which is an epidemiological scenario simulator developed in the context of the fight against the pandemic caused by coronavirus SARS-CoV-2 on a global scale. LOIMOS has been fully developed under the paradigm of membrane computing using transition P systems with communication rules, active membranes and a stochastic simulator engine. In this paper we detail the main components of the system and we report some examples of epidemiological scenarios evaluated with LOIMOS.

Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19

We introduce the concept of epidemic-fitted wavelets which comprise, in particular, as special cases the number I(t) of infectious individuals at time t in classical SIR models and their derivatives. We present a novel method for modelling epidemic dynamics by a model selection method using wavelet theory and, for its applications, machine learning-based curve fitting techniques. Our universal models are functions that are finite linear combinations of epidemic-fitted wavelets. We apply our method by modelling and forecasting, based on the Johns Hopkins University dataset, the spread of the current Covid-19 (SARS-CoV-2) epidemic in France, Germany, Italy and the Czech Republic, as well as in the US federal states New York and Florida.

Real-time neural network based predictor for cov19 virus spread

Since the epidemic outbreak in early months of 2020 the spread of COVID-19 has grown rapidly in most countries and regions across the World. Because of that, SARS-CoV-2 was declared as a Public Health Emergency of International Concern (PHEIC) on January 30, 2020, by The World Health Organization (WHO). That’s why many scientists are working on new methods to reduce further growth of new cases and, by intelligent patients allocation, reduce number of patients per doctor, what can lead to more successful treatments. However to properly manage the COVID-19 spread there is a need for real-time prediction models which can reliably support various decisions both at national and international level. The problem in developing such system is the lack of general knowledge how the virus spreads and what would be the number of cases each day. Therefore prediction model must be able to conclude the situation from past data in the way that results will show a future trend and will possibly closely relate to the real numbers. In our opinion Artificial Intelligence gives a possibility to do it. In this article we present a model which can work as a part of an online system as a real-time predictor to help in estimation of COVID-19 spread. This prediction model is developed using Artificial Neural Networks (ANN) to estimate the future situation by the use of geo-location and numerical data from past 2 weeks. The results of our model are confirmed by comparing them with real data and, during our research the model was correctly predicting the trend and very closely matching the numbers of new cases in each day.

Estimation of COVID-19 risk-stratified epidemiological parameters and policy implications for Los Angeles County through an integrated risk and stochastic epidemiological model

Background

Health disparities have emerged with the COVID-19 epidemic because the risk of exposure to infection and the prevalence of risk factors for severe outcomes given infection vary within and between populations. However, estimated epidemic quantities such as rates of severe illness and death, the case fatality rate (CFR), and infection fatality rate (IFR), are often expressed in terms of aggregated population-level estimates due to the lack of epidemiological data at the refined subpopulation level. For public health policy makers to better address the pandemic, stratified estimates are necessary to investigate the potential outcomes of policy scenarios targeting specific subpopulations.

Methods

We develop a framework for using available data on the prevalence of COVID-19 risk factors (age, comorbidities, BMI, smoking status) in subpopulations, and epidemic dynamics at the population level and stratified by age, to estimate subpopulation-stratified probabilities of severe illness and the CFR (as deaths over observed infections) and IFR (as deaths over estimated total infections) across risk profiles representing all combinations of risk factors including age, comorbidities, obesity class, and smoking status. A dynamic epidemic model is integrated with a relative risk model to produce time-varying subpopulation-stratified estimates. The integrated model is used to analyze dynamic outcomes and parameters by population and subpopulation, and to simulate alternate policy scenarios that protect specific at-risk subpopulations or modify the population-wide transmission rate. The model is calibrated to data from the Los Angeles County population during the period March 1 - October 15 2020.

