A method of non-parametric back-projection and its application to AIDS data

Estimation of the Time-Varying Effective Reproductive Number of COVID-19 Based on Multivariate Time Series of Severe Health Outcomes

The time-varying effective reproduction number (Rt at time t) measures the transmissibility of SARS-CoV-2 and is conventionally based on daily case counts, which may suffer from time-varying ascertainment. We analyzed Rt estimates from case counts and severe COVID-19 (intensive care unit admissions, severe or critical cases, and mortality) across 2022 in Hong Kong's fifth and sixth waves of infection. Within the fifth wave, the severe disease-based Rt (3.5) was significantly higher than the case-based Rt (2.4) but not in the sixth wave. During periods with fluctuating underreporting, data based on severe diseases may provide more reliable Rt estimates.

Association of air pollution and weather conditions during infection course with COVID-19 case fatality rate in the United Kingdom

Although the relationship between the environmental factors, such as weather conditions and air pollution, and COVID-19 case fatality rate (CFR) has been found, the impacts of these factors to which infected cases are exposed at different infectious stages (e.g., virus exposure time, incubation period, and at or after symptom onset) are still unknown. Understanding this link can help reduce mortality rates. During the first wave of COVID-19 in the United Kingdom (UK), the CFR varied widely between and among the four countries of the UK, allowing such differential impacts to be assessed. We developed a generalized linear mixed-effect model combined with distributed lag nonlinear models to estimate the odds ratio of the weather factors (i.e., temperature, sunlight, relative humidity, and rainfall) and air pollution (i.e., ozone, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) using data between March 26, 2020 and September 15, 2020 in the UK. After retrospectively time adjusted CFR was estimated using back-projection technique, the stepwise model selection method was used to choose the best model based on Akaike information criteria and the closeness between the predicted and observed values of CFR. The risk of death reached its maximum level when the low temperature (6 °C) occurred 1 day before (OR 1.59; 95% CI 1.52-1.63), prolonged sunlight duration (11-14 h) 3 days after (OR 1.24; 95% CI 1.18-1.30) and increased [Formula: see text] (19 μg/m3) 1 day after the onset of symptom (OR 1.12; 95% CI 1.09-1.16). After reopening, many COVID-19 cases will be identified after their symptoms appear. The findings highlight the importance of designing different preventive measures against severe illness or death considering the time before and after symptom onset.

Dynamics-informed deconvolutional neural networks for super-resolution identification of regime changes in epidemiological time series

The ability to infer the timing and amplitude of perturbations in epidemiological systems from their stochastically spread low-resolution outcomes is crucial for multiple applications. However, the general problem of connecting epidemiological curves with the underlying incidence lacks the highly effective methodology present in other inverse problems, such as super-resolution and dehazing from computer vision. Here, we develop an unsupervised physics-informed convolutional neural network approach in reverse to connect death records with incidence that allows the identification of regime changes at single-day resolution. Applied to COVID-19 data with proper regularization and model-selection criteria, the approach can identify the implementation and removal of lockdowns and other nonpharmaceutical interventions (NPIs) with 0.93-day accuracy over the time span of a year.

Joint Analysis of the Epidemic Evolution and Human Mobility During the First Wave of COVID-19 in Spain: Retrospective Study

BACKGROUND

The initial wave of the COVID-19 pandemic placed a tremendous strain on health care systems worldwide. To mitigate the spread of the virus, many countries implemented stringent nonpharmaceutical interventions (NPIs), which significantly altered human behavior both before and after their enactment. Despite these efforts, a precise assessment of the impact and efficacy of these NPIs, as well as the extent of human behavioral changes, remained elusive.

OBJECTIVE

In this study, we conducted a retrospective analysis of the initial wave of COVID-19 in Spain to better comprehend the influence of NPIs and their interaction with human behavior. Such investigations are vital for devising future mitigation strategies to combat COVID-19 and enhance epidemic preparedness more broadly.

METHODS

We used a combination of national and regional retrospective analyses of pandemic incidence alongside large-scale mobility data to assess the impact and timing of government-implemented NPIs in combating COVID-19. Additionally, we compared these findings with a model-based inference of hospitalizations and fatalities. This model-based approach enabled us to construct counterfactual scenarios that gauged the consequences of delayed initiation of epidemic response measures.

RESULTS

Our analysis demonstrated that the pre-national lockdown epidemic response, encompassing regional measures and heightened individual awareness, significantly contributed to reducing the disease burden in Spain. The mobility data indicated that people adjusted their behavior in response to the regional epidemiological situation before the nationwide lockdown was implemented. Counterfactual scenarios suggested that without this early epidemic response, there would have been an estimated 45,400 (95% CI 37,400-58,000) fatalities and 182,600 (95% CI 150,400-233,800) hospitalizations compared to the reported figures of 27,800 fatalities and 107,600 hospitalizations, respectively.

CONCLUSIONS

Our findings underscore the significance of self-implemented prevention measures by the population and regional NPIs before the national lockdown in Spain. The study also emphasizes the necessity for prompt and precise data quantification prior to enacting enforced measures. This highlights the critical interplay between NPIs, epidemic progression, and human behavior. This interdependence presents a challenge in predicting the impact of NPIs before they are implemented.

