Comparing methods for estimating R0 from the size distribution of subcritical transmission chains

Inference of epidemic dynamics in the COVID-19 era and beyond

The COVID-19 pandemic demonstrated the key role that epidemiology and modelling play in analysing infectious threats and supporting decision making in real-time. Motivated by the unprecedented volume and breadth of data generated during the pandemic, we review modern opportunities for analysis to address questions that emerge during a major modern epidemic. Following the broad chronology of insights required - from understanding initial dynamics to retrospective evaluation of interventions, we describe the theoretical foundations of each approach and the underlying intuition. Through a series of case studies, we illustrate real life applications, and discuss implications for future work.

Estimating the reproduction number and transmission heterogeneity from the size distribution of clusters of identical pathogen sequences

Quantifying transmission intensity and heterogeneity is crucial to ascertain the threat posed by infectious diseases and inform the design of interventions. Methods that jointly estimate the reproduction number R and the dispersion parameter k have however mainly remained limited to the analysis of epidemiological clusters or contact tracing data, whose collection often proves difficult. Here, we show that clusters of identical sequences are imprinted by the pathogen offspring distribution, and we derive an analytical formula for the distribution of the size of these clusters. We develop and evaluate an inference framework to jointly estimate the reproduction number and the dispersion parameter from the size distribution of clusters of identical sequences. We then illustrate its application across a range of epidemiological situations. Finally, we develop a hypothesis testing framework relying on clusters of identical sequences to determine whether a given pathogen genetic subpopulation is associated with increased or reduced transmissibility. Our work provides tools to estimate the reproduction number and transmission heterogeneity from pathogen sequences without building a phylogenetic tree, thus making it easily scalable to large pathogen genome datasets.

Underdetected dispersal and extensive local transmission drove the 2022 mpox epidemic

The World Health Organization declared mpox a public health emergency of international concern in July 2022. To investigate global mpox transmission and population-level changes associated with controlling spread, we built phylogeographic and phylodynamic models to analyze MPXV genomes from five global regions together with air traffic and epidemiological data. Our models reveal community transmission prior to detection, changes in case reporting throughout the epidemic, and a large degree of transmission heterogeneity. We find that viral introductions played a limited role in prolonging spread after initial dissemination, suggesting that travel bans would have had only a minor impact. We find that mpox transmission in North America began declining before more than 10% of high-risk individuals in the USA had vaccine-induced immunity. Our findings highlight the importance of broader routine specimen screening surveillance for emerging infectious diseases and of joint integration of genomic and epidemiological information for early outbreak control.

Transmission bottleneck size estimation from de novo viral genetic variation

Sequencing of viral infections has become increasingly common over the last decade. Deep sequencing data in particular have proven useful in characterizing the roles that genetic drift and natural selection play in shaping within-host viral populations. They have also been used to estimate transmission bottleneck sizes from identified donor-recipient pairs. These bottleneck sizes quantify the number of viral particles that establish genetic lineages in the recipient host and are important to estimate due to their impact on viral evolution. Current approaches for estimating bottleneck sizes exclusively consider the subset of viral sites that are observed as polymorphic in the donor individual. However, allele frequencies can change dramatically over the course of an individual's infection, such that sites that are polymorphic in the donor at the time of transmission may not be polymorphic in the donor at the time of sampling and allele frequencies at donor-polymorphic sites may change dramatically over the course of a recipient's infection. Because of this, transmission bottleneck sizes estimated using allele frequencies observed at a donor's polymorphic sites may be considerable underestimates of true bottleneck sizes. Here, we present a new statistical approach for instead estimating bottleneck sizes using patterns of viral genetic variation that arose de novo within a recipient individual. Specifically, our approach makes use of the number of clonal viral variants observed in a transmission pair, defined as the number of viral sites that are monomorphic in both the donor and the recipient but carry different alleles. We first test our approach on a simulated dataset and then apply it to both influenza A virus sequence data and SARS-CoV-2 sequence data from identified transmission pairs. Our results confirm the existence of extremely tight transmission bottlenecks for these two respiratory viruses, using an approach that does not tend to underestimate transmission bottleneck sizes.

A statistical framework for tracking the time-varying superspreading potential of COVID-19 epidemic

Timely detection of an evolving event of an infectious disease with superspreading potential is imperative for territory-wide disease control as well as preventing future outbreaks. While the reproduction number (R) is a commonly-adopted metric for disease transmissibility, the transmission heterogeneity quantified by dispersion parameter k, a metric for superspreading potential is seldom tracked. In this study, we developed an estimation framework to track the time-varying risk of superspreading events (SSEs) and demonstrated the method using the three epidemic waves of COVID-19 in Hong Kong. Epidemiological contact tracing data of the confirmed COVID-19 cases from 23 January 2020 to 30 September 2021 were obtained. By applying branching process models, we jointly estimated the time-varying R and k. Individual-based outbreak simulations were conducted to compare the time-varying assessment of the superspreading potential with the typical non-time-varying estimate of k over a period of time. We found that the COVID-19 transmission in Hong Kong exhibited substantial superspreading during the initial phase of the epidemics, with only 1 % (95 % Credible interval [CrI]: 0.6-2 %), 5 % (95 % CrI: 3-7 %) and 10 % (95 % CrI: 8-14 %) of the most infectious cases generated 80 % of all transmission for the first, second and third epidemic waves, respectively. After implementing local public health interventions, R estimates dropped gradually and k estimates increased thereby reducing the risk of SSEs to approaching zero. Outbreak simulations indicated that the non-time-varying estimate of k may overlook the possibility of large outbreaks. Hence, an estimation of the time-varying k as a compliment of R as a monitoring of both disease transmissibility and superspreading potential, particularly when public health interventions were relaxed is crucial for minimizing the risk of future outbreaks.