Findings

We estimate a rate of 0.23 (95% CI: 0.13,0.33) of infections observed before April 15, which increased over the epidemic course to 0.41 (0.11,0.69). Overall population-average IFR( t ) estimates for LAC peaked at 0.77% (0.38%,1.15%) on May 15 and decreased to 0.55% (0.24%,0.90%) by October 15. The population-average IFR( t ) stratified by age group varied extensively across subprofiles representing each combination of the additional risk factors considered (comorbidities, BMI, smoking). We found median IFRs ranging from 0.009%-0.04% in the youngest age group (0-19), from 0.1%-1.8% for those aged 20-44, 0.36%-4.3% for those aged 45-64, and 1.02%-5.42% for those aged 65+. In the group aged 65+ for which the rate of unobserved infections is likely much lower, we find median CFRs in the range 4.4%-23.45%. The initial societal lockdown period avoided overwhelming healthcare capacity and greatly reduced the observed death count. In comparative scenario analysis, alternative policies in which the population-wide transmission rate is reduced to a moderate and sustainable level of non-pharmaceutical interventions (NPIs) would not have been sufficient to avoid overwhelming healthcare capacity, and additionally would have exceeded the observed death count. Combining the moderate NPI policy with stringent protection of the at-risk subpopulation of individuals 65+ would have resulted in a death count similar to observed levels, but hospital counts would have approached capacity limits.

Interpretation

The risk of severe illness and death of COVID-19 varies tremendously across subpopulations and over time, suggesting that it is inappropriate to summarize epidemiological parameters for the entire population and epidemic time period. This includes variation not only across age groups, but also within age categories combined with other risk factors analyzed in this study (comorbidities, obesity status, smoking). In the policy analysis accounting for differences in IFR across risk groups in comparing the control of infections and protection of higher risk groups, we find that the strict initial lockdown period in LAC was effective because it both reduced overall transmission and protected individuals at greater risk, resulting in preventing both healthcare overload and deaths. While similar numbers of deaths as observed in LAC could have been achieved with a more moderate NPI policy combined with greater protection of individuals 65+, this would have come at the expense of overwhelming the healthcare system. In anticipation of a continued rise in cases in LAC this winter, policy makers need to consider the trade offs of various policy options on the numbers of the overall population that may become infected, severely ill, and that die when considering policies targeted at subpopulations at greatest risk of transmitting infection and at greatest risk for developing severe outcomes.

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.

Rethinking Elective Cataract Surgery Diagnostics, Assessments, and Tools after the COVID-19 Pandemic Experience and Beyond: Insights from the EUROCOVCAT Group

The progressive deterioration of the visual function in patients on waiting lists for cataract surgery has a negative impact on their quality of life, especially in the elderly population. Patient waiting times for cataract surgeries in many healthcare settings have increased recently due to the prolonged stop or slowdown of elective cataract surgery as a result of coronavirus disease 19 (COVID-19). The aim of this review is to highlight the impact of such a "de-prioritization" of cataract surgery and to summarize some critical issues and useful hints on how to reorganize cataract pathways, with a special focus on perioperative diagnostic tools during the recovery phase and beyond. The experiences of a group of surgeons originating from nine different countries, named the European COVID-19 Cataract Group (EUROCOVCAT), have been combined with the literature and recommendations from scientific ophthalmic societies and healthcare institutions. Key considerations for elective cataract surgery should include the reduction of the number of unnecessary visits and examinations, adoption of precautionary measures, and implementation of telemedicine instruments. New strategies should be adopted to provide an adequate level of assistance and to guarantee safety conditions. Flexibility will be the watchword and regular updates would be necessary following scientific insights and the development of the pandemic.

A logistic model and predictions for the spread of the COVID-19 pandemic

The rapid spread of COVID-19 worldwide presents a great challenge to epidemic modelers. Model outcomes vary widely depending on the characteristics of a pathogen and the models. Here, we present a logistic model for the epidemic spread and divide the spread of the novel coronavirus into two phases: the first phase is a natural exponential growth phase that occurs in the absence of intervention and the second phase is a regulated growth phase that is affected by enforcing social distancing and isolation. We apply the model to a number of pandemic centers. Our results are in good agreement with the data to date and show that social distancing significantly reduces the epidemic spread and flattens the curve. Predictions on the spreading trajectory including the total infections and peak time of new infections for a community of any size are made weeks ahead, providing the vital information and lead time needed to prepare for and mitigate the epidemic. The methodology presented here has immediate and far-reaching applications for ongoing outbreaks or similar future outbreaks of other emergent infectious diseases.