Biology-Informed Recurrent Neural Network for Pandemic Prediction Using Multimodal Data

In the biomedical field, the time interval from infection to medical diagnosis is a random variable that obeys the log-normal distribution in general. Inspired by this biological law, we propose a novel back-projection infected-susceptible-infected-based long short-term memory (BPISI-LSTM) neural network for pandemic prediction. The multimodal data, including disease-related data and migration information, are used to model the impact of social contact on disease transmission. The proposed model not only predicts the number of confirmed cases, but also estimates the number of infected cases. We evaluate the proposed model on the COVID-19 datasets from India, Austria, and Indonesia. In terms of predicting the number of confirmed cases, our model outperforms the latest epidemiological modeling methods, such as vSIR, and intelligent algorithms, such as LSTM, for both short-term and long-term predictions, which shows the superiority of bio-inspired intelligent algorithms. In general, the use of mobility information improves the prediction accuracy of the model. Moreover, the number of infected cases in these three countries is also estimated, which is an unobservable but crucial indicator for the control of the pandemic.

Accounting for the Potential of Overdispersion in Estimation of the Time-varying Reproduction Number

BACKGROUND

The time-varying reproduction number, Rt, is commonly used to monitor the transmissibility of an infectious disease during an epidemic, but standard methods for estimating Rt seldom account for the impact of overdispersion on transmission.

METHODS

We developed a negative binomial framework to estimate Rt and a time-varying dispersion parameter (kt). We applied the framework to COVID-19 incidence data in Hong Kong in 2020 and 2021. We conducted a simulation study to compare the performance of our model with the conventional Poisson-based approach.

RESULTS

Our framework estimated an Rt peaking around 4 (95% credible interval = 3.13, 4.30), similar to that from the Poisson approach but with a better model fit. Our approach further estimated kt <0.5 at the start of both waves, indicating appreciable heterogeneity in transmission. We also found that kt decreased sharply to around 0.4 when a large cluster of infections occurred.

CONCLUSIONS

Our proposed approach can contribute to the estimation of Rt and monitoring of the time-varying dispersion parameters to quantify the role of superspreading.

Estimating the infection burden of COVID-19 in Malaysia

Malaysia has reported 2.75 million cases and 31,485 deaths as of 30 December 2021. Underestimation remains an issue due to the underdiagnosis of mild and asymptomatic cases. We aimed to estimate the burden of COVID-19 cases in Malaysia based on an adjusted case fatality rate (aCFR). Data on reported cases and mortalities were collated from the Ministry of Health official GitHub between 1 March 2020 and 30 December 2021. We estimated the total and age-stratified monthly incidence rates, mortality rates, and aCFR. Estimated new infections were inferred from the age-stratified aCFR. The total estimated infections between 1 March 2020 and 30 December 2021 was 9,955,000-cases (95% CI: 6,626,000-18,985,000). The proportion of COVID-19 infections in ages 0-11, 12-17, 18-50, 51-65, and above 65 years were 19.9% (n = 1,982,000), 2.4% (n = 236,000), 66.1% (n = 6,577,000), 9.1% (n = 901,000), 2.6% (n = 256,000), respectively. Approximately 32.8% of the total population in Malaysia was estimated to have been infected with COVID-19 by the end of December 2021. These estimations highlight a more accurate infection burden in Malaysia. It provides the first national-level prevalence estimates in Malaysia that adjusted for underdiagnosis. Naturally acquired community immunity has increased, but approximately 68.1% of the population remains susceptible. Population estimates of the infection burden are critical to determine the need for booster doses and calibration of public health measures.

Meta-analysis of the severe acute respiratory syndrome coronavirus 2 serial intervals and the impact of parameter uncertainty on the coronavirus disease 2019 reproduction number

The serial interval of an infectious disease, commonly interpreted as the time between the onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections), and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions, and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early coronavirus disease 2019 data. In this paper, we estimate these key quantities in the context of coronavirus disease 2019 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean of 5.9 (95% CI 5.2; 6.7) and SD 4.1 (95% CI 3.8; 4.7) days (empirical distribution), the generation interval with a mean of 4.9 (95% CI 4.2; 5.5) and SD 2.0 (95% CI 0.5; 3.2) days (fitted gamma distribution), and the incubation period with a mean 5.2 (95% CI 4.9; 5.5) and SD 5.5 (95% CI 5.1; 5.9) days (fitted log-normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period, and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modeling coronavirus disease 2019 transmission.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Commentary on the use of the reproduction number R during the COVID-19 pandemic

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

Statistical Deconvolution for Inference of Infection Time Series

Accurate measurement of daily infection incidence is crucial to epidemic response. However, delays in symptom onset, testing, and reporting obscure the dynamics of transmission, necessitating methods to remove the effects of stochastic delays from observed data. Existing estimators can be sensitive to model misspecification and censored observations; many analysts have instead used methods that exhibit strong bias. We develop an estimator with a regularization scheme to cope with stochastic delays, which we term the robust incidence deconvolution estimator. We compare the method to existing estimators in a simulation study, measuring accuracy in a variety of experimental conditions. We then use the method to study COVID-19 records in the United States, highlighting its stability in the face of misspecification and right censoring. To implement the robust incidence deconvolution estimator, we release incidental, a ready-to-use R implementation of our estimator that can aid ongoing efforts to monitor the COVID-19 pandemic.

Assessment of the fatality rate and transmissibility taking account of undetected cases during an unprecedented COVID-19 surge in Taiwan

Background

During the COVID-19 outbreak in Taiwan between May 11 and June 20, 2021, the observed fatality rate (FR) was 5.3%, higher than the global average at 2.1%. The high number of reported deaths suggests that many patients were not treated promptly or effectively. However, many unexplained deaths were subsequently identified as cases, indicating a few undetected cases, resulting in a higher estimate of FR. Whether the true FR is exceedingly high and what factors determine the detection of cases remain unknown. Estimating the true number of total infected cases (i.e. including undetected cases) can allow an accurate estimation of FR and effective reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt).