Quantifying Mycobacterium tuberculosis Transmission Dynamics Across Global Settings: A Systematic Analysis

The degree to which individual heterogeneity in the production of secondary cases ("superspreading") affects tuberculosis (TB) transmission has not been systematically studied. We searched for population-based or surveillance studies in which whole genome sequencing was used to estimate TB transmission and in which the size distributions of putative TB transmission clusters were enumerated. We fitted cluster-size-distribution data to a negative binomial branching process model to jointly infer the transmission parameters $R$ (the reproduction number) and the dispersion parameter, $k$, which quantifies the propensity of superspreading in a population (generally, lower values of $k$ ($<1.0$) suggest increased heterogeneity). Of 4,796 citations identified in our initial search, 9 studies from 8 global settings met the inclusion criteria (n = 5 studies of all TB; n = 4 studies of drug-resistant TB). Estimated $R$ values (range, 0.10-0.73) were below 1.0, consistent with declining epidemics in the included settings; estimated $k$ values were well below 1.0 (range, 0.02-0.48), indicating the presence of substantial individual-level heterogeneity in transmission across all settings. We estimated that a minority of cases (range, 2%-31%) drive the majority (80%) of ongoing TB transmission at the population level. Identifying sources of heterogeneity and accounting for them in TB control may have a considerable impact on mitigating TB transmission.

The Impact of Emerging Plasmodium knowlesi on Accurate Diagnosis by Light Microscopy: A Systematic Review and Modeling Analysis

The five major Plasmodium spp. that cause human malaria appear similar under light microscopy, which raises the possibility that misdiagnosis could routinely occur in clinical settings. Assessing the extent of misdiagnosis is of particular importance for monitoring P. knowlesi, which cocirculates with the other Plasmodium spp. We performed a systematic review and meta-analysis of studies comparing the performance of microscopy and polymerase chain reaction (PCR) for diagnosing malaria in settings with co-circulation of the five Plasmodium spp. We assessed the extent to which co-circulation of Plasmodium parasites affects diagnostic outcomes. We fit a Bayesian hierarchical latent class model to estimate variation in microscopy sensitivity and specificity measured against PCR as the gold standard. Mean sensitivity of microscopy was low, yet highly variable across Plasmodium spp., ranging from 65.7% (95% confidence interval: 48.1-80.3%) for P. falciparum to 0.525% (95% confidence interval 0.0210-3.11%) for P. ovale. Observed PCR prevalence was positively correlated with estimated microscopic sensitivity and negatively correlated with estimated microscopic specificity, though the strength of the associations varied by species. Our analysis suggests that cocirculation of Plasmodium spp. undermines the accuracy of microscopy. Sensitivity was considerably lower for P. knowlesi, P. malariae, and P. ovale. The negative association between specificity and prevalence imply that less frequently encountered species may be misdiagnosed as more frequently encountered species. Together, these results suggest that the burden of P. knowlesi, P. malariae, and P. ovale may be underappreciated in a clinical setting.

Model-based Analysis of Tuberculosis Genotype Clusters in the United States Reveals High Degree of Heterogeneity in Transmission and State-level Differences Across California, Florida, New York, and Texas

BACKGROUND

Reductions in tuberculosis (TB) transmission have been instrumental in lowering TB incidence in the United States. Sustaining and augmenting these reductions are key public health priorities.

METHODS

We fit mechanistic transmission models to distributions of genotype clusters of TB cases reported to the Centers for Disease Control and Prevention during 2012-2016 in the United States and separately in California, Florida, New York, and Texas. We estimated the mean number of secondary cases generated per infectious case (R0) and individual-level heterogeneity in R0 at state and national levels and assessed how different definitions of clustering affected these estimates.

RESULTS

In clusters of genotypically linked TB cases that occurred within a state over a 5-year period (reference scenario), the estimated R0 was 0.29 (95% confidence interval [CI], .28-.31) in the United States. Transmission was highly heterogeneous; 0.24% of simulated cases with individual R0 >10 generated 19% of all recent secondary transmissions. R0 estimate was 0.16 (95% CI, .15-.17) when a cluster was defined as cases occurring within the same county over a 3-year period. Transmission varied across states: estimated R0s were 0.34 (95% CI, .3-.4) in California, 0.28 (95% CI, .24-.36) in Florida, 0.19 (95% CI, .15-.27) in New York, and 0.38 (95% CI, .33-.46) in Texas.

CONCLUSIONS

TB transmission in the United States is characterized by pronounced heterogeneity at the individual and state levels. Improving detection of transmission clusters through incorporation of whole-genome sequencing and identifying the drivers of this heterogeneity will be essential to reducing TB transmission.

Estimating the basic reproduction number at the beginning of an outbreak

We compare several popular methods of estimating the basic reproduction number, R₀, focusing on the early stages of an epidemic, and assuming weekly reports of new infecteds. We study the situation when data is generated by one of three standard epidemiological compartmental models: SIR, SEIR, and SEAIR; and examine the sensitivity of the estimators to the model structure. As some methods are developed assuming specific epidemiological models, our work adds a study of their performance in both a well-specified (data generating model and method model are the same) and miss-specified (data generating model and method model differ) settings. We also study R₀ estimation using Canadian COVID-19 case report data. In this study we focus on examples of influenza and COVID-19, though the general approach is easily extendable to other scenarios. Our simulation study reveals that some estimation methods tend to work better than others, however, no singular best method was clearly detected. In the discussion, we provide recommendations for practitioners based on our results.

Characterizing tuberculosis transmission dynamics in high-burden urban and rural settings

Mycobacterium tuberculosis transmission dynamics in high-burden settings are poorly understood. Growing evidence suggests transmission may be characterized by extensive individual heterogeneity in secondary cases (i.e., superspreading), yet the degree and influence of such heterogeneity is largely unknown and unmeasured in high burden-settings. We conducted a prospective, population-based molecular epidemiology study of TB transmission in both an urban and rural setting of Botswana, one of the highest TB burden countries in the world. We used these empirical data to fit two mathematical models (urban and rural) that jointly quantified both the effective reproductive number, [Formula: see text], and the propensity for superspreading in each population. We found both urban and rural populations were characterized by a high degree of individual heterogeneity, however such heterogeneity disproportionately impacted the rural population: 99% of secondary transmission was attributed to only 19% of infectious cases in the rural population compared to 60% in the urban population and the median number of incident cases until the first outbreak of 30 cases was only 32 for the rural model compared to 791 in the urban model. These findings suggest individual heterogeneity plays a critical role shaping local TB epidemiology within subpopulations.

Inferring person-to-person networks of Plasmodium falciparum transmission: are analyses of routine surveillance data up to the task?