Virions and respiratory droplets in air: Diffusion, drift, and contact with the epithelium

Some infections, including e.g. influenza and currently active COVID 19, may be transmitted via air during sneezing, coughing, and talking. This pathway occurs via diffusion and gravity-induced drift of single virions and respiratory droplets consisting primarily of water, including small fraction of nonvolatile matter, and containing virions. These processes are accompanied by water evaporation resulting in reduction of the droplet size. The manifold of information concerning these steps is presented in textbooks and articles not related to virology and the focus is there frequently on biologically irrelevant conditions and/or droplet sizes. In this brief review, we systematically describe the behavior of virions and virion-carrying droplets in air with emphasis on various regimes of diffusion, drift, and evaporation, and estimate the rates of all these steps under virologically relevant conditions. In addition, we discuss the kinetic aspects of the first steps of infection after attachment of virions or virion-carrying droplets to the epithelium, i.e., virion diffusion in the mucus and periciliary layers, penetration into the cells, and the early stage of replication. The presentation is oriented to virologists who are interested in the corresponding physics and to physicists who are interested in application of the physics to virology.

Analyzing the dominant SARS-CoV-2 transmission routes toward an ab initio disease spread model

Identifying the relative importance of the different transmission routes of the SARS-CoV-2 virus is an urgent research priority. To that end, the different transmission routes and their role in determining the evolution of the Covid-19 pandemic are analyzed in this work. The probability of infection caused by inhaling virus-laden droplets (initial ejection diameters between 0.5 µm and 750 µm, therefore including both airborne and ballistic droplets) and the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation are individually calculated. At typical, air-conditioned yet quiescent indoor space, for average viral loading, cough droplets of initial diameter between 10 µm and 50 µm are found to have the highest infection probability. However, by the time they are inhaled, the diameters reduce to about 1/6th of their initial diameters. While the initially near unity infection probability due to droplets rapidly decays within the first 25 s, the small yet persistent infection probability of desiccated nuclei decays appreciably only by O ( 1000 s ) , assuming that the virus sustains equally well within the dried droplet nuclei as in the droplets. Combined with molecular collision theory adapted to calculate the frequency of contact between the susceptible population and the droplet/nuclei cloud, infection rate constants are derived ab initio, leading to a susceptible-exposed-infectious-recovered-deceased model applicable for any respiratory event-vector combination. The viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector, and dilution of the respiratory jet/puff by the entraining air are shown to mechanistically determine specific physical modes of transmission and variation in the basic reproduction numberR 0 from first-principles calculations.

A parsimonious approach for spatial transmission and heterogeneity in the COVID-19 propagation

Raw data on the number of deaths at a country level generally indicate a spatially variable distribution of COVID-19 incidence. An important issue is whether this pattern is a consequence of environmental heterogeneities, such as the climatic conditions, during the course of the outbreak. Another fundamental issue is to understand the spatial spreading of COVID-19. To address these questions, we consider four candidate epidemiological models with varying complexity in terms of initial conditions, contact rates and non-local transmissions, and we fit them to French mortality data with a mixed probabilistic-ODE approach. Using statistical criteria, we select the model with non-local transmission corresponding to a diffusion on the graph of counties that depends on the geographic proximity, with time-dependent contact rate and spatially constant parameters. This suggests that in a geographically middle size centralized country such as France, once the epidemic is established, the effect of global processes such as restriction policies and sanitary measures overwhelms the effect of local factors. Additionally, this approach reveals the latent epidemiological dynamics including the local level of immunity, and allows us to evaluate the role of non-local interactions on the future spread of the disease.

Novel Indicator to Ascertain the Status and Trend of COVID-19 Spread: Modeling Study

Background

In the fight against the pandemic of COVID-19, it is important to ascertain the status and trend of the infection spread quickly and accurately.

Objective

The purpose of our study is to formulate a new and simple indicator that represents the COVID-19 spread rate by using publicly available data.

Methods

The new indicator K is a backward difference approximation of the logarithmic derivative of the cumulative number of cases with a time interval of 7 days. It is calculated as a ratio of the number of newly confirmed cases in a week to the total number of cases.

