Modeling and forecasting the COVID-19 pandemic time-series data

OBJECTIVE

We analyze the number of recorded cases and deaths of COVID-19 in many parts of the world, with the aim to understand the complexities of the data, and produce regular forecasts.

METHODS

The SARS-CoV-2 virus that causes COVID-19 has affected societies in all corners of the globe but with vastly differing experiences across countries. Health-care and economic systems vary significantly across countries, as do policy responses, including testing, intermittent lockdowns, quarantine, contact tracing, mask wearing, and social distancing. Despite these challenges, the reported data can be used in many ways to help inform policy. We describe how to decompose the reported time series of confirmed cases and deaths into a trend, seasonal, and irregular component using machine learning methods.

RESULTS

This decomposition enables statistical computation of measures of the mortality ratio and reproduction number for any country, and we conduct a counterfactual exercise assuming that the United States had a summer outcome in 2020 similar to that of the European Union. The decomposition is also used to produce forecasts of cases and deaths, and we undertake a forecast comparison which highlights the importance of seasonality in the data and the difficulties of forecasting too far into the future.

CONCLUSION

Our adaptive data-based methods and purely statistical forecasts provide a useful complement to the output from epidemiological models.

The impact of long-term non-pharmaceutical interventions on COVID-19 epidemic dynamics and control: the value and limitations of early models

Mathematical models of epidemics are important tools for predicting epidemic dynamics and evaluating interventions. Yet, because early models are built on limited information, it is unclear how long they will accurately capture epidemic dynamics. Using a stochastic SEIR model of COVID-19 fitted to reported deaths, we estimated transmission parameters at different time points during the first wave of the epidemic (March-June, 2020) in Santa Clara County, California. Although our estimated basic reproduction number ([Formula: see text]) remained stable from early April to late June (with an overall median of 3.76), our estimated effective reproduction number ([Formula: see text]) varied from 0.18 to 1.02 in April before stabilizing at 0.64 on 27 May. Between 22 April and 27 May, our model accurately predicted dynamics through June; however, the model did not predict rising summer cases after shelter-in-place orders were relaxed in June, which, in early July, was reflected in cases but not yet in deaths. While models are critical for informing intervention policy early in an epidemic, their performance will be limited as epidemic dynamics evolve. This paper is one of the first to evaluate the accuracy of an early epidemiological compartment model over time to understand the value and limitations of models during unfolding epidemics.

Joint Estimation Of Generation Time And Incubation Period For Coronavirus Disease (Covid-19)

Background

Coronavirus disease 2019 (COVID-19) has caused a heavy disease burden globally. The impact of process and timing of data collection on the accuracy of estimation of key epidemiological distributions are unclear. Because infection times are typically unobserved, there are relatively few estimates of generation time distribution.

Methods

We developed a statistical framework to jointly estimate generation time and incubation period from human-to-human transmission pairs, accounting for sampling biases. We applied the framework on 80 laboratory-confirmed human-to-human transmission pairs in China. We further inferred the infectiousness profile, serial interval distribution, proportions of presymptomatic transmission, and basic reproduction number (R0) for COVID-19.

Results

The estimated mean incubation period was 4.8 days (95% confidence interval [CI], 4.1–5.6), and mean generation time was 5.7 days (95% CI, 4.8–6.5). The estimated R0 based on the estimated generation time was 2.2 (95% CI, 1.9–2.4). A simulation study suggested that our approach could provide unbiased estimates, insensitive to the width of exposure windows.

Conclusions

Properly accounting for the timing and process of data collection is critical to have correct estimates of generation time and incubation period. R0 can be biased when it is derived based on serial interval as the proxy of generation time.

Severe Acute Respiratory Syndrome Coronavirus 2 Transmission in Georgia, USA, February 1-July 13, 2020

The serial interval and effective reproduction number for coronavirus disease (COVID-19) are heterogenous, varying by demographic characteristics, region, and period. During February 1–July 13, 2020, we identified 4,080 transmission pairs in Georgia, USA, by using contact tracing information from COVID-19 cases reported to the Georgia Department of Public Health. We examined how various transmission characteristics were affected by symptoms, demographics, and period (during shelter-in-place and after subsequent reopening) and estimated the time course of reproduction numbers for all 159 Georgia counties. Transmission varied by time and place but also by persons’ sex and race. The mean serial interval decreased from 5.97 days in February–April to 4.40 days in June–July. Younger adults (20–50 years of age) were involved in most transmission events occurring during or after reopening. The shelter-in-place period was not long enough to prevent sustained virus transmission in densely populated urban areas connected by major transportation links.

