A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data

Tracking pathogen transmissibility during infectious disease outbreaks is essential for assessing the effectiveness of public health measures and planning future control strategies. A key measure of transmissibility is the time-dependent reproduction number, which has been estimated in real-time during outbreaks of a range of pathogens from disease incidence time series data. While commonly used approaches for estimating the time-dependent reproduction number can be reliable when disease incidence is recorded frequently, such incidence data are often aggregated temporally (for example, numbers of cases may be reported weekly rather than daily). As we show, commonly used methods for estimating transmissibility can be unreliable when the timescale of transmission is shorter than the timescale of data recording. To address this, here we develop a simulation-based approach involving Approximate Bayesian Computation for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. We first use a simulated dataset representative of a situation in which daily disease incidence data are unavailable and only weekly summary values are reported, demonstrating that our method provides accurate estimates of the time-dependent reproduction number under such circumstances. We then apply our method to two outbreak datasets consisting of weekly influenza case numbers in 2019-20 and 2022-23 in Wales (in the United Kingdom). Our simple-to-use approach will allow accurate estimates of time-dependent reproduction numbers to be obtained from temporally aggregated data during future infectious disease outbreaks.

Marburg virus disease outbreaks, mathematical models, and disease parameters: a systematic review

The 2023 Marburg virus disease outbreaks in Equatorial Guinea and Tanzania highlighted the importance of better understanding this lethal pathogen. We did a systematic review (PROSPERO CRD42023393345) of peer-reviewed articles reporting historical outbreaks, modelling studies, and epidemiological parameters focused on Marburg virus disease. We searched PubMed and Web of Science from database inception to March 31, 2023. Two reviewers evaluated all titles and abstracts with consensus-based decision making. To ensure agreement, 13 (31%) of 42 studies were double-extracted and a custom-designed quality assessment questionnaire was used for risk of bias assessment. We present detailed information on 478 reported cases and 385 deaths from Marburg virus disease. Analysis of historical outbreaks and seroprevalence estimates suggests the possibility of undetected Marburg virus disease outbreaks, asymptomatic transmission, or cross-reactivity with other pathogens, or a combination of these. Only one study presented a mathematical model of Marburg virus transmission. We estimate an unadjusted, pooled total random effect case fatality ratio of 61·9% (95% CI 38·8-80·6; I2=93%). We identify epidemiological parameters relating to transmission and natural history, for which there are few estimates. This systematic review and the accompanying database provide a comprehensive overview of Marburg virus disease epidemiology and identify key knowledge gaps, contributing crucial information for mathematical models to support future Marburg virus disease epidemic responses.

Retrospective evaluation of real-time estimates of global COVID-19 transmission trends and mortality forecasts

Since 8th March 2020 up to the time of writing, we have been producing near real-time weekly estimates of SARS-CoV-2 transmissibility and forecasts of deaths due to COVID-19 for all countries with evidence of sustained transmission, shared online. We also developed a novel heuristic to combine weekly estimates of transmissibility to produce forecasts over a 4-week horizon. Here we present a retrospective evaluation of the forecasts produced between 8th March to 29th November 2020 for 81 countries. We evaluated the robustness of the forecasts produced in real-time using relative error, coverage probability, and comparisons with null models. During the 39-week period covered by this study, both the short- and medium-term forecasts captured well the epidemic trajectory across different waves of COVID-19 infections with small relative errors over the forecast horizon. The model was well calibrated with 56.3% and 45.6% of the observations lying in the 50% Credible Interval in 1-week and 4-week ahead forecasts respectively. The retrospective evaluation of our models shows that simple transmission models calibrated using routine disease surveillance data can reliably capture the epidemic trajectory in multiple countries. The medium-term forecasts can be used in conjunction with the short-term forecasts of COVID-19 mortality as a useful planning tool as countries continue to relax public health measures.