Results

The analysis of the current status of COVID-19 spreading over countries showed an approximate linear decrease in the time evolution of the K value. The slope of the linear decrease differed from country to country. In addition, it was steeper for East and Southeast Asian countries than for European countries. The regional difference in the slope seems to reflect both social and immunological circumstances for each country.

Conclusions

The approximate linear decrease of the K value indicates that the COVID-19 spread does not grow exponentially but starts to attenuate from the early stage. The K trajectory in a wide range was successfully reproduced by a phenomenological model with the constant attenuation assumption, indicating that the total number of the infected people follows the Gompertz curve. Focusing on the change in the value of K will help to improve and refine epidemiological models of COVID-19.

To Freeze or Not to Freeze? Epidemic Prevention and Control in the DSGE Model Using an Agent-Based Epidemic Component

The ongoing COVID-19 pandemic has raised numerous questions concerning the shape and range of state interventions the goals of which are to reduce the number of infections and deaths. The lockdowns, which have become the most popular response worldwide, are assessed as being an outdated and economically inefficient way to fight the disease. However, in the absence of efficient cures and vaccines, there is a lack of viable alternatives. In this paper we assess the economic consequences of the epidemic prevention and control schemes that were introduced in order to respond to the COVID-19 pandemic. The analyses report the results of epidemic simulations that were obtained using the agent-based modelling methods under the different response schemes and their use in order to provide conditional forecasts of the standard economic variables. The forecasts were obtained using the dynamic stochastic general equilibrium model (DSGE) with the labour market component.

Strategies for the efficient use of diagnostic resource under constraints: a model-based study on overflow of patients and insufficient diagnostic kits

This article addresses an optimisation problem of distributing rapid diagnostic kits among patients when the demands far surpass the supplies. This problem has not been given much attention in the field, and therefore, this article aims to provide a preliminary result in this problem domain. First, we describe the problem and define the goal of the optimisation by introducing an evaluation metric that measures the efficiency of the distribution strategies. Then, we propose two simple strategies, and a strategy that incorporates a prediction of patients' visits utilising a standard epidemic model. The strategies were evaluated using the metric, with past statistics in Kitami City, Hokkaido, Japan, and the prediction-based strategy outperformed the other distribution strategies. We discuss the properties of the strategies and the limitations of the proposed approach. Although the problem must be generalised before the actual deployment of the suggested strategy, the preliminary result is promising in its ability to address the shortage of diagnostic capacity currently observed worldwide because of the ongoing coronavirus disease pandemic.

COVID-19 and the epistemology of epidemiological models at the dawn of AI

The models used to estimate disease transmission, susceptibility and severity determine what epidemiology can (and cannot tell) us about COVID-19. These include: 'model organisms' chosen for their phylogenetic/aetiological similarities; multivariable statistical models to estimate the strength/direction of (potentially causal) relationships between variables (through 'causal inference'), and the (past/future) value of unmeasured variables (through 'classification/prediction'); and a range of modelling techniques to predict beyond the available data (through 'extrapolation'), compare different hypothetical scenarios (through 'simulation'), and estimate key features of dynamic processes (through 'projection'). Each of these models: address different questions using different techniques; involve assumptions that require careful assessment; and are vulnerable to generic and specific biases that can undermine the validity and interpretation of their findings. It is therefore necessary that the models used: can actually address the questions posed; and have been competently applied. In this regard, it is important to stress that extrapolation, simulation and projection cannot offer accurate predictions of future events when the underlying mechanisms (and the contexts involved) are poorly understood and subject to change. Given the importance of understanding such mechanisms/contexts, and the limited opportunity for experimentation during outbreaks of novel diseases, the use of multivariable statistical models to estimate the strength/direction of potentially causal relationships between two variables (and the biases incurred through their misapplication/misinterpretation) warrant particular attention. Such models must be carefully designed to address: 'selection-collider bias', 'unadjusted confounding bias' and 'inferential mediator adjustment bias' - all of which can introduce effects capable of enhancing, masking or reversing the estimated (true) causal relationship between the two variables examined.1 Selection-collider bias occurs when these two variables independently cause a third (the 'collider'), and when this collider determines/reflects the basis for selection in the analysis. It is likely to affect all incompletely representative samples, although its effects will be most pronounced wherever selection is constrained (e.g. analyses focusing on infected/hospitalised individuals). Unadjusted confounding bias disrupts the estimated (true) causal relationship between two variables when: these share one (or more) common cause(s); and when the effects of these causes have not been adjusted for in the analyses (e.g. whenever confounders are unknown/unmeasured). Inferentially similar biases can occur when: one (or more) variable(s) (or 'mediators') fall on the causal path between the two variables examined (i.e. when such mediators are caused by one of the variables and are causes of the other); and when these mediators are adjusted for in the analysis. Such adjustment is commonplace when: mediators are mistaken for confounders; prediction models are mistakenly repurposed for causal inference; or mediator adjustment is used to estimate direct and indirect causal relationships (in a mistaken attempt at 'mediation analysis'). These three biases are central to ongoing and unresolved epistemological tensions within epidemiology. All have substantive implications for our understanding of COVID-19, and the future application of artificial intelligence to 'data-driven' modelling of similar phenomena. Nonetheless, competently applied and carefully interpreted, multivariable statistical models may yet provide sufficient insight into mechanisms and contexts to permit more accurate projections of future disease outbreaks.