A multivariate statistical approach to predict COVID-19 count data with epidemiological interpretation and uncertainty quantification

For the analysis of COVID‐19 pandemic data, we propose Bayesian multinomial and Dirichlet‐multinomial autoregressive models for time‐series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number Rt. All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet‐multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.

Predicted Impact of Vaccination and Active Case Finding Measures to Control Epidemic of Coronavirus Disease 2019 in a Migrant-Populated Area in Thailand

Background

Thailand experienced the first wave of Coronavirus Disease 2019 (COVID-19) during March–May 2020 and has been facing the second wave since December 2020. The area facing the greatest impact was Samut Sakhon, a main migrant-receiving province in the country. The Department of Disease Control (DDC) of the Thai Ministry of Public Health (MOPH) considered initiating a vaccination strategy in combination with active case finding (ACF) in the epidemic area. The DDC commissioned a research team to predict the impact of various vaccination and ACF policy scenarios in terms of case reduction and deaths averted, which is the objective of this study.

Methods

The design of this study was a secondary analysis of quantitative data. Most of the data were obtained from the DDC, MOPH. Deterministic system dynamics and compartmental models were exercised. A basic reproductive number (R₀) was estimated at 3 from the beginning. Vaccine efficacy against disease transmission was assumed to be 50%. A total of 10,000 people were estimated as an initial population size.

Results

The findings showed that the greater the vaccination coverage, the smaller the size of incident and cumulative cases. Compared with a no-vaccination and no-ACF scenario, the 90%-vaccination coverage combined with 90%-ACF coverage contributed to a reduction of cumulative cases by 33%. The case reduction benefit would be greater when R₀ was smaller (~53% and ~51% when R₀ equated 2 and 1.5, respectively).

Conclusion

This study reaffirmed the idea that a combination of vaccination and ACF measures contributed to favourable results in reducing the number of COVID-19 cases and deaths, relative to the implementation of only a single measure. The greater the vaccination and ACF coverage, the greater the volume of cases saved. Though we demonstrated the benefit of vaccination strategies in this setting, actual implementation should consider many more policy angles, such as social acceptability, cost-effectiveness and operational feasibility. Further studies that address these topics based on empirical evidence are of great value.

Estimating the Effect of Social Distancing Interventions on COVID-19 in the United States

Since its global emergence in 2020, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused multiple epidemics in the United States. Because medical treatments for the virus are still emerging and a vaccine is not yet available, state and local governments have sought to limit its spread by enacting various social distancing interventions such as school closures and lockdown, but the effectiveness of these interventions is unknown. We applied an established, semi-mechanistic Bayesian hierarchical model of these interventions on SARS-CoV-2 spread in Europe to the United States, using case fatalities from February 29, 2020 up to April 25, 2020, when some states began reversing their interventions. We estimated the effect of interventions across all states, contrasted the estimated reproduction number, R_t, for each state before and after lockdown, and contrasted predicted future fatalities with actual fatalities as a check on the model’s validity. Overall, school closures and lockdown are the only interventions modeled that have a reliable impact on R_t, and lockdown appears to have played a key role in reducing R_t below 1.0. We conclude that reversal of lockdown, without implementation of additional, equally effective interventions, will enable continued, sustained transmission of SARS-CoV-2 in the United States.

How Transportation Restriction Shapes the Relationship Between Ambient Nitrogen Dioxide and COVID-19 Transmissibility: An Exploratory Analysis

Background: Several recent studies reported a positive (statistical) association between ambient nitrogen dioxide (NO₂) and COVID-19 transmissibility. However, considering the intensive transportation restriction due to lockdown measures that would lead to declines in both ambient NO₂ concentration and COVID-19 spread, the crude or insufficiently adjusted associations between NO₂ and COVID-19 transmissibility might be confounded. This study aimed to investigate whether transportation restriction confounded, mediated, or modified the association between ambient NO₂ and COVID-19 transmissibility.