Methods

We aimed at quantifying the time-varying FR and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt using the estimated true numbers of cases; and, exploring the relationship between the true case number and test and trace data. After adjusting for reporting delays, we developed a model to estimate the number of undetected cases using reported deaths that were and were not previously detected. The daily FR and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt were calculated using the true number of cases. Afterwards, a logistic regression model was used to assess the impact of daily testing and tracing data on the detection ratio of deaths.

Results

The estimated true daily case number at the peak of the outbreak on May 22 was 897, which was 24.3% higher than the reported number, but the difference became less than 4% on June 9 and afterwards. After taking account of undetected cases, our estimated mean FR (4.7%) was still high but the daily rate showed a large decrease from 6.5% on May 19 to 2.8% on June 6. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt reached a maximum value of 6.4 on May 11, compared to 6.0 estimated using the reported case number. The decreasing proportion of undetected cases was found to be associated with the increases in the ratio of the number of tests conducted to reported cases, and the proportion of cases that are contact traced before symptom onset.

Conclusions

Increasing testing capacity and contact tracing coverage without delays not only improve parameter estimation by reducing hidden cases but may also reduce fatality rates.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-022-07190-z.

Incorporating temporal distribution of population-level viral load enables real-time estimation of COVID-19 transmission

Many locations around the world have used real-time estimates of the time-varying effective reproductive number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt) of COVID-19 to provide evidence of transmission intensity to inform control strategies. Estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt are typically based on statistical models applied to case counts and typically suffer lags of more than a week because of the latent period and reporting delays. Noting that viral loads tend to decline over time since illness onset, analysis of the distribution of viral loads among confirmed cases can provide insights into epidemic trajectory. Here, we analyzed viral load data on confirmed cases during two local epidemics in Hong Kong, identifying a strong correlation between temporal changes in the distribution of viral loads (measured by RT-qPCR cycle threshold values) and estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt based on case counts. We demonstrate that cycle threshold values could be used to improve real-time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{t}$$\end{document}Rt estimation, enabling more timely tracking of epidemic dynamics.

The time-varying effective reproductive number (Rt) is useful for monitoring transmission of infections such as COVID-19, but reporting delays impact case count-based estimation methods. Here, the authors demonstrate and validate a method for estimation of Rt based on viral load data from Hong Kong that does not require accurate daily counts.

Inferring SARS-CoV-2 RNA shedding into wastewater relative to the time of infection

Since the start of the coronavirus disease-2019 (COVID-19) pandemic, there has been interest in using wastewater monitoring as an approach for disease surveillance. A significant uncertainty that would improve the interpretation of wastewater monitoring data is the intensity and timing with which individuals shed RNA from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) into wastewater. By combining wastewater and case surveillance data sets from a university campus during a period of heightened surveillance, we inferred that individual shedding of RNA into wastewater peaks on average 6 days (50% uncertainty interval (UI): 6-7; 95% UI: 4-8) following infection, and that wastewater measurements are highly overdispersed [negative binomial dispersion parameter, k = 0.39 (95% credible interval: 0.32-0.48)]. This limits the utility of wastewater surveillance as a leading indicator of secular trends in SARS-CoV-2 transmission during an epidemic, and implies that it could be most useful as an early warning of rising transmission in areas where transmission is low or clinical testing is delayed or of limited capacity.

Inferring SARS-CoV-2 RNA shedding into wastewater relative to the time of infection

Since the start of the coronavirus disease-2019 (COVID-19) pandemic, there has been interest in using wastewater monitoring as an approach for disease surveillance. A significant uncertainty that would improve the interpretation of wastewater monitoring data is the intensity and timing with which individuals shed RNA from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) into wastewater. By combining wastewater and case surveillance data sets from a university campus during a period of heightened surveillance, we inferred that individual shedding of RNA into wastewater peaks on average 6 days (50% uncertainty interval (UI): 6-7; 95% UI: 4-8) following infection, and that wastewater measurements are highly overdispersed [negative binomial dispersion parameter, k = 0.39 (95% credible interval: 0.32-0.48)]. This limits the utility of wastewater surveillance as a leading indicator of secular trends in SARS-CoV-2 transmission during an epidemic, and implies that it could be most useful as an early warning of rising transmission in areas where transmission is low or clinical testing is delayed or of limited capacity.

The impact of temperature on the transmissibility potential and virulence of COVID-19 in Tokyo, Japan

Assessing the impact of temperature on COVID-19 epidemiology is critical for implementing non-pharmaceutical interventions. However, few studies have accounted for the nature of contagious diseases, i.e., their dependent happenings. We aimed to quantify the impact of temperature on the transmissibility and virulence of COVID-19 in Tokyo, Japan, employing two epidemiological measurements of transmissibility and severity: the effective reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt) and case fatality risk (CFR). We estimated the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt and time-delay adjusted CFR and to subsequently assess the nonlinear and delayed effect of temperature on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt and time-delay adjusted CFR. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt at low temperatures, the cumulative relative risk (RR) at the first temperature percentile (3.3 °C) was 1.3 (95% confidence interval (CI): 1.1–1.7). As for the virulence to humans, moderate cold temperatures were associated with higher CFR, and CFR also increased as the temperature rose. The cumulative RR at the 10th and 99th percentiles of temperature (5.8 °C and 30.8 °C) for CFR were 3.5 (95% CI: 1.3–10.0) and 6.4 (95% CI: 4.1–10.1). Our results suggest the importance to take precautions to avoid infection in both cold and warm seasons to avoid severe cases of COVID-19. The results and our proposed approach will also help in assessing the possible seasonal course of COVID-19 in the future.