BACKGROUND

Inference of person-to-person transmission networks using surveillance data is increasingly used to estimate spatiotemporal patterns of pathogen transmission. Several data types can be used to inform transmission network inferences, yet the sensitivity of those inferences to different data types is not routinely evaluated.

METHODS

The influence of different combinations of spatial, temporal, and travel-history data on transmission network inferences for Plasmodium falciparum malaria were evaluated.

RESULTS

The information content of these data types may be limited for inferring person-to-person transmission networks and may lead to an overestimate of transmission. Only when outbreaks were temporally focal or travel histories were accurate was the algorithm able to accurately estimate the reproduction number under control, R_c. Applying this approach to data from Eswatini indicated that inferences of R_c and spatiotemporal patterns therein depend upon the choice of data types and assumptions about travel-history data.

CONCLUSIONS

These results suggest that transmission network inferences made with routine malaria surveillance data should be interpreted with caution.

Many but small HIV-1 non-B transmission chains in the Netherlands

OBJECTIVE

The aim of this study was to investigate introductions and spread of different HIV-1 subtypes in the Netherlands.

DESIGN

We identified distinct HIV-1 transmission chains in the Netherlands within the global epidemic context through viral phylogenetic analysis of partial HIV-1 polymerase sequences from individuals enrolled in the ATHENA national HIV cohort of all persons in care since 1996, and publicly available international background sequences.

METHODS

Viral lineages circulating in the Netherlands were identified through maximum parsimony phylogeographic analysis. The proportion of HIV-1 infections acquired in-country among heterosexuals and MSM was estimated from phylogenetically observed, national transmission chains using a branching process model that accounts for incomplete sampling.

RESULTS

As of 1 January 2019, 2589 (24%) of 10 971 (41%) HIV-1 sequenced individuals in ATHENA had non-B subtypes (A1, C, D, F, G) or circulating recombinant forms (CRF01AE, CRF02AG, CRF06-cpx). The 1588 heterosexuals were in 1224, and 536 MSM in 270 phylogenetically observed transmission chains. After adjustments for incomplete sampling, most heterosexual (75%) and MSM (76%) transmission chains were estimated to include only the individual introducing the virus (size = 1). Onward transmission occurred mostly in chains size 2-5 amongst heterosexuals (62%) and in chains size at least 10 amongst MSM (64%). Considering some chains originated in-country from other risk-groups, 40% (95% confidence interval: 36-44) of non-B-infected heterosexuals and 62% (95% confidence interval: 49-73) of MSM-acquired infection in-country.

CONCLUSION

Although most HIV-1 non-B introductions showed no or very little onward transmission, a considerable proportion of non-B infections amongst both heterosexuals and MSM in the Netherlands have been acquired in-country.

Decrease in overdispersed secondary transmission of COVID-19 over time in Japan

Coronavirus disease 2019 (COVID-19) has been described as having an overdispersed offspring distribution, i.e. high variation in the number of secondary transmissions of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) per single primary COVID-19 case. Accordingly, countermeasures focused on high-risk settings and contact tracing could efficiently reduce secondary transmissions. However, as variants of concern with elevated transmissibility continue to emerge, controlling COVID-19 with such focused approaches has become difficult. It is vital to quantify temporal variations in the offspring distribution dispersibility. Here, we investigated offspring distributions for periods when the ancestral variant was still dominant (summer, 2020; wave 2) and when Alpha variant (B.1.1.7) was prevailing (spring, 2021; wave 4). The dispersion parameter (k) was estimated by analysing contact tracing data and fitting a negative binomial distribution to empirically observed offspring distributions from Nagano, Japan. The offspring distribution was less dispersed in wave 4 (k = 0.32; 95% confidence interval (CI) 0.24-0.43) than in wave 2 (k = 0.21 (95% CI 0.13-0.36)). A high proportion of household transmission was observed in wave 4, although the proportion of secondary transmissions generating more than five secondary cases did not vary over time. With this decreased variation, the effectiveness of risk group-focused interventions may be diminished.

Surveillance and identification of clusters of healthcare workers with coronavirus disease 2019 (COVID-19): Multidimensional interventions at a comprehensive cancer center

BACKGROUND

Cases of novel coronavirus disease 2019 (COVID-19) were first reported in Wuhan, China, in December 2019. In this report, we describe 3 clusters of COVID-19 infections among healthcare workers (HCWs), not associated with patient exposure, and the interventions undertaken to halt ongoing exposure and transmission at our cancer center.

METHODS

A cluster of cases was defined as 2 or more cases of severe acute respiratory coronavirus virus 2 (SARS-CoV-2)-positive COVID-19 among HCWs who work in the same unit area at the same time. Cases were identified by real-time reverse transcription polymerase chain reaction testing. Contact tracing, facility observations, and infection prevention assessments were performed to investigate the 3 clusters between March 1 and April 30, 2020, with subsequent implementation of containment strategies.

RESULTS

The initial cluster involved HCWs from an ancillary services unit, with contacts traced back to a gathering in a break room in which 1 employee was symptomatic, although not yet diagnosed with COVID-19, with subsequent transmission to 7 employees. The second cluster involved 4 employees and was community related. The third cluster involved only 2 employees with possible transmission while working in the same office at the same time. A step-up approach was implemented to control the spread of infection among employees, including universal masking, enhanced cleaning, increase awareness, and surveillance testing. No nosocomial transmission to patients transpired.

CONCLUSIONS

To our knowledge, this is the first report of a hospital-based cluster of COVID-19 infections among HCWs in a cancer hospital describing our steps to mitigate further transmission.

The epidemicity index of recurrent SARS-CoV-2 infections

Several indices can predict the long-term fate of emerging infectious diseases and the effect of their containment measures, including a variety of reproduction numbers (e.g. [Formula: see text]). Other indices evaluate the potential for transient increases of epidemics eventually doomed to disappearance, based on generalized reactivity analysis. They identify conditions for perturbations to a stable disease-free equilibrium ([Formula: see text]) to grow, possibly causing significant damage. Here, we introduce the epidemicity index e0, a threshold-type indicator: if e0 > 0, initial foci may cause infection peaks even if [Formula: see text]. Therefore, effective containment measures should achieve a negative epidemicity index. We use spatially explicit models to rank containment measures for projected evolutions of the ongoing pandemic in Italy. There, we show that, while the effective reproduction number was below one for a sizable timespan, epidemicity remained positive, allowing recurrent infection flare-ups well before the major epidemic rebounding observed in the fall.