Methods: The time-varying reproduction number (R_t) was calculated to quantify the instantaneous COVID-19 transmissibility in 31 Chinese cities from January 1, 2020, to February 29, 2020. For each city, we evaluated the relationships between ambient NO₂, transportation restriction, and COVID-19 transmission under three scenarios, including simple linear regression, mediation analysis, and adjusting transportation restriction as a confounder. The statistical significance (p-value < 0.05) of the three scenarios in 31 cities was summarized.

Results: We repeated the crude correlational analysis, and also found the significantly positive association between NO₂ and COVID-19 transmissibility. We found that little evidence supported NO₂ as a mediator between transportation restriction and COVID-19 transmissibility. The association between NO₂ and COVID-19 transmissibility appears less likely after adjusting the effects of transportation restriction.

Conclusions: Our findings suggest that the crude association between NO₂ and COVID-19 transmissibility is likely confounded by the transportation restriction in the early COVID-19 outbreak. After adjusting the confounders, the association between NO₂ and COVID-19 transmissibility appears unlikely. Further studies are warranted to validate the findings in other regions.

Toward Achieving a Vaccine-Derived Herd Immunity Threshold for COVID-19 in the U.S

A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that inflicted unprecedented public health and economic burden in all nooks and corners of the world. Although the control of COVID-19 largely focused on the use of basic public health measures (primarily based on using non-pharmaceutical interventions, such as quarantine, isolation, social-distancing, face mask usage, and community lockdowns) initially, three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc., and Pfizer Inc.), were approved for use in humans in December 2020. We present a new mathematical model for assessing the population-level impact of these vaccines on curtailing the burden of COVID-19. The model stratifies the total population into two subgroups, based on whether or not they habitually wear face mask in public. The resulting multigroup model, which takes the form of a deterministic system of nonlinear differential equations, is fitted and parameterized using COVID-19 cumulative mortality data for the third wave of the COVID-19 pandemic in the United States. Conditions for the asymptotic stability of the associated disease-free equilibrium, as well as an expression for the vaccine-derived herd immunity threshold, are rigorously derived. Numerical simulations of the model show that the size of the initial proportion of individuals in the mask-wearing group, together with positive change in behavior from the non-mask wearing group (as well as those in the mask-wearing group, who do not abandon their mask-wearing habit) play a crucial role in effectively curtailing the COVID-19 pandemic in the United States. This study further shows that the prospect of achieving vaccine-derived herd immunity (required for COVID-19 elimination) in the U.S., using the Pfizer or Moderna vaccine, is quite promising. In particular, our study shows that herd immunity can be achieved in the U.S. if at least 60% of the population are fully vaccinated. Furthermore, the prospect of eliminating the pandemic in the U.S. in the year 2021 is significantly enhanced if the vaccination program is complemented with non-pharmaceutical interventions at moderate increased levels of compliance (in relation to their baseline compliance). The study further suggests that, while the waning of natural and vaccine-derived immunity against COVID-19 induces only a marginal increase in the burden and projected time-to-elimination of the pandemic, adding the impacts of therapeutic benefits of the vaccines into the model resulted in a dramatic reduction in the burden and time-to-elimination of the pandemic.

Estimates of regional infectivity of COVID-19 in the United Kingdom following imposition of social distancing measures

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reproduction number has become an essential parameter for monitoring disease transmission across settings and guiding interventions. The UK published weekly estimates of the reproduction number in the UK starting in May 2020 which are formed from multiple independent estimates. In this paper, we describe methods used to estimate the time-varying SARS-CoV-2 reproduction number for the UK. We used multiple data sources and estimated a serial interval distribution from published studies. We describe regional variability and how estimates evolved during the early phases of the outbreak, until the relaxing of social distancing measures began to be introduced in early July. Our analysis is able to guide localized control and provides a longitudinal example of applying these methods over long timescales. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