The interplay of movement and spatiotemporal variation in transmission degrades pandemic control

Successful public health regimes for COVID-19 push below unity long-term regional R_t —the average number of secondary cases caused by an infectious individual. We use a susceptible-infectious-recovered (SIR) model for two coupled populations to make the conceptual point that asynchronous, variable local control, together with movement between populations, elevates long-term regional R_t, and cumulative cases, and may even prevent disease eradication that is otherwise possible. For effective pandemic mitigation strategies, it is critical that models encompass both spatiotemporal heterogeneity in transmission and movement.

The scale and dynamics of COVID-19 epidemics across Europe

The number of COVID-19 deaths reported from European countries has varied more than 100-fold. In terms of coronavirus transmission, the relatively low death rates in some countries could be due to low intrinsic (e.g. low population density) or imposed contact rates (e.g. non-pharmaceutical interventions) among individuals, or because fewer people were exposed or susceptible to infection (e.g. smaller populations). Here, we develop a flexible empirical model (skew-logistic) to distinguish among these possibilities. We find that countries reporting fewer deaths did not generally have intrinsically lower rates of transmission and epidemic growth, and flatter epidemic curves. Rather, countries with fewer deaths locked down earlier, had shorter epidemics that peaked sooner and smaller populations. Consequently, as lockdowns were eased, we expected, and duly observed, a resurgence of COVID-19 across Europe.

Analytical solution of SEIR model describing the free spread of the COVID-19 pandemic

We analytically study the SEIR (Susceptible Exposed Infectious Removed) epidemic model. The aim is to provide simple analytical expressions for the peak and asymptotic values and their characteristic times of the populations affected by the COVID-19 pandemic.

Forecasting of COVID19 per regions using ARIMA models and polynomial functions

COVID-2019 is a global threat, for this reason around the world, researches have been focused on topics such as to detect it, prevent it, cure it, and predict it. Different analyses propose models to predict the evolution of this epidemic. These analyses propose models for specific geographical areas, specific countries, or create a global model. The models give us the possibility to predict the virus behavior, it could be used to make future response plans. This work presents an analysis of COVID-19 spread that shows a different angle for the whole world, through 6 geographic regions (continents). We propose to create a relationship between the countries, which are in the same geographical area to predict the advance of the virus. The countries in the same geographic region have variables with similar values (quantifiable and non-quantifiable), which affect the spread of the virus. We propose an algorithm to performed and evaluated the ARIMA model for 145 countries, which are distributed into 6 regions. Then, we construct a model for these regions using the ARIMA parameters, the population per 1M people, the number of cases, and polynomial functions. The proposal is able to predict the COVID-19 cases with a RMSE average of 144.81. The main outcome of this paper is showing a relation between COVID-19 behavior and population in a region, these results show us the opportunity to create more models to predict the COVID-19 behavior using variables as humidity, climate, culture, among others.