Controlling emerging zoonoses at the animal-human interface

BACKGROUND

For many emerging or re-emerging pathogens, cases in humans arise from a mixture of introductions (via zoonotic spillover from animal reservoirs or geographic spillover from endemic regions) and secondary human-to-human transmission. Interventions aiming to reduce incidence of these infections can be focused on preventing spillover or reducing human-to-human transmission, or sometimes both at once, and typically are governed by resource constraints that require policymakers to make choices. Despite increasing emphasis on using mathematical models to inform disease control policies, little attention has been paid to guiding rational disease control at the animal-human interface.

METHODS

We introduce a modeling framework to analyze the impacts of different disease control policies, focusing on pathogens exhibiting subcritical transmission among humans (i.e. pathogens that cannot establish sustained human-to-human transmission). We quantify the relative effectiveness of measures to reduce spillover (e.g. reducing contact with animal hosts), human-to-human transmission (e.g. case isolation), or both at once (e.g. vaccination), across a range of epidemiological contexts.

RESULTS

We provide guidelines for choosing which mode of control to prioritize in different epidemiological scenarios and considering different levels of resource and relative costs. We contextualize our analysis with current zoonotic pathogens and other subcritical pathogens, such as post-elimination measles, and control policies that have been applied.

CONCLUSIONS

Our work provides a model-based, theoretical foundation to understand and guide policy for subcritical zoonoses, integrating across disciplinary and species boundaries in a manner consistent with One Health principles.

Real-time monitoring the transmission potential of COVID-19 in Singapore, March 2020

BACKGROUND

As of March 31, 2020, the ongoing COVID-19 epidemic that started in China in December 2019 is now generating local transmission around the world. The geographic heterogeneity and associated intervention strategies highlight the need to monitor in real time the transmission potential of COVID-19. Singapore provides a unique case example for monitoring transmission, as there have been multiple disease clusters, yet transmission remains relatively continued.

METHODS

Here we estimate the effective reproduction number, Rt, of COVID-19 in Singapore from the publicly available daily case series of imported and autochthonous cases by date of symptoms onset, after adjusting the local cases for reporting delays as of March 17, 2020. We also derive the reproduction number from the distribution of cluster sizes using a branching process analysis that accounts for truncation of case counts.

RESULTS

The local incidence curve displays sub-exponential growth dynamics, with the reproduction number following a declining trend and reaching an estimate at 0.7 (95% CI 0.3, 1.0) during the first transmission wave by February 14, 2020, while the overall R based on the cluster size distribution as of March 17, 2020, was estimated at 0.6 (95% CI 0.4, 1.02). The overall mean reporting delay was estimated at 6.4 days (95% CI 5.8, 6.9), but it was shorter among imported cases compared to local cases (mean 4.3 vs. 7.6 days, Wilcoxon test, p < 0.001).

CONCLUSION

The trajectory of the reproduction number in Singapore underscores the significant effects of successful containment efforts in Singapore, but it also suggests the need to sustain social distancing and active case finding efforts to stomp out all active chains of transmission.

Real-time monitoring the transmission potential of COVID-19 in Singapore, March 2020

Background

As of March 31, 2020 the ongoing COVID-19 epidemic that started in China in December 2019 is now generating local transmission around the world. The geographic heterogeneity and associated intervention strategies highlight the need to monitor in real time the transmission potential of COVID-19. Singapore provides a unique case example for monitoring transmission, as there have been multiple disease clusters, yet transmission remains relatively continued.

Methods

Here we estimate the effective reproduction number, Rt, of COVID-19 in Singapore from the publicly available daily case series of imported and autochthonous cases by date of symptoms onset, after adjusting the local cases for reporting delays as of March 17, 2020. We also derive the reproduction number from the distribution of cluster sizes using a branching process analysis that accounts for truncation of case counts.

Results

The local incidence curve displays sub-exponential growth dynamics, with the reproduction number following a declining trend and reaching an estimate at 0.7 (95% CI: 0.3, 1.0) during the first transmission wave by February 14, 2020 while the overall R based on the cluster size distribution as of March 17, 2020 was estimated at 0.6 (95% CI: 0.4, 1.02). The overall mean reporting delay was estimated at 6.4 days (95% CI: 5.8, 6.9), but it was shorter among imported cases compared to local cases (mean 4.3 vs. 7.6 days, Wilcoxon test, p<0.001).

Conclusion

The trajectory of the reproduction number in Singapore underscores the significant effects of successful containment efforts in Singapore, but it also suggests the need to sustain social distancing and active case finding efforts to stomp out all active chains of transmission.

Quantifying the risk of Zika virus spread in Asia during the 2015-16 epidemic in Latin America and the Caribbean: A modeling study

Background

No large-scale Zika epidemic has been observed to date in Southeast Asia following the 2015-16 Latin American and the Caribbean epidemic. One hypothesis is Southeast Asian populations’ partial immunity to Zika.

Method

We estimated the two conditions for a Zika outbreak emergence in Southeast Asia: (i) the risk of Zika introduction from Latin America and the Caribbean and, (ii) the risk of autochthonous transmission under varying assumptions on population immunity. We also validated the model used to estimate the risk of introduction by comparing the estimated number of Zika seeds introduced into the United States with case counts reported by the Centers for Disease Control and Prevention (CDC).

Results

There was good agreement between our estimates and case counts reported by the CDC. We thus applied the model to Southeast Asia and estimated that, on average, 1–10 seeds were introduced into Indonesia, Malaysia, the Philippines, Singapore, Thailand and Vietnam. We also found increasing population immunity levels from 0 to 90% reduced probability of autochthonous transmission by 40% and increasing individual variation in transmission further reduced the outbreak probability.

Conclusions

Population immunity, combined with heterogeneity in transmission, can explain why no large-scale outbreak was observed in Southeast Asia during the 2015-16 epidemic.