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

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

Using Proper Mean Generation Intervals in Modeling of COVID-19

In susceptible-exposed-infectious-recovered (SEIR) epidemic models, with the exponentially distributed duration of exposed/infectious statuses, the mean generation interval (GI, time lag between infections of a primary case and its secondary case) equals the mean latent period (LP) plus the mean infectious period (IP). It was widely reported that the GI for COVID-19 is as short as 5 days. However, many works in top journals used longer LP or IP with the sum (i.e., GI), e.g., >7 days. This discrepancy will lead to overestimated basic reproductive number and exaggerated expectation of infection attack rate (AR) and control efficacy. We argue that it is important to use suitable epidemiological parameter values for proper estimation/prediction. Furthermore, we propose an epidemic model to assess the transmission dynamics of COVID-19 for Belgium, Israel, and the United Arab Emirates (UAE). We estimated a time-varying reproductive number [R0(t)] based on the COVID-19 deaths data and we found that Belgium has the highest AR followed by Israel and the UAE.

A Comparative Analysis of Statistical Methods to Estimate the Reproduction Number in Emerging Epidemics, With Implications for the Current Coronavirus Disease 2019 (COVID-19) Pandemic

BACKGROUND

As the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic continues its rapid global spread, quantification of local transmission patterns has been, and will continue to be, critical for guiding the pandemic response. Understanding the accuracy and limitations of statistical methods to estimate the basic reproduction number, R0, in the context of emerging epidemics is therefore vital to ensure appropriate interpretation of results and the subsequent implications for control efforts.

METHODS

Using simulated epidemic data, we assess the performance of 7 commonly used statistical methods to estimate R0 as they would be applied in a real-time outbreak analysis scenario: fitting to an increasing number of data points over time and with varying levels of random noise in the data. Method comparison was also conducted on empirical outbreak data, using Zika surveillance data from the 2015-2016 epidemic in Latin America and the Caribbean.

RESULTS

We find that most methods considered here frequently overestimate R0 in the early stages of epidemic growth on simulated data, the magnitude of which decreases when fitted to an increasing number of time points. This trend of decreasing bias over time can easily lead to incorrect conclusions about the course of the epidemic or the need for control efforts.

CONCLUSIONS

We show that true changes in pathogen transmissibility can be difficult to disentangle from changes in methodological accuracy and precision in the early stages of epidemic growth, particularly for data with significant over-dispersion. As localized epidemics of SARS-CoV-2 take hold around the globe, awareness of this trend will be important for appropriately cautious interpretation of results and subsequent guidance for control efforts.

Impact of the COVID-19 Epidemic: Scenario in a Tropical Environment

The present study investigates the association of COVID-19 virus transmission with atmospheric and air quality parameters including temperature, moisture, particulate matter (PM), and nitrogen dioxide (NO₂). The variation in the reproduction number (R ₀; a measure to reflect the infectiousness of a disease) for COVID-19 transmission is evaluated for tropical and mid-latitude countries. Results suggest that mid-latitude atmospheric conditions are more favorable to COVID-19 transmission as compared to the tropical atmosphere. The peak value of R ₀ was noted as 2.35 (95% CI 2.11-2.57) on 23 March 2020, and it decreased significantly due to strict lockdown from 25 March 2020 to 1 April 2020. The R ₀ value further increased after 1 April 2020 over India, and the value of R ₀ was found to be greater than 1, indicating that the epidemic was active. Moreover, the present study was also extended to understand the impact of global/Indian lockdowns on air quality and R ₀ value for COVID-19 transmission. Our findings revealed that the global/Indian lockdown helped reduce the R ₀ value of COVID-19 transmission, which is associated with atmospheric and air quality parameters. Furthermore, a significant reduction in air pollution over India during the lockdown also has implications for continued exploration of clean energy prospects in the future.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00024-021-02793-0.