The German version of the pandemic-related pregnancy stress scale: A validation study

OBJECTIVE

The consequences of the COVID-19 pandemic may lead to exceptional stress in pregnant women. In order to evaluate stress levels of pregnant woman in this difficult time, the Pandemic-Related Pregnancy Scale (PREPS) was introduced in the US. The present study introduces and validates the German version of the PREPS.

STUDY DESIGN

In total, 1364 German-speaking pregnant women from Germany and Switzerland took part in this online cohort study and completed the PREPS as well as gave information on sociodemographic, obstetric and other psychological factors.

RESULTS

A confirmatory factor analysis of the PREPS showed very good psychometric values and confirmed the structure of the original questionnaire. The PREPS comprises three dimensions: Infection Stress (5 items), Preparedness Stress (7 items) and Positive Appraisal (3 items). Furthermore, correlations between the PREPS and other psychological factors such as Pregnancy Specific Stress and Fear of Childbirth highlight convergent validity. The sensitivity of the questionnaire was demonstrated by its associations with several obstetric and COVID-19 related factors.

CONCLUSION

The German PREPS showed good psychometric properties and is a useful instrument for future studies which aim to investigate the impact of pandemic-related stress on birth outcomes and postpartum factors.

COVID-19 Transmission: Bangladesh Perspective

The sudden emergence of the COVID-19 pandemic has tested the strength of the public health system of the most developed nations and created a “new normal”. Many nations are struggling to curb the epidemic in spite of expanding testing facilities. In this study, we consider the case of Bangladesh, and fit a simple compartmental model holding a feature to distinguish between identified infected and infectious with time series data using least square fitting as well as the likelihood approach; prior to which, dynamics of the model were analyzed mathematically and the identifiability of the parameters has also been confirmed. The performance of the likelihood approach was found to be more promising and was used for further analysis. We performed fitting for different lengths of time intervals starting from the beginning of the outbreak, and examined the evolution of the key parameters from Bangladesh’s perspective. In addition, we deduced profile likelihood and 95% confidence interval for each of the estimated parameters. Our study demonstrates that the parameters defining the infectious and quarantine rates change with time as a consequence of the change in lock-down strategies and expansion of testing facilities. As a result, the value of the basic reproduction number R0 was shown to be between 1.5 and 12. The analysis reveals that the projected time and amplitude of the peak vary following the change in infectious and quarantine rates obtained through different lock-down strategies and expansion of testing facilities. The identification rate determines whether the observed peak shows the true prevalence. We find that by restricting the spread through quick identification and quarantine, or by implementing lock-down to reduce overall contact rate, the peak could be delayed, and the amplitude of the peak could be reduced. Another novelty of this study is that the model presented here can infer the unidentified COVID cases besides estimating the officially confirmed COVID cases.

Safety-Critical Control of Active Interventions for COVID-19 Mitigation

The world has recently undergone the most ambitious mitigation effort in a century, consisting of wide-spread quarantines aimed at preventing the spread of COVID-19. The use of influential epidemiological models of COVID-19 helped to encourage decision makers to take drastic non-pharmaceutical interventions. Yet, inherent in these models are often assumptions that the active interventions are static, e.g., that social distancing is enforced until infections are minimized, which can lead to inaccurate predictions that are ever evolving as new data is assimilated. We present a methodology to dynamically guide the active intervention by shifting the focus from viewing epidemiological models as systems that evolve in autonomous fashion to control systems with an "input" that can be varied in time in order to change the evolution of the system. We show that a safety-critical control approach to COVID-19 mitigation gives active intervention policies that formally guarantee the safe evolution of compartmental epidemiological models. This perspective is applied to current US data on cases while taking into account reduction of mobility, and we find that it accurately describes the current trends when time delays associated with incubation and testing are incorporated. Optimal active intervention policies are synthesized to determine future mitigations necessary to bound infections, hospitalizations, and death, both at national and state levels. We therefore provide means in which to model and modulate active interventions with a view toward the phased reopenings that are currently beginning across the US and the world in a decentralized fashion. This framework can be converted into public policies, accounting for the fractured landscape of COVID-19 mitigation in a safety-critical fashion.

When is SARS-CoV-2 in your shopping list?