Measles transmission during a large outbreak in California

A large measles outbreak in 2014–2015, linked to Disneyland theme parks, attracted international attention, and led to changes in California vaccine policy. We use dates of symptom onset and known epidemic links for California cases in this outbreak to estimate time-varying transmission in the outbreak, and to estimate generation membership of cases probabilistically. We find that transmission declined significantly during the course of the outbreak (p = 0.012), despite also finding that estimates of transmission rate by day or by generation can overestimate temporal decline. We additionally find that the outbreak size and duration alone are sufficient in this case to distinguish temporal decline from time-invariant transmission (p = 0.014). As use of a single large outbreak can lead to underestimates of immunity, however, we urge caution in interpretation of quantities estimated from this outbreak alone. Further research is needed to distinguish causes of temporal decline in transmission rates.

Genotype-Specific Measles Transmissibility: A Branching Process Analysis

Background

Substantial heterogeneity in measles outbreak sizes may be due to genotype-specific transmissibility. Using a branching process analysis, we characterize differences in measles transmission by estimating the association between genotype and the reproduction number R among postelimination California measles cases during 2000-2015 (400 cases, 165 outbreaks).

Methods

Assuming a negative binomial secondary case distribution, we fit a branching process model to the distribution of outbreak sizes using maximum likelihood and estimated the reproduction number R for a multigenotype model.

Results

Genotype B3 is found to be significantly more transmissible than other genotypes (P = .01) with an R of 0.64 (95% confidence interval [CI], .48-.71), while the R for all other genotypes combined is 0.43 (95% CI, .28-.54). This result is robust to excluding the 2014-2015 outbreak linked to Disneyland theme parks (referred to as "outbreak A" for conciseness and clarity) (P = .04) and modeling genotype as a random effect (P = .004 including outbreak A and P = .02 excluding outbreak A). This result was not accounted for by season of introduction, age of index case, or vaccination of the index case. The R for outbreaks with a school-aged index case is 0.69 (95% CI, .52-.78), while the R for outbreaks with a non-school-aged index case is 0.28 (95% CI, .19-.35), but this cannot account for differences between genotypes.

Conclusions

Variability in measles transmissibility may have important implications for measles control; the vaccination threshold required for elimination may not be the same for all genotypes or age groups.

Projections of epidemic transmission and estimation of vaccination impact during an ongoing Ebola virus disease outbreak in Northeastern Democratic Republic of Congo, as of Feb. 25, 2019

BACKGROUND

As of February 25, 2019, 875 cases of Ebola virus disease (EVD) were reported in North Kivu and Ituri Provinces, Democratic Republic of Congo. Since the beginning of October 2018, the outbreak has largely shifted into regions in which active armed conflict has occurred, and in which EVD cases and their contacts have been difficult for health workers to reach. We used available data on the current outbreak, with case-count time series from prior outbreaks, to project the short-term and long-term course of the outbreak.

METHODS

For short- and long-term projections, we modeled Ebola virus transmission using a stochastic branching process that assumes gradually quenching transmission rates estimated from past EVD outbreaks, with outbreak trajectories conditioned on agreement with the course of the current outbreak, and with multiple levels of vaccination coverage. We used two regression models to estimate similar projection periods. Short- and long-term projections were estimated using negative binomial autoregression and Theil-Sen regression, respectively. We also used Gott's rule to estimate a baseline minimum-information projection. We then constructed an ensemble of forecasts to be compared and recorded for future evaluation against final outcomes. From August 20, 2018 to February 25, 2019, short-term model projections were validated against known case counts.

RESULTS

During validation of short-term projections, from one week to four weeks, we found models consistently scored higher on shorter-term forecasts. Based on case counts as of February 25, the stochastic model projected a median case count of 933 cases by February 18 (95% prediction interval: 872-1054) and 955 cases by March 4 (95% prediction interval: 874-1105), while the auto-regression model projects median case counts of 889 (95% prediction interval: 876-933) and 898 (95% prediction interval: 877-983) cases for those dates, respectively. Projected median final counts range from 953 to 1,749. Although the outbreak is already larger than all past Ebola outbreaks other than the 2013-2016 outbreak of over 26,000 cases, our models do not project that it is likely to grow to that scale. The stochastic model estimates that vaccination coverage in this outbreak is lower than reported in its trial setting in Sierra Leone.

CONCLUSIONS

Our projections are concentrated in a range up to about 300 cases beyond those already reported. While a catastrophic outbreak is not projected, it is not ruled out, and prevention and vigilance are warranted. Prospective validation of our models in real time allowed us to generate more accurate short-term forecasts, and this process may prove useful for future real-time short-term forecasting. We estimate that transmission rates are higher than would be seen under target levels of 62% coverage due to contact tracing and vaccination, and this model estimate may offer a surrogate indicator for the outbreak response challenges.

Downgrading disease transmission risk estimates using terminal importations

As emerging and re-emerging infectious arboviruses like dengue, chikungunya, and Zika threaten new populations worldwide, officials scramble to assess local severity and transmissibility, with little to no epidemiological history to draw upon. Indirect estimates of risk from vector habitat suitability maps are prone to great uncertainty, while direct estimates from epidemiological data are only possible after cases accumulate and, given environmental constraints on arbovirus transmission, cannot be widely generalized beyond the focal region. Combining these complementary methods, we use disease importation and transmission data to improve the accuracy and precision of a priori ecological risk estimates. We demonstrate this approach by estimating the spatiotemporal risks of Zika virus transmission throughout Texas, a high-risk region in the southern United States. Our estimates are, on average, 80% lower than published ecological estimates-with only six of 254 Texas counties deemed capable of sustaining a Zika epidemic-and they are consistent with the number of autochthonous cases detected in 2017. Importantly our method provides a framework for model comparison, as our mechanistic understanding of arbovirus transmission continues to improve. Real-time updating of prior risk estimates as importations and outbreaks arise can thereby provide critical, early insight into local transmission risks as emerging arboviruses expand their global reach.