Characterizing Norovirus Transmission from Outbreak Data, United States

Norovirus is the leading cause of acute gastroenteritis outbreaks in the United States. We estimated the basic (R₀) and effective (R_e) reproduction numbers for 7,094 norovirus outbreaks reported to the National Outbreak Reporting System (NORS) during 2009–2017 and used regression models to assess whether transmission varied by outbreak setting. The median R₀ was 2.75 (interquartile range [IQR] 2.38–3.65), and median R_e was 1.29 (IQR 1.12–1.74). Long-term care and assisted living facilities had an R₀ of 3.35 (95% CI 3.26–3.45), but R₀ did not differ substantially for outbreaks in other settings, except for outbreaks in schools, colleges, and universities, which had an R₀ of 2.92 (95% CI 2.82–3.03). Seasonally, R₀ was lowest (3.11 [95% CI 2.97–3.25]) in summer and peaked in fall and winter. Overall, we saw little variability in transmission across different outbreaks settings in the United States.

Mobility-Guided Estimation of COVID-19 Transmission Rates

It is of critical importance to estimate changing transmission rates and their dependence on population mobility. A common approach to this problem involves fitting daily transmission rates using a Susceptive Exposed Infected Recovered (SEIR) model (regularizing them to avoid overfitting), and then computing the relationship between the estimated transmission rate and mobility. Unfortunately, there are often several, very different transmission rate trajectories that can fit the reported cases well, meaning that the choice of regularization determines the final solution (and thus the mobility-transmission rate relationship) selected by the SEIR model. Moreover, the classical approaches to regularization—penalizing the derivative of the transmission rate trajectory—do not correspond to realistic properties of pandemic spread. Consequently, models fit using derivative-based regularization are often biased toward underestimating the current transmission rate and future deaths. In this work, we propose mobility-driven regularization of the SEIR transmission rate trajectory. This method rectifies the artificial regularization problem, produces more accurate and unbiased forecasts of future deaths, and estimates a highly interpretable relationship between mobility and the transmission rate. Mobility data for this analysis was collected by Safegraph (San Francisco, CA) from major US cities between March and August 2020.

Mathematical model, forecast and analysis on the spread of COVID-19

Pandemic COVID-19 which has infected more than 35,027,546 people and death more than 1,034,837 people in 235 countries as on October 05, 2020 has created a chaos across the globe. In this paper, we develop a compartmental epidemic model to understand the spreading behaviour of the disease in human population with a special case of Bhilwara, a desert town in India where successful control measures TTT (tracking, testing and treatment) was adopted to curb the disease in the very early phase of the spread of the disease in India. Local and global asymptotic stability is established for endemic equilibrium. Extensive numerical simulations with real parametric values are performed to validate the analytical results. Trend analysis of fatality rate, infection rate, and impact of lockdown is performed for USA, European countries, Russia, Iran, China, Japan, S. Korea with a comparative assessment by India. Kruskal - Wallis test is performed to test the null hypothesis for infected cases during the four lockdown phases in India. It has been observed that there is a significant difference at both 95% and 99% confidence interval in the infected cases, recovered cases and the case fatality rate during all the four phases of the lockdown.

Spatially Refined Time-Varying Reproduction Numbers of COVID-19 by Health District in Georgia, USA, March-December 2020

This study quantifies the transmission potential of SARS-CoV-2 across public health districts in Georgia, USA, and tests if per capita cumulative case count varies across counties. To estimate the time-varying reproduction number, R_t of SARS-CoV-2 in Georgia and its 18 public health districts, we apply the R package 'EpiEstim' to the time series of historical daily incidence of confirmed cases, 2 March-15 December 2020. The epidemic curve is shifted backward by nine days to account for the incubation period and delay to testing. Linear regression is performed between log₁₀-transformed per capita cumulative case count and log₁₀-transformed population size. We observe R_t fluctuations as state and countywide policies are implemented. Policy changes are associated with increases or decreases at different time points. R_t increases, following the reopening of schools for in-person instruction in August. Evidence suggests that counties with lower population size had a higher per capita cumulative case count on June 15 (slope = -0.10, p = 0.04) and October 15 (slope = -0.05, p = 0.03), but not on August 15 (slope = -0.04, p = 0.09), nor December 15 (slope = -0.02, p = 0.41). We found extensive community transmission of SARS-CoV-2 across all 18 health districts in Georgia with median 7-day-sliding window R_t estimates between 1 and 1.4 after March 2020.