Wuhan's experience in curbing the spread of coronavirus disease (COVID-19)

BACKGROUND

Since December 2019, coronavirus disease (COVID-19) has affected over 50 000 people in Wuhan, China. However, the number of daily infection cases, hospitalization rate, lag time from onset to diagnosis date and their associations with measures introduced to slow down the spread of COVID-19 have not been fully explored.

METHODS

This study recruited 6872 COVID-19 patients in the Wuchang district, Wuhan. All of the patients had an onset date from 21 December 2019 to 23 February 2020. The overall and weekly hospitalization rate and lag time from onset to diagnosis date were calculated. The number of daily infections was estimated by the back-projection method based on the number of daily onset cases. Their association with major government reactions and measures was analyzed narratively.

RESULTS

The overall hospitalization rate was 45.9% (95% CI 44.7 to 47.1%) and the mean lag time from onset to diagnosis was 11.1±7.4 d. The estimated infection curve was constructed for the period from 14 December 2019 to 23 February 2020. Raising public awareness regarding self-protecting and social distancing, as well as the provision of timely testing and inpatient services, were coincident with the decline in the daily number of infections.

CONCLUSION

Early public awareness, early identification and early quarantine, supported by appropriate infrastructure, are important elements for containing the spread of COVID-19 in the community.

Effect of specific non-pharmaceutical intervention policies on SARS-CoV-2 transmission in the counties of the United States

Non-pharmaceutical interventions (NPIs) remain the only widely available tool for controlling the ongoing SARS-CoV-2 pandemic. We estimated weekly values of the effective basic reproductive number (Reff) using a mechanistic metapopulation model and associated these with county-level characteristics and NPIs in the United States (US). Interventions that included school and leisure activities closure and nursing home visiting bans were all associated with a median Reff below 1 when combined with either stay at home orders (median Reff 0.97, 95% confidence interval (CI) 0.58-1.39) or face masks (median Reff 0.97, 95% CI 0.58-1.39). While direct causal effects of interventions remain unclear, our results suggest that relaxation of some NPIs will need to be counterbalanced by continuation and/or implementation of others.

Socioeconomic status determines COVID-19 incidence and related mortality in Santiago, Chile

The COVID-19 pandemic has affected cities particularly hard. Here, we provide an in-depth characterization of disease incidence and mortality and their dependence on demographic and socioeconomic strata in Santiago, a highly segregated city and the capital of Chile. Our analyses show a strong association between socioeconomic status and both COVID-19 outcomes and public health capacity. People living in municipalities with low socioeconomic status did not reduce their mobility during lockdowns as much as those in more affluent municipalities. Testing volumes may have been insufficient early in the pandemic in those places, and both test positivity rates and testing delays were much higher. We find a strong association between socioeconomic status and mortality, measured by either COVID-19-attributed deaths or excess deaths. Finally, we show that infection fatality rates in young people are higher in low-income municipalities. Together, these results highlight the critical consequences of socioeconomic inequalities on health outcomes.

COVID-19 non-pharmaceutical intervention portfolio effectiveness and risk communication predominance

Non-pharmaceutical interventions (NPIs) including resource allocation, risk communication, social distancing and travel restriction, are mainstream actions to control the spreading of Coronavirus disease 2019 (COVID-19) worldwide. Different countries implemented their own combinations of NPIs to prevent local epidemics and healthcare system overloaded. Portfolios, as temporal sets of NPIs have various systemic impacts on preventing cases in populations. Here, we developed a probabilistic modeling framework to evaluate the effectiveness of NPI portfolios at the macroscale. We employed a deconvolution method to back-calculate incidence of infections and estimate the effective reproduction number by using the package EpiEstim. We then evaluated the effectiveness of NPIs using ratios of the reproduction numbers and considered them individually and as a portfolio systemically. Based on estimates from Japan, we estimated time delays of symptomatic-to-confirmation and infection-to-confirmation as 7.4 and 11.4 days, respectively. These were used to correct surveillance data of other countries. Considering 50 countries, risk communication and returning to normal life were the most and least effective yielding the aggregated effectiveness of 0.11 and - 0.05 that correspond to a 22.4% and 12.2% reduction and increase in case growth. The latter is quantified by the change in reproduction number before and after intervention implementation. Countries with the optimal NPI portfolio are along an empirical Pareto frontier where mean and variance of effectiveness are maximized and minimized independently of incidence levels. Results indicate that implemented interventions, regardless of NPI portfolios, had distinct incidence reductions and a clear timing effect on infection dynamics measured by sequences of reproduction numbers. Overall, the successful suppression of the epidemic cannot work without the non-linear effect of NPI portfolios whose effectiveness optimality may relate to country-specific socio-environmental factors.

Assessing Interventions against Coronavirus Disease 2019 (COVID-19) in Osaka, Japan: A Modeling Study

Estimation of the effective reproduction number, R(t), of coronavirus disease (COVID-19) in real-time is a continuing challenge. R(t) reflects the epidemic dynamics based on readily available illness onset data, and is useful for the planning and implementation of public health and social measures. In the present study, we proposed a method for computing the R(t) of COVID-19, and applied this method to the epidemic in Osaka prefecture from February to September 2020. We estimated R(t) as a function of the time of infection using the date of illness onset. The epidemic in Osaka came under control around 2 April during the first wave, and 26 July during the second wave. R(t) did not decline drastically following any single intervention. However, when multiple interventions were combined, the relative reductions in R(t) during the first and second waves were 70% and 51%, respectively. Although the second wave was brought under control without declaring a state of emergency, our model comparison indicated that relying on a single intervention would not be sufficient to reduce R(t) < 1. The outcome of the COVID-19 pandemic continues to rely on political leadership to swiftly design and implement combined interventions capable of broadly and appropriately reducing contacts.