Sub- or supercritical transmissibilities in a finite disease outbreak: Symmetry in outbreak properties of a disease conditioned on extinction

This work is concerned with the transmissibility of a disease, on observation of an outbreak of limited size. When such an outbreak occurs, an accurate estimate of the transmissibility of the responsible pathogen is essential for an appropriate response to future outbreaks. Transmissibility is usually characterised in terms of the reproduction number, R, which is the mean number of new cases of infection produced by a single infectious individual. A subcritical reproduction number (R < 1) guarantees that an outbreak will eventually die out of its own accord. By contrast, a supercritical reproduction number (R > 1) does not guarantee spread of the disease, since even with appreciable transmissibility, an outbreak may become extinct due to stochastic effects associated with a small number of infected individuals. Once the number of infectious individuals is conditioned on extinction, we show that an exact symmetry of the underlying theory ensures two distinct values of R, one larger than unity, the other smaller than unity, for which all outbreak properties are identical, with no signature of difference. Therefore a disease with a subcritical R, or its supercritical counterpart, when conditioned on extinction, have, for a given outbreak, identical individual likelihoods. In the full likelihood, this symmetry is lost, since the individual likelihood for a subcritical R is weighted by an extinction probability of unity, but the individual likelihood of a supercritical R is weighted by a sub-unity extinction probability. However, the inference can still benefit from the underlying symmetry, since it yields a mapping of all supercritical reproduction numbers onto the subcritical domain (R < 1), thereby speeding up evaluation of the likelihood profile. The symmetry holds in the standard situation, where the distribution of secondary cases is Poisson, as well as where this distribution has a negative binomial form and super-spreading can occur.

Projections of Ebola outbreak size and duration with and without vaccine use in Équateur, Democratic Republic of Congo, as of May 27, 2018

As of May 27, 2018, 6 suspected, 13 probable and 35 confirmed cases of Ebola virus disease (EVD) had been reported in Équateur Province, Democratic Republic of Congo. We used reported case counts and time series from prior outbreaks to estimate the total outbreak size and duration with and without vaccine use. We modeled Ebola virus transmission using a stochastic branching process model that included reproduction numbers from past Ebola outbreaks and a particle filtering method to generate a probabilistic projection of the outbreak size and duration conditioned on its reported trajectory to date; modeled using high (62%), low (44%), and zero (0%) estimates of vaccination coverage (after deployment). Additionally, we used the time series for 18 prior Ebola outbreaks from 1976 to 2016 to parameterize the Thiel-Sen regression model predicting the outbreak size from the number of observed cases from April 4 to May 27. We used these techniques on probable and confirmed case counts with and without inclusion of suspected cases. Probabilistic projections were scored against the actual outbreak size of 54 EVD cases, using a log-likelihood score. With the stochastic model, using high, low, and zero estimates of vaccination coverage, the median outbreak sizes for probable and confirmed cases were 82 cases (95% prediction interval [PI]: 55, 156), 104 cases (95% PI: 58, 271), and 213 cases (95% PI: 64, 1450), respectively. With the Thiel-Sen regression model, the median outbreak size was estimated to be 65.0 probable and confirmed cases (95% PI: 48.8, 119.7). Among our three mathematical models, the stochastic model with suspected cases and high vaccine coverage predicted total outbreak sizes closest to the true outcome. Relatively simple mathematical models updated in real time may inform outbreak response teams with projections of total outbreak size and duration.

Fogarty International Center collaborative networks in infectious disease modeling: Lessons learnt in research and capacity building

Due to a combination of ecological, political, and demographic factors, the emergence of novel pathogens has been increasingly observed in animals and humans in recent decades. Enhancing global capacity to study and interpret infectious disease surveillance data, and to develop data-driven computational models to guide policy, represents one of the most cost-effective, and yet overlooked, ways to prepare for the next pandemic. Epidemiological and behavioral data from recent pandemics and historic scourges have provided rich opportunities for validation of computational models, while new sequencing technologies and the 'big data' revolution present new tools for studying the epidemiology of outbreaks in real time. For the past two decades, the Division of International Epidemiology and Population Studies (DIEPS) of the NIH Fogarty International Center has spearheaded two synergistic programs to better understand and devise control strategies for global infectious disease threats. The Multinational Influenza Seasonal Mortality Study (MISMS) has strengthened global capacity to study the epidemiology and evolutionary dynamics of influenza viruses in 80 countries by organizing international research activities and training workshops. The Research and Policy in Infectious Disease Dynamics (RAPIDD) program and its precursor activities has established a network of global experts in infectious disease modeling operating at the research-policy interface, with collaborators in 78 countries. These activities have provided evidence-based recommendations for disease control, including during large-scale outbreaks of pandemic influenza, Ebola and Zika virus. Together, these programs have coordinated international collaborative networks to advance the study of emerging disease threats and the field of computational epidemic modeling. A global community of researchers and policy-makers have used the tools and trainings developed by these programs to interpret infectious disease patterns in their countries, understand modeling concepts, and inform control policies. Here we reflect on the scientific achievements and lessons learnt from these programs (h-index = 106 for RAPIDD and 79 for MISMS), including the identification of outstanding researchers and fellows; funding flexibility for timely research workshops and working groups (particularly relative to more traditional investigator-based grant programs); emphasis on group activities such as large-scale modeling reviews, model comparisons, forecasting challenges and special journal issues; strong quality control with a light touch on outputs; and prominence of training, data-sharing, and joint publications.

How Modelling Can Enhance the Analysis of Imperfect Epidemic Data

Mathematical models play an increasingly important role in our understanding of the transmission and control of infectious diseases. Here, we present concrete examples illustrating how mathematical models, paired with rigorous statistical methods, are used to parse data of different levels of detail and breadth and estimate key epidemiological parameters (e.g., transmission and its determinants, severity, impact of interventions, drivers of epidemic dynamics) even when these parameters are not directly measurable, when data are limited, and when the epidemic process is only partially observed. Finally, we assess the hurdles to be taken to increase availability and applicability of these approaches in an effort to ultimately enhance their public health impact.

Many data can be used to estimate the transmission potential of a pathogen, including descriptions of the transmission chains, human cluster sizes, sources of infection, and epidemic curves.

An important agenda in public health is understanding the impact of control methods. However, the dynamic nature of epidemics makes this task challenging. Models can disentangle the natural course of outbreaks from the effect of external factors.

In the absence of reliable surveillance data, models can reconstruct epidemic history by combining age-specific seroprevalence data with an understanding of the natural history of infection.

Mechanisms of immunity are hard to observe at an individual level, yet they affect population-level dynamics. Models can tease out such signatures.