The long-term changing dynamics of dengue infectivity in Guangdong, China, from 2008-2018: a modelling analysis

BACKGROUND

Dengue remains a severe threat to public health in tropical and subtropical regions. In China, over 85% of domestic dengue cases are in the Guangdong province and there were 53 139 reported cases during 2008-2018. In Guangdong, the 2014 dengue outbreak was the largest in the last 20 y and it was probably triggered by a new strain imported from other regions.

METHODS

We studied the long-term patterns of dengue infectivity in Guangdong from 2008-2018 and compared the infectivity estimates across different periods.

RESULTS

We found that the annual epidemics approximately followed exponential growth during 2011-2014. The transmission rates were at a low level during 2008-2012, significantly increased 1.43-fold [1.22, 1.69] during 2013-2014 and then decreased back to a low level after 2015. By using the mosquito index and the likelihood-inference approach, we found that the new strain most likely invaded Guangdong in April 2014.

CONCLUSIONS

The long-term changing dynamics of dengue infectivity are associated with the new dengue virus strain invasion and public health control programmes. The increase in infectiousness indicates the potential for dengue to go from being imported to becoming an endemic in Guangdong, China.

Using Unstated Cases to Correct for COVID-19 Pandemic Outbreak and Its Impact on Easing the Intervention for Qatar

Simple Summary

A modified SIR model was applied to provide COVID-19 pandemic analysis and predictions for Gulf Cooperation Council countries, as well as representative countries in Europe and New York City. We estimated reported, infected, and unreported cases from cumulative reported cases and simulated data. We also estimated the basic reproduction rates at different phases of the pandemic. Outputs show that the modified SIR model fits very well with the outcome of the COVID-19 pandemic for the studied countries and could be generalized to other countries. The model prediction emphasizes the value of significant interventions in public health in regulating the epidemic taking into account that a constant fraction of the infected cases remain unreported during the pandemic. We report and analyze the effectiveness of preventive/intervention measures applied to the overall community to curb the severity of the pandemic. Our model could be used to support public health authorities with respect to post-outbreak reopening decisions, highlighting effective measures that need to be maintained, eased, or implemented to support safe reopening strategies in the GCC countries.

Abstract

Epidemiological Modeling supports the evaluation of various disease management activities. The value of epidemiological models lies in their ability to study various scenarios and to provide governments with a priori knowledge of the consequence of disease incursions and the impact of preventive strategies. A prevalent method of modeling the spread of pandemics is to categorize individuals in the population as belonging to one of several distinct compartments, which represents their health status with regard to the pandemic. In this work, a modified SIR epidemic model is proposed and analyzed with respect to the identification of its parameters and initial values based on stated or recorded case data from public health sources to estimate the unreported cases and the effectiveness of public health policies such as social distancing in slowing the spread of the epidemic. The analysis aims to highlight the importance of unreported cases for correcting the underestimated basic reproduction number. In many epidemic outbreaks, the number of reported infections is likely much lower than the actual number of infections which can be calculated from the model’s parameters derived from reported case data. The analysis is applied to the COVID-19 pandemic for several countries in the Gulf region and Europe.

Monitoring COVID-19 contagion growth

We present a statistical model that can be employed to monitor the time evolution of the COVID‐19 contagion curve and the associated reproduction rate. The model is a Poisson autoregression of the daily new observed cases and dynamically adapt its estimates to explain the evolution of contagion in terms of a short‐term and long‐term dependence of case counts, allowing for a comparative evaluation of health policy measures. We have applied the model to 2020 data from the countries most hit by the virus. Our empirical findings show that the proposed model describes the evolution of contagion dynamics and determines whether contagion growth can be affected by health policies. Based on our findings, we can draw two health policy conclusions that can be useful for all countries in the world. First, policy measures aimed at reducing contagion are very useful when contagion is at its peak to reduce the reproduction rate. Second, the contagion curve should be accurately monitored over time to apply policy measures that are cost‐effective.