Analysis of the early COVID-19 epidemic curve in Germany by regression models with change points

We analysed the coronavirus disease 2019 epidemic curve from March to the end of April 2020 in Germany. We use statistical models to estimate the number of cases with disease onset on a given day and use back-projection techniques to obtain the number of new infections per day. The respective time series are analysed by a trend regression model with change points. The change points are estimated directly from the data. We carry out the analysis for the whole of Germany and the federal state of Bavaria, where we have more detailed data. Both analyses show a major change between 9 and 13 March for the time series of infections: from a strong increase to a decrease. Another change was found between 25 March and 29 March, where the decline intensified. Furthermore, we perform an analysis stratified by age. A main result is a delayed course of the pandemic for the age group 80 + resulting in a turning point at the end of March. Our results differ from those by other authors as we take into account the reporting delay, which turned out to be time dependent and therefore changes the structure of the epidemic curve compared to the curve of newly reported cases.

Adaptive Time-Dependent Priors and Bayesian Inference to Evaluate SARS-CoV-2 Public Health Measures Validated on 31 Countries

With the rapid spread of the SARS-CoV-2 virus since the end of 2019, public health confinement measures to contain the propagation of the pandemic have been implemented. Our method to estimate the reproduction number using Bayesian inference with time-dependent priors enhances previous approaches by considering a dynamic prior continuously updated as restrictive measures and comportments within the society evolve. In addition, to allow direct comparison between reproduction number and introduction of public health measures in a specific country, the infection dates are inferred from daily confirmed cases and confirmed death. The evolution of this reproduction number in combination with the stringency index is analyzed on 31 European countries. We show that most countries required tough state interventions with a stringency index equal to 79.6 out of 100 to reduce their reproduction number below one and control the progression of the pandemic. In addition, we show a direct correlation between the time taken to introduce restrictive measures and the time required to contain the spread of the pandemic with a median time of 8 days. This analysis is validated by comparing the excess deaths and the time taken to implement restrictive measures. Our analysis reinforces the importance of having a fast response with a coherent and comprehensive set of confinement measures to control the pandemic. Only restrictions or combinations of those have shown to effectively control the pandemic.

Spatial modeling of individual-level infectious disease transmission: Tuberculosis data in Manitoba, Canada

Geographically dependent individual level models (GD-ILMs) are a class of statistical models that can be used to study the spread of infectious disease through a population in discrete-time in which covariates can be measured both at individual and area levels. The typical ILMs to illustrate spatial data are based on the distance between susceptible and infectious individuals. A key feature of GD-ILMs is that they take into account the spatial location of the individuals in addition to the distance between susceptible and infectious individuals. As a motivation of this article, we consider tuberculosis (TB) data which is an infectious disease which can be transmitted through individuals. It is also known that certain areas/demographics/communities have higher prevalent of TB (see Section 4 for more details). It is also of interest of policy makers to identify those areas with higher infectivity rate of TB for possible preventions. Therefore, we need to analyze this data properly to address those concerns. In this article, the expectation conditional maximization algorithm is proposed for estimating the parameters of GD-ILMs to be able to predict the areas with the highest average infectivity rates of TB. We also evaluate the performance of our proposed approach through some simulations. Our simulation results indicate that the proposed method provides reliable estimates of parameters which confirms accuracy of the infectivity rates.

Socioeconomic status determines COVID-19 incidence and related mortality in Santiago, Chile

The current coronavirus disease 2019 (COVID-19) pandemic has impacted dense urban populations particularly hard. Here, we provide an in-depth characterization of disease incidence and mortality patterns, and their dependence on demographic and socioeconomic strata in Santiago, a highly segregated city and the capital of Chile. We find that among all age groups, there is a strong association between socioeconomic status and both mortality -measured either by direct COVID-19 attributed deaths or excess deaths- and public health capacity. Specifically, we show that behavioral factors like human mobility, as well as health system factors such as testing volumes, testing delays, and test positivity rates are associated with disease outcomes. These robust patterns suggest multiple possibly interacting pathways that can explain the observed disease burden and mortality differentials: (i) in lower socioeconomic status municipalities, human mobility was not reduced as much as in more affluent municipalities; (ii) testing volumes in these locations were insufficient early in the pandemic and public health interventions were applied too late to be effective; (iii) test positivity and testing delays were much higher in less affluent municipalities, indicating an impaired capacity of the health-care system to contain the spread of the epidemic; and (iv) infection fatality rates appear much higher in the lower end of the socioeconomic spectrum. Together, these findings highlight the exacerbated consequences of health-care inequalities in a large city of the developing world, and provide practical methodological approaches useful for characterizing COVID-19 burden and mortality in other segregated urban centers.

Practical considerations for measuring the effective reproductive number, Rt

Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

Construction of the Infection Curve of Local Cases of COVID-19 in Hong Kong using Back-Projection

This study aimed to estimate the infection curve of local cases of the coronavirus disease (COVID-19) in Hong Kong and identify major events and preventive measures associated with the trajectory of the infection curve in the first two waves. The daily number of onset local cases was used to estimate the daily number of infections based on back-projection. The estimated infection curve was examined to identify the preventive measures or major events associated with its trajectory. Until 30 April 2020, there were 422 confirmed local cases. The infection curve of the local cases in Hong Kong was constructed and used for evaluating the impacts of various policies and events in a narrative manner. Social gatherings and some pre-implementation announcements on inbound traveler policies coincided with peaks on the infection curve.