Morbidity and mortality can be difficult to estimate when many infections are unobserved and severe infections are reported more often. Models can be used to correct for under-reporting and selection bias.

Estimation of the Basic Reproduction Number and Vaccination Coverage of Influenza in the United States (2017-18)

BACKGROUND

Determining the epidemic threshold parameter helps health providers calculate the coverage while guiding them in planning the process of vaccination strategy. Since the trend and mechanism of influenza is very similar in different countries, we planned a study with the mentioned goal by using data of US from 2017 to 2018.

STUDY DESIGN

A secondary study.

METHODS

R0 and corresponding vaccination coverage are estimated using the national and state-level data of the US from the 40th in 2017 to the 5th week in 2018. Four methods maximum likelihood (ML), exponential growth (EG), time-dependent reproduction numbers (TD), and sequential Bayesian (SB) are used to calculate minimum vaccination coverage. The gamma distribution is considered as the distribution and the generation of time.

RESULTS

The peak of epidemy in most states has occurred in the 15th week after the beginning of the epidemics. The generation time obey the Gamma distribution with mean and standard deviation of 3.6 and 1.6, respectively, was utilized for the generation time. The R0 (vaccination coverage) equaled 1.94 (48.4%), 1.80 (44.4%), 3.06 (67.3%), and 2.11 (52.6%) for EG, ML, SB, and TD methods at the national level, respectively.

CONCLUSION

The R0 estimations were in the range of 1.8-3.06, indicating that an epidemic has occurred in the US (R0>1). Thus, it is required to vaccinate at least 44.4% to 67.3% to prevent the next epidemics of influenza. The findings of this study assist futures studies to apply disease control by vaccination strategies in order to prevent a national disaster.

The distribution of district-level leprosy incidence in India is geometric-stable, consistent with subcriticality

Mathematical models predict that the community-level incidence of a controlled infectious disease across a region approaches a geometric distribution. This could hold over larger regions, if new cases remain proportional to existing cases. Leprosy has been disappearing for centuries, making an excellent candidate for testing this hypothesis. Here, we show the annual new case detection rate of leprosy in Indian districts to be consistent with a geometric distribution. For 2008-2013, goodness-of-fit testing was unable to exclude the geometric, and the shape parameter of the best fit negative binomial distribution was close to unity (0.95, 95% CI 0.87-1.03). Ramifications include that a district-level cross-sectional survey may reveal whether an infectious disease is headed towards elimination, that apparent outliers are expected and not necessarily representative of program failure, and that proportion 1/e of a small geographical unit may not meet a control threshold even when a larger area has.

Spatial clustering of measles vaccination coverage among children in sub-Saharan Africa

Background

During the past two decades, vaccination programs have greatly reduced global morbidity and mortality due to measles, but recently this progress has stalled. Even in countries that report high vaccination coverage rates, transmission has continued, particularly in spatially clustered subpopulations with low vaccination coverage.

Methods

We examined the spatial heterogeneity of measles vaccination coverage among children aged 12–23 months in ten Sub-Saharan African countries. We used the Anselin Local Moran’s I to estimate clustering of vaccination coverage based on data from Demographic and Health Surveys conducted between 2008 and 2013. We also examined the role of sociodemographic factors to explain clustering of low vaccination.

Results

We detected 477 spatial clusters with low vaccination coverage, many of which were located in countries with relatively high nationwide vaccination coverage rates such as Zambia and Malawi. We also found clusters in border areas with transient populations. Clustering of low vaccination coverage was related to low health education and limited access to healthcare.

Conclusions

Systematically monitoring clustered populations with low vaccination coverage can inform supplemental immunization activities and strengthen elimination programs. Metrics of spatial heterogeneity should be used routinely to determine the success of immunization programs and the risk of disease persistence.

Assessing the danger of self-sustained HIV epidemics in heterosexuals by population based phylogenetic cluster analysis

Assessing the danger of transition of HIV transmission from a concentrated to a generalized epidemic is of major importance for public health. In this study, we develop a phylogeny-based statistical approach to address this question. As a case study, we use this to investigate the trends and determinants of HIV transmission among Swiss heterosexuals. We extract the corresponding transmission clusters from a phylogenetic tree. To capture the incomplete sampling, the delayed introduction of imported infections to Switzerland, and potential factors associated with basic reproductive number R0, we extend the branching process model to infer transmission parameters. Overall, the R0 is estimated to be 0.44 (95%-confidence interval 0.42—0.46) and it is decreasing by 11% per 10 years (4%—17%). Our findings indicate rather diminishing HIV transmission among Swiss heterosexuals far below the epidemic threshold. Generally, our approach allows to assess the danger of self-sustained epidemics from any viral sequence data.

In epidemiology, the “basic reproductive number” describes how efficiently a disease is transmitted, and represents the average number of new infections that an infected individual causes. If this number is less than one, many people do not infect anybody and hence the transmission chains die out. On the other hand, if the basic reproductive number is larger than one, an infected person infects on average more than one new individual, which leads to the virus or bacteria spreading in a self-sustained way.

Turk et al. have now developed a method to estimate the basic reproductive number using the genetic sequences of the virus or bacteria, and have used it to investigate how efficiently HIV spreads among Swiss heterosexuals. The results show that the basic reproductive number of HIV in this group is far below the critical value of one and that over the last years this number has been decreasing. Furthermore, the basic reproductive number differs for different subtypes of the HIV virus, indicating that the geographical region where the infection was acquired may play a role in transmission. Turk et al. also found that people who are diagnosed later or who often have sex with occasional partners spread the virus more efficiently.

These findings might be helpful for policy makers as they indicate that the risk of self-sustained transmission in this group in Switzerland is small. Furthermore the method allows HIV epidemics to be monitored at high resolution using sequence data, assesses the success of currently implemented preventive measures, and helps to target subgroups who are at higher risk of an infection – for instance, by supporting frequent HIV testing of these people. The method developed by Turk et al. could also prove useful for assessing the danger of other epidemics.

Assessing real-time Zika risk in the United States

Background

Confirmed local transmission of Zika Virus (ZIKV) in Texas and Florida have heightened the need for early and accurate indicators of self-sustaining transmission in high risk areas across the southern United States. Given ZIKV’s low reporting rates and the geographic variability in suitable conditions, a cluster of reported cases may reflect diverse scenarios, ranging from independent introductions to a self-sustaining local epidemic.