The Tipping Effect of Delayed Interventions on the Evolution of COVID-19 Incidence

We combine infectious disease transmission and the non-pharmaceutical (NPI) intervention response to disease incidence into one closed model consisting of two coupled delay differential equations for the incidence rate and the time-dependent reproduction number. The model contains three parameters, the initial reproduction number, the intervention strength, and the response delay. The response is modeled by assuming that the rate of change of the reproduction number is proportional to the negative deviation of the incidence rate from an intervention threshold. This delay dynamical system exhibits damped oscillations in one part of the parameter space, and growing oscillations in another, and these are separated by a surface where the solution is a strictly periodic nonlinear oscillation. For the COVID-19 pandemic, the tipping transition from damped to growing oscillations occurs for response delays of about one week, and suggests that, without vaccination, effective control and mitigation of successive epidemic waves cannot be achieved unless NPIs are implemented in a precautionary manner, rather as a response to the present incidence rate. Vaccination increases the quiet intervals between waves, but with delayed response, future flare-ups can only be prevented by establishing a post-pandemic normal with lower basic reproduction number.

A Hybrid Modeling Technique of Epidemic Outbreaks with Application to COVID-19 Dynamics in West Africa

The widely used logistic model for epidemic case reporting data may be either restrictive or unrealistic in presence of containment measures when implemented after an epidemic outbreak. For flexibility in epidemic case reporting data modeling, we combined an exponential growth curve for the early epidemic phase with a flexible growth curve to account for the potential change in growth pattern after implementation of containment measures. We also fitted logistic regression models to recoveries and deaths from the confirmed positive cases. In addition, the growth curves were integrated into a SIQR (Susceptible, Infective, Quarantined, Recovered) model framework to provide an overview on the modeled epidemic wave. We focused on the estimation of: (1) the delay between the appearance of the first infectious case in the population and the outbreak ("epidemic latency period"); (2) the duration of the exponential growth phase; (3) the basic and the time-varying reproduction numbers; and (4) the peaks (time and size) in confirmed positive cases, active cases and new infections. The application of this approach to COVID-19 data from West Africa allowed discussion on the effectiveness of some containment measures implemented across the region.

Adaptive Susceptible-Infectious-Removed Model for Continuous Estimation of the COVID-19 Infection Rate and Reproduction Number in the United States: Modeling Study

BACKGROUND

The dynamics of the COVID-19 pandemic vary owing to local population density and policy measures. During decision-making, policymakers consider an estimate of the effective reproduction number Rt, which is the expected number of secondary infections spread by a single infected individual.

OBJECTIVE

We propose a simple method for estimating the time-varying infection rate and the Rt.

METHODS

We used a sliding window approach with a Susceptible-Infectious-Removed (SIR) model. We estimated the infection rate from the reported cases over a 7-day window to obtain a continuous estimation of Rt. A proposed adaptive SIR (aSIR) model was applied to analyze the data at the state and county levels.

RESULTS

The aSIR model showed an excellent fit for the number of reported COVID-19 cases, and the 1-day forecast mean absolute prediction error was <2.6% across all states. However, the 7-day forecast mean absolute prediction error approached 16.2% and strongly overestimated the number of cases when the Rt was rapidly decreasing. The maximal Rt displayed a wide range of 2.0 to 4.5 across all states, with the highest values for New York (4.4) and Michigan (4.5). We found that the aSIR model can rapidly adapt to an increase in the number of tests and an associated increase in the reported cases of infection. Our results also suggest that intensive testing may be an effective method of reducing Rt.

CONCLUSIONS

The aSIR model provides a simple and accurate computational tool for continuous Rt estimation and evaluation of the efficacy of mitigation measures.

Statistical Estimation of the Reproductive Number From Case Notification Data

The reproductive number, or reproduction number, is a valuable metric in understanding infectious disease dynamics. There is a large body of literature related to its use and estimation. In the last 15 years, there has been tremendous progress in statistically estimating this number using case notification data. These approaches are appealing because they are relevant in an ongoing outbreak (e.g., for assessing the effectiveness of interventions) and do not require substantial modeling expertise to be implemented. In this article, we describe these methods and the extensions that have been developed. We provide insight into the distinct interpretations of the estimators proposed and provide real data examples to illustrate how they are implemented. Finally, we conclude with a discussion of available software and opportunities for future development.