Practical considerations for measuring the effective reproductive number, R t

Estimation of the effective reproductive number, R t , is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using R t to assess the effectiveness of interventions and to inform policy. However, estimation of R t from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of R t , we recommend the approach of Cori et al. (2013), which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis (2004), are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to spread. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting R t estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in R t estimation.

Declining trend in HIV new infections in Guangxi, China: insights from linking reported HIV/AIDS cases with CD4-at-diagnosis data

Background

The Guangxi Zhuang Autonomous Region bears a relatively high burden of HIV/AIDS infection. The number of accumulatively reported HIV/AIDS cases in Guangxi is the third highest among 31 provinces or Autonomous Region from 2004 to 2007, changed to the second highest between 2011 and 2013, then returned to the third highest again after 2014. We aim to estimate the new infections and evaluate the real-time HIV epidemic in Guangxi, China, in order to reveal the rule of HIV transmission.

Methods

Firstly, the number of annually reported HIV and AIDS cases, as well as the number of cases linked with CD4 data are extracted from the HIV/AIDS information system in China. Secondly, two CD4-staged models are formulated by linking the with-host information on CD4 level to between-host transmission and surveillance data. Thirdly, new HIV infections, diagnosis rates and undiagnosed infections over time are estimated by using Bayesian method and Maximum Likelihood Estimation method.

Results

The data reveal that the newly reported cases have been decreasing since 2011, while lots of cases are identified at late CD4 stage. The data fitted results indicate that both models can describe the trend of the epidemic well. The estimation results show that the new and undiagnosed infections began to decrease from the period2006 - 2008. However, the diagnosis probabilities/rates keep at a very low level, and there are still a large number of infections undiagnosed, most of which have a large probability to be identified at late CD4 stage.

Conclusions

Our findings suggest that HIV/AIDS epidemic in Guangxi has been controlled to a certain extent, while the diagnosis rate still needs to be improved. More attentions should be paid to identify infections at their early CD4 stages. Meanwhile, comprehensive intervention measures should be continually strengthened in avoid of the rebound of new infections.

Back-projection of COVID-19 diagnosis counts to assess infection incidence and control measures: analysis of Australian data

Back-projection is an epidemiological analysis method that was developed to estimate HIV incidence using surveillance data on AIDS diagnoses. It was used extensively during the 1990s for this purpose as well as in other epidemiological contexts. Surveillance data on COVID-19 diagnoses can be analysed by the method of back-projection using information about the probability distribution of the time between infection and diagnosis, which is primarily determined by the incubation period. This paper demonstrates the value of such analyses using daily diagnoses from Australia. It is shown how back-projection can be used to assess the pattern of COVID-19 infection incidence over time and to assess the impact of control measures by investigating their temporal association with changes in incidence patterns. For Australia, these analyses reveal that peak infection incidence coincided with the introduction of border closures and social distancing restrictions, while the introduction of subsequent social distancing measures coincided with a continuing decline in incidence to very low levels. These associations were not directly discernible from the daily diagnosis counts, which continued to increase after the first stage of control measures. It is estimated that a one week delay in peak incidence would have led to a fivefold increase in total infections. Furthermore, at the height of the outbreak, half to three-quarters of all infections remained undiagnosed. Automated data analytics of routinely collected surveillance data are a valuable monitoring tool for the COVID-19 pandemic and may be useful for calibrating transmission dynamics models.

Modeling methods for estimating HIV incidence: a mathematical review

Estimating HIV incidence is crucial for monitoring the epidemiology of this infection, planning screening and intervention campaigns, and evaluating the effectiveness of control measures. However, owing to the long and variable period from HIV infection to the development of AIDS and the introduction of highly active antiretroviral therapy, accurate incidence estimation remains a major challenge. Numerous estimation methods have been proposed in epidemiological modeling studies, and here we review commonly-used methods for estimation of HIV incidence. We review the essential data required for estimation along with the advantages and disadvantages, mathematical structures and likelihood derivations of these methods. The methods include the classical back-calculation method, the method based on CD4+ T-cell depletion, the use of HIV case reporting data, the use of cohort study data, the use of serial or cross-sectional prevalence data, and biomarker approach. By outlining the mechanistic features of each method, we provide guidance for planning incidence estimation efforts, which may depend on national or regional factors as well as the availability of epidemiological or laboratory datasets.

Extending Bayesian back-calculation to estimate age and time specific HIV incidence

CD4-based multi-state back-calculation methods are key for monitoring the HIV epidemic, providing estimates of HIV incidence and diagnosis rates by disentangling their inter-related contribution to the observed surveillance data. This paper, extends existing approaches to age-specific settings, permitting the joint estimation of age- and time-specific incidence and diagnosis rates and the derivation of other epidemiological quantities of interest. This allows the identification of specific age-groups at higher risk of infection, which is crucial in directing public health interventions. We investigate, through simulation studies, the suitability of various bivariate splines for the non-parametric modelling of the latent age- and time-specific incidence and illustrate our method on routinely collected data from the HIV epidemic among gay and bisexual men in England and Wales.

Tackling the burden of the hepatitis C virus in the UK: characterizing and assessing the clinical and economic consequences

OBJECTIVES

The hepatitis C virus (HCV) remains a significant public health issue. This study aimed to quantify the clinical and economic burden of chronic hepatitis C in the UK, stratified by disease severity, age and awareness of infection, with concurrent assessment of the impact of implementing a treatment prioritization approach.

STUDY DESIGN AND METHODS

A previously published back projection, natural history and cost-effectiveness HCV model was adapted to a UK setting to estimate the disease burden of chronic hepatitis C and end-stage liver disease (ESLD) between 1980 and 2035. A published meta-regression analysis informed disease progression, and UK-specific data informed other model inputs.