Extending EpiEstim to estimate the transmission advantage of pathogen variants in real-time: SARS-CoV-2 as a case-study

The evolution of SARS-CoV-2 has demonstrated that emerging variants can set back the global COVID-19 response. The ability to rapidly assess the threat of new variants is critical for timely optimisation of control strategies. We present a novel method to estimate the effective transmission advantage of a new variant compared to a reference variant combining information across multiple locations and over time. Through an extensive simulation study designed to mimic real-time epidemic contexts, we show that our method performs well across a range of scenarios and provide guidance on its optimal use and interpretation of results. We also provide an open-source software implementation of our method. The computational speed of our tool enables users to rapidly explore spatial and temporal variations in the estimated transmission advantage. We estimate that the SARS-CoV-2 Alpha variant is 1.46 (95% Credible Interval 1.44-1.47) and 1.29 (95% CrI 1.29-1.30) times more transmissible than the wild type, using data from England and France respectively. We further estimate that Delta is 1.77 (95% CrI 1.69-1.85) times more transmissible than Alpha (England data). Our approach can be used as an important first step towards quantifying the threat of emerging or co-circulating variants of infectious pathogens in real-time.

Estimating the epidemic reproduction number from temporally aggregated incidence data: A statistical modelling approach and software tool

The time-varying reproduction number (Rt) is an important measure of epidemic transmissibility that directly informs policy decisions and the optimisation of control measures. EpiEstim is a widely used opensource software tool that uses case incidence and the serial interval (SI, time between symptoms in a case and their infector) to estimate Rt in real-time. The incidence and the SI distribution must be provided at the same temporal resolution, which can limit the applicability of EpiEstim and other similar methods, e.g. for contexts where the time window of incidence reporting is longer than the mean SI. In the EpiEstim R package, we implement an expectation-maximisation algorithm to reconstruct daily incidence from temporally aggregated data, from which Rt can then be estimated. We assess the validity of our method using an extensive simulation study and apply it to COVID-19 and influenza data. For all datasets, the influence of intra-weekly variability in reported data was mitigated by using aggregated weekly data. Rt estimated on weekly sliding windows using incidence reconstructed from weekly data was strongly correlated with estimates from the original daily data. The simulation study revealed that Rt was well estimated in all scenarios and regardless of the temporal aggregation of the data. In the presence of weekend effects, Rt estimates from reconstructed data were more successful at recovering the true value of Rt than those obtained from reported daily data. These results show that this novel method allows Rt to be successfully recovered from aggregated data using a simple approach with very few data requirements. Additionally, by removing administrative noise when daily incidence data are reconstructed, the accuracy of Rt estimates can be improved.

Real-time estimation of the epidemic reproduction number: Scoping review of the applications and challenges

The time-varying reproduction number (Rt) is an important measure of transmissibility during outbreaks. Estimating whether and how rapidly an outbreak is growing (Rt > 1) or declining (Rt < 1) can inform the design, monitoring and adjustment of control measures in real-time. We use a popular R package for Rt estimation, EpiEstim, as a case study to evaluate the contexts in which Rt estimation methods have been used and identify unmet needs which would enable broader applicability of these methods in real-time. A scoping review, complemented by a small EpiEstim user survey, highlight issues with the current approaches, including the quality of input incidence data, the inability to account for geographical factors, and other methodological issues. We summarise the methods and software developed to tackle the problems identified, but conclude that significant gaps remain which should be addressed to enable easier, more robust and applicable estimation of Rt during epidemics.

Optimising the deployment of vector control tools against malaria: a data-informed modelling study

BACKGROUND

Concern that insecticide resistant mosquitoes are threatening malaria control has driven the development of new types of insecticide treated nets (ITNs) and indoor residual spraying (IRS) of insecticide. Malaria control programmes have a choice of vector control interventions although it is unclear which controls should be used to combat the disease. The study aimed at producing a framework to easily compare the public health impact and cost-effectiveness of different malaria prevention measures currently in widespread use.