Methods

We present a quantitative framework for real-time ZIKV risk assessment that captures uncertainty in case reporting, importations, and vector-human transmission dynamics.

Results

We assessed county-level risk throughout Texas, as of summer 2016, and found that importation risk was concentrated in large metropolitan regions, while sustained ZIKV transmission risk is concentrated in the southeastern counties including the Houston metropolitan region and the Texas-Mexico border (where the sole autochthonous cases have occurred in 2016). We found that counties most likely to detect cases are not necessarily the most likely to experience epidemics, and used our framework to identify triggers to signal the start of an epidemic based on a policymakers propensity for risk.

Conclusions

This framework can inform the strategic timing and spatial allocation of public health resources to combat ZIKV throughout the US, and highlights the need to develop methods to obtain reliable estimates of key epidemiological parameters.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-017-2394-9) contains supplementary material, which is available to authorized users.

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

The devastation caused by periodic measles outbreaks motivated efforts over more than a century to mathematically model measles disease and transmission. Following the identification of rubella, which similarly presents with fever and rash and causes congenital rubella syndrome (CRS) in infants born to women first infected with rubella early in pregnancy, modelers also began to characterize rubella disease and transmission. Despite the relatively large literature, no comprehensive review to date provides an overview of dynamic transmission models for measles and rubella developed to support risk and policy analysis. This systematic review of the literature identifies quantitative measles and/or rubella dynamic transmission models and characterizes key insights relevant for prospective modeling efforts. Overall, measles and rubella represent some of the relatively simplest viruses to model due to their ability to impact only humans and the apparent life-long immunity that follows survival of infection and/or protection by vaccination, although complexities arise due to maternal antibodies and heterogeneity in mixing and some models considered potential waning immunity and reinfection. This review finds significant underreporting of measles and rubella infections and widespread recognition of the importance of achieving and maintaining high population immunity to stop and prevent measles and rubella transmission. The significantly lower transmissibility of rubella compared to measles implies that all countries could eliminate rubella and CRS by using combination of measles- and rubella-containing vaccines (MRCVs) as they strive to meet regional measles elimination goals, which leads to the recommendation of changing the formulation of national measles-containing vaccines from measles only to MRCV as the standard of care.

Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting

The development of novel approaches that combine epidemiological and genomic data provides new opportunities to reveal the spatiotemporal dynamics of infectious diseases and determine the processes responsible for their spread and maintenance. Taking advantage of detailed epidemiological time series and viral sequence data from more than 20 years reported by the National Reference Centre for Rabies of Bangui, the capital city of Central African Republic, we used a combination of mathematical modeling and phylogenetic analysis to determine the spatiotemporal dynamics of rabies in domestic dogs as well as the frequency of extinction and introduction events in an African city. We show that although dog rabies virus (RABV) appears to be endemic in Bangui, its epidemiology is in fact shaped by the regular extinction of local chains of transmission coupled with the introduction of new lineages, generating successive waves of spread. Notably, the effective reproduction number during each wave was rarely above the critical value of 1, such that rabies is not self-sustaining in Bangui. In turn, this suggests that rabies at local geographic scales is driven by human-mediated dispersal of RABV among sparsely connected peri-urban and rural areas as opposed to dispersion in a relatively large homogenous urban dog population. This combined epidemiological and genomic approach enables development of a comprehensive framework for understanding disease persistence and informing control measures, indicating that control measures are probably best targeted towards areas neighbouring the city that appear as the source of frequent incursions seeding outbreaks in Bangui.

Transmission characteristics of MERS and SARS in the healthcare setting: a comparative study

BACKGROUND

The Middle East respiratory syndrome (MERS) coronavirus has caused recurrent outbreaks in the Arabian Peninsula since 2012. Although MERS has low overall human-to-human transmission potential, there is occasional amplification in the healthcare setting, a pattern reminiscent of the dynamics of the severe acute respiratory syndrome (SARS) outbreaks in 2003. Here we provide a head-to-head comparison of exposure patterns and transmission dynamics of large hospital clusters of MERS and SARS, including the most recent South Korean outbreak of MERS in 2015.

METHODS

To assess the unexpected nature of the recent South Korean nosocomial outbreak of MERS and estimate the probability of future large hospital clusters, we compared exposure and transmission patterns for previously reported hospital clusters of MERS and SARS, based on individual-level data and transmission tree information. We carried out simulations of nosocomial outbreaks of MERS and SARS using branching process models rooted in transmission tree data, and inferred the probability and characteristics of large outbreaks.

RESULTS

A significant fraction of MERS cases were linked to the healthcare setting, ranging from 43.5 % for the nosocomial outbreak in Jeddah, Saudi Arabia, in 2014 to 100 % for both the outbreak in Al-Hasa, Saudi Arabia, in 2013 and the outbreak in South Korea in 2015. Both MERS and SARS nosocomial outbreaks are characterized by early nosocomial super-spreading events, with the reproduction number dropping below 1 within three to five disease generations. There was a systematic difference in the exposure patterns of MERS and SARS: a majority of MERS cases occurred among patients who sought care in the same facilities as the index case, whereas there was a greater concentration of SARS cases among healthcare workers throughout the outbreak. Exposure patterns differed slightly by disease generation, however, especially for SARS. Moreover, the distributions of secondary cases per single primary case varied highly across individual hospital outbreaks (Kruskal-Wallis test; P < 0.0001), with significantly higher transmission heterogeneity in the distribution of secondary cases for MERS than SARS. Simulations indicate a 2-fold higher probability of occurrence of large outbreaks (>100 cases) for SARS than MERS (2 % versus 1 %); however, owing to higher transmission heterogeneity, the largest outbreaks of MERS are characterized by sharper incidence peaks. The probability of occurrence of MERS outbreaks larger than the South Korean cluster (n = 186) is of the order of 1 %.

CONCLUSIONS

Our study suggests that the South Korean outbreak followed a similar progression to previously described hospital clusters involving coronaviruses, with early super-spreading events generating a disproportionately large number of secondary infections, and the transmission potential diminishing greatly in subsequent generations. Differences in relative exposure