RESULTS

At 2015, prevalence of chronic hepatitis C is estimated to be 241,487 with 22.20%, 33.72%, 17.22%, 16.67% and 10.19% of patients in METAVIR stages F0, F1, F2, F3 and F4, respectively, but is estimated to fall to 193,999 by 2035. ESLD incidence is predicted to peak in 2031. Assuming all patients are diagnosed and treatment is prioritized in F3 and F4 using highly efficacious direct-acting antiviral (DAA) regimens, a 69.85% reduction in ESLD incidence is predicted between 2015 and 2035, and the cumulative discounted medical expenditure associated with the lifetime management of incident ESLD events is estimated to be £1,202,827,444.

CONCLUSIONS

The prevalence of chronic hepatitis C is expected to fall in coming decades; however, the ongoing financial burden is expected to be high due to an increase in ESLD incidence. This study highlights the significant costs of managing ESLD that are likely to be incurred without the employment of effective treatment approaches.

A review of back-calculation techniques and their potential to inform mitigation strategies with application to non-transmissible acute infectious diseases

Back-calculation is a process whereby generally unobservable features of an event leading to a disease outbreak can be inferred either in real-time or shortly after the end of the outbreak. These features might include the time when persons were exposed and the source of the outbreak. Such inferences are important as they can help to guide the targeting of mitigation strategies and to evaluate the potential effectiveness of such strategies. This article reviews the process of back-calculation with a particular emphasis on more recent applications concerning deliberate and naturally occurring aerosolized releases. The techniques can be broadly split into two themes: the simpler temporal models and the more sophisticated spatio-temporal models. The former require input data in the form of cases' symptom onset times, whereas the latter require additional spatial information such as the cases' home and work locations. A key aspect in the back-calculation process is the incubation period distribution, which forms the initial topic for consideration. Links between atmospheric dispersion modelling, within-host dynamics and back-calculation are outlined in detail. An example of how back-calculation can inform mitigation strategies completes the review by providing improved estimates of the duration of antibiotic prophylaxis that would be required in the response to an inhalational anthrax outbreak.

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.

Associations of age and sex with the clinical outcome and incubation period of Shiga toxin-producing Escherichia coli O104:H4 infections, 2011

We pooled data on adults who reported diarrhea or developed life-threatening hemolytic uremic syndrome (HUS) in any of 6 closed cohorts from 4 countries (1 cohort each in Denmark, France, and Sweden and 3 in Germany) that were investigated during a large outbreak of Shiga toxin-producing Escherichia coli (STEC) O104:H4 infection in 2011. Logistic regression and Weibull regression for interval censored data were used to assess the relation of age and sex with clinical outcome and with incubation period. Information on the latter was used in a nonparametric back-projection context to estimate when adult cases reported in Germany were exposed to STEC O104:H4. Overall, data from 119 persons (median age, 49 years; 80 women) were analyzed. Bloody diarrhea and HUS were recorded as the most severe outcome for 44 and 26 individuals, respectively. Older age was significantly associated with bloody diarrhea but not with HUS. Woman had nonsignificantly higher odds for bloody diarrhea (odds ratio = 1.81) and developing HUS (odds ratio = 1.83) than did men. Older participants had a statistically significantly reduced incubation period. The shortest interval that included 75% of exposures in adults spanned only 12 days and preceded outbreak detection. In conclusion, the frequency of bloody diarrhea but not of HUS and the length of the incubation period depended on the age of individuals infected with STEC O104:H4. A large number of people were exposed to STEC O104:H4 for a short period of time.

Disproportionate impact of combination antiretroviral therapy on AIDS incidence in Australia: results from a modified back-projection model

The objective of the current study is to describe the impact of Combination antiretroviral therapy (cART) on trends in AIDS incidence over time for selected population groups in Australia, specifically, men who have sex with men (MSM) and injecting drug users (IDUs). A modified back-projection modeling technique was used to predict the number of AIDS diagnoses without cART based on Australia's HIV/AIDS surveillance system database. Modelled estimates indicate that since 1996, the effective cART has reduced overall AIDS cases by ~70 and ~10% among MSM and IDUs respectively. The predicted reduction in AIDS cases among IDUs aged less than 40 years was 36% while there was no reduction predicted for those aged 40 years or older. The impact of cART on AIDS diagnoses has been modest among IDUs. Late presentation, poor access to health services and barriers to uptake of cART may account for the divergence between these population groups.

A nonparametric estimation of the infection curve

Predicting the future course of an epidemic depends on being able to estimate the current numbers of infected individuals. However, while back-projection techniques allow reliable estimation of the numbers of infected individuals in the more distant past, they are less reliable in the recent past. We propose two new nonparametric methods to estimate the unobserved numbers of infected individuals in the recent past in an epidemic. The proposed methods are noniterative, easily computed and asymptotically normal with simple variance formulas. Simulations show that the proposed methods are much more robust and accurate than the existing back projection method, especially for the recent past, which is our primary interest. We apply the proposed methods to the 2003 Severe Acute Respiratory Syndorme (SARS) epidemic in Hong Kong.

Increasing HIV transmission through male homosexual and heterosexual contact in Australia: results from an extended back-projection approach

OBJECTIVES

The aim of the study was to reconstruct the HIV epidemic in Australia for selected populations categorized by exposure route; namely, transmission among men who have sex with men (MSM), transmission among injecting drug users (IDUs), and transmission among heterosexual men and women in Australia.