METHODS

We used published data from experimental hut trials conducted across Africa to characterise the entomological effect of pyrethroid-only ITNs versus ITNs combining a pyrethroid insecticide with the synergist piperonyl butoxide (PBO). We use these estimates to parameterise a dynamic mathematical model of Plasmodium falciparum malaria which is validated for two sites by comparing simulated results to empirical data from randomised control trials (RCTs) in Tanzania and Uganda. We extrapolated model simulations for a series of potential scenarios likely across the sub-Saharan African region and include results in an online tool (Malaria INtervention Tool [MINT]) that aims to identify optimum vector control intervention packages for scenarios with varying budget, price, entomological and epidemiological factors.

FINDINGS

Our model indicates that switching from pyrethroid-only to pyrethroid-PBO ITNs could averted up to twice as many cases, although the additional benefit is highly variable and depends on the setting conditions. We project that annual delivery of long-lasting, non-pyrethroid IRS would prevent substantially more cases over 3-years, while pyrethroid-PBO ITNs tend to be the most cost-effective intervention per case averted. The model was able to predict prevalence and efficacy against prevalence in both RCTs for the intervention types tested. MINT is applicable to regions of sub-Saharan Africa with endemic malaria and provides users with a method of designing intervention packages given their setting and budget.

INTERPRETATION

The most cost-effective vector control package will vary locally. Models able to recreate results of RCTs can be used to extrapolate outcomes elsewhere to support evidence-based decision making for investment in vector control.

FUNDING

Medical Research Council, IVCC, Wellcome Trust.

TRANSLATION

For the French translation of the abstract see Supplementary Materials section.

Systematic review of the entomological impact of insecticide-treated nets evaluated using experimental hut trials in Africa

Resistance of anopheline mosquitoes to pyrethroid insecticides is spreading rapidly across sub-Saharan Africa, diminishing the efficacy of insecticide-treated nets (ITNs) - the primary tool for preventing malaria. The entomological efficacy of indoor vector control interventions can be measured in experimental hut trials (EHTs), where hut structures resemble local housing, but allow the collection of mosquitoes that entered, exited, blood-fed and/or died. There is a need to understand how the spread of resistance changes ITN efficacy and to elucidate factors influencing EHT results, including differences in experimental hut design, to support the development of novel vector control tools. A comprehensive database of EHTs was compiled following a systematic review to identify all known trials investigating ITNs or indoor residual spraying across sub-Saharan Africa. This analysis focuses on EHTs investigating ITNs and uses Bayesian statistical models to characterise the complex interaction between ITNs and mosquitoes, the between-study variability, and the impact of pyrethroid resistance. As resistance rises, the entomological efficacy of ITNs declines. They induce less mortality and are less likely to deter mosquitoes from entering huts. Despite this, ITNs continue to offer considerable personal protection by reducing mosquito feeding until resistance reaches high levels. There are clear associations between the different entomological impacts of ITNs, though there is still substantial variability between studies, some of which can be accounted for by hut design. The relationship between EHT outcomes and the level of resistance (as measured by discriminating dose bioassays) is highly uncertain. The meta-analyses show that EHTs are an important reproducible assay for capturing the complex entomological efficacy of ITNs on blood-feeding mosquitoes. The impact of pyrethroid resistance on these measures appears broadly consistent across a wide geographical area once hut design is accounted for, suggesting results can be extrapolated beyond the sites where the trials were conducted. Further work is needed to understand factors influencing EHT outcomes and how the relationship between outcomes and resistance varies when different methods are used to assess the level of resistance in wild mosquito populations. This will allow more precise estimates of the efficacy of these important vector control tools.

Core competencies create value

In the past, healthcare providers have created value by delivering care on demand to their patients. In the future, however, providers will create value by mastering four core competencies: effective management of health and wellness, effective care delivery, effective population enrollment, and effective management of financial risk.