The pandemic of coronavirus disease 2019 (COVID-19) has caused several million confirmed cases worldwide. The necessity of keeping open and accessible public commercial establishments such as supermarkets or pharmacies increases during the pandemic provided that distancing rules and crowd control are satisfied. Herein, using agent-based models, we explore the potential spread of the novel SARS-CoV-2 considering the case of a small size supermarket. For diverse distancing rules and number of simultaneous users (customers), we question flexible and limited movement policies, guiding the flow and interactions of users in place. Results indicate that a guided, limited in movement and well-organized policy combined with a distance rule of at least 1 m and a small number of users may aid in the mitigation of potential new contagions in more than 90% compared to the usual policy of flexible movement with more users which may reach up to 64% of mitigation of potential new infections under the same distancing conditions. This study may guide novel strategies for the mitigation of the current COVID-19 pandemic, at any stage, and prevention of future outbreaks of SARS-CoV-2 or related viruses.

The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics

Mathematical models of the dynamics of infectious disease transmission are used to forecast epidemics and assess mitigation strategies. In this article, we highlight the analogy between the dynamics of disease transmission and chemical reaction kinetics while providing an exposition on the classic Susceptible–Infectious–Removed (SIR) epidemic model. Particularly, the SIR model resembles a dynamic model of a batch reactor carrying out an autocatalytic reaction with catalyst deactivation. This analogy between disease transmission and chemical reaction enables the exchange of ideas between epidemic and chemical kinetic modeling communities.

Hanias M, Kampitakis M, Papadopoulos P, Picos R, M. Potirakis S. A Universal Physics-Based Model Describing COVID-19 Dynamics in Europe

The self-organizing mechanism is a universal approach that is widely followed in nature. In this work, a novel self-organizing model describing diffusion over a lattice is introduced. Simulation results for the model's active lattice sites demonstrate an evolution curve that is very close to those describing the evolution of infected European populations by COVID-19. The model was further examined against real data regarding the COVID-19 epidemic for seven European countries (with a total population of 290 million) during the periods in which social distancing measures were imposed, namely Italy and Spain, which had an enormous spread of the disease; the successful case of Greece; and four central European countries: France, Belgium, Germany and the Netherlands. The value of the proposed model lies in its simplicity and in the fact that it is based on a universal natural mechanism, which through the presentation of an equivalent dynamical system apparently documents and provides a better understanding of the dynamical process behind viral epidemic spreads in general-even pandemics, such as in the case of COVID-19-further allowing us to come closer to controlling such situations. Finally, this model allowed the study of dynamical characteristics such as the memory effect, through the autocorrelation function, in the studied epidemiological dynamical systems.

Regional Infoveillance of COVID-19 Case Rates: Analysis of Search-Engine Query Patterns

BACKGROUND

Timely allocation of medical resources for coronavirus disease (COVID-19) requires early detection of regional outbreaks. Internet browsing data may predict case outbreaks in local populations that are yet to be confirmed.

OBJECTIVE

We investigated whether search-engine query patterns can help to predict COVID-19 case rates at the state and metropolitan area levels in the United States.

METHODS

We used regional confirmed case data from the New York Times and Google Trends results from 50 states and 166 county-based designated market areas (DMA). We identified search terms whose activity precedes and correlates with confirmed case rates at the national level. We used univariate regression to construct a composite explanatory variable based on best-fitting search queries offset by temporal lags. We measured the raw and z-transformed Pearson correlation and root-mean-square error (RMSE) of the explanatory variable with out-of-sample case rate data at the state and DMA levels.

RESULTS

Predictions were highly correlated with confirmed case rates at the state (mean r=0.69, 95% CI 0.51-0.81; median RMSE 1.27, IQR 1.48) and DMA levels (mean r=0.51, 95% CI 0.39-0.61; median RMSE 4.38, IQR 1.80), using search data available up to 10 days prior to confirmed case rates. They fit case-rate activity in 49 of 50 states and in 103 of 166 DMA at a significance level of .05.

CONCLUSIONS

Identifiable patterns in search query activity may help to predict emerging regional outbreaks of COVID-19, although they remain vulnerable to stochastic changes in search intensity.