DESIGN

Statistical back-projection techniques were extended to reconstruct the historical HIV infection curve using surveillance data. Methods We developed and used a novel modified back-projection modelling technique that makes maximal use of all available surveillance data sources in Australia, namely, (1) newly diagnosed HIV infections, (2) newly acquired HIV infections and (3) AIDS diagnoses.

RESULTS

The analyses suggest a peak HIV incidence in Australian MSM of approximately 2000 new infections per year in the late 1980s, followed by a rapid decline to a low of <500 in the early 1990s. We estimate that, by 2007, cumulatively approximately 20 000 MSM were infected with HIV, of whom 13% were not diagnosed with HIV infection. Similarly, a total of approximately 1050 and approximately 2600 individuals were infected through sharing needles and heterosexual contact, respectively, and in 12% and 23% of these individuals, respectively, the infection remained undetected.

DISCUSSION

Male homosexual contact accounts for the majority of new HIV infections in Australia. However, the transmission route distribution of new HIV infections has changed over time. The number of HIV infections is increasing substantially among MSM, increasing moderately in those infected via heterosexual exposure, and decreasing in IDUs.

Some statistics in bioinformatics: the fifth Armitage Lecture

The spirit and content of the 2007 Armitage Lecture are presented in this paper. To begin, two areas of Peter Armitage's early work are distinguished: his pioneering research on sequential methods intended for use in medical trials and the comparison of survival curves. Their influence on much later work is highlighted, and motivate the proposal of several statistical 'truths' that are presented in the paper. The illustration of these truths demonstrates biology's new morphology and its dominance over statistics in this century. An overview of a recent proteomics ovarian cancer study is given as a warning of what can happen when bioinformatics meets epidemiology badly, in particular, when the study design is poor. A statistical bioinformatics success story is outlined, in which gene profiling is helping to identify novel genes and networks involved in mouse embryonic stem cell development. Some concluding thoughts are given.

Characterizing trends in HIV infection among men who have sex with men in Australia by birth cohorts: results from a modified back-projection method

Background

We set out to estimate historical trends in HIV incidence in Australian men who have sex with men with respect to age at infection and birth cohort.

Methods

A modified back-projection technique is applied to data from the HIV/AIDS Surveillance System in Australia, including "newly diagnosed HIV infections", "newly acquired HIV infections" and "AIDS diagnoses", to estimate trends in HIV incidence over both calendar time and age at infection.

Results

Our results demonstrate that since 2000, there has been an increase in new HIV infections in Australian men who have sex with men across all age groups. The estimated mean age at infection increased from ~35 years in 2000 to ~37 years in 2007. When the epidemic peaked in the mid 1980s, the majority of the infections (56%) occurred among men aged 30 years and younger; 30% occurred in ages 31 to 40 years; and only ~14% of them were attributed to the group who were older than 40 years of age. In 2007, the proportion of infections occurring in persons 40 years or older doubled to 31% compared to the mid 1980s, while the proportion of infections attributed to the group younger than 30 years of age decreased to 36%.

Conclusion

The distribution of HIV incidence for birth cohorts by infection year suggests that the HIV epidemic continues to affect older homosexual men as much as, if not more than, younger men. The results are useful for evaluating the impact of the epidemic across successive birth cohorts and study trends among the age groups most at risk.

Trends in three decades of HIV/AIDS epidemic in Thailand by nonparametric backcalculation method

OBJECTIVES

To reconstruct the past HIV incidence and prevalence in Thailand from 1980 to 2008 and predict the country's AIDS incidence from 2009 to 2011.

METHODS

Nonparametric backcalculation was adopted utilizing 100 quarterly observed new AIDS counts excluding pediatric cases. The accuracy of data was enhanced through a series of data adjustments using the weight method to account for several surveillance reporting issues. The mixture of time-dependent distributions allowed the effects of age at seroconversion and antiretroviral therapy to be incorporated simultaneously. Sensitivity analyses were conducted to assess model variations that were subject to major uncertainties. Future AIDS incidence was projected for various predetermined HIV incidence patterns.

RESULTS

HIV incidence in Thailand reached its peak in 1992 with approximately 115,000 cases. A steep decline thereafter discontinued in 1997 and was followed by another strike of 42,000 cases in 1999. The second surge, which happened concurrently with the major economic crisis, brought on 60,000 new infections. As of December 2008, more than 1 million individuals had been infected and around 430,000 adults were living with HIV corresponding to a prevalence rate of 1.2%. The incidence rate had become less than 0.1% since 2002. The backcalculated estimates were dominated by postulated median AIDS progression time and adjustments to surveillance data.

CONCLUSION

Our analysis indicated that, thus far, the 1990s was the most severe era of HIV/AIDS epidemic in Thailand with two HIV incidence peaks. A drop in new infections led to a decrease in recent AIDS incidence, and this tendency is likely to remain unchanged until 2011, if not further.

Two Critical Issues in Quantitative Modeling of Communicable Diseases: Inference of Unobservables and Dependent Happening

In this chapter, we discuss two critical issues which must be remembered whenever we examine epidemiologic data of directly transmitted infectious diseases. Firstly, we would like the readers to recognize the difference between observable and unobservable events in infectious disease epidemiology. Since both infection event and acquisition of infectiousness are generally not directly observable, the total number of infected individuals could not be counted at a point of time, unless very rigorous contact tracing and microbiological examinations were performed. Directly observable intrinsic parameters, such as the incubation period and serial interval, play key roles in translating observable to unobservable information. Secondly, the concept of dependent happening must be remembered to identify a risk of an infectious disease or to assess vaccine efficacy. Observation of a single infected individual is not independent of observing other individuals. A simple solution for dependent happening is to employ the transmission probability which is conditioned on an exposure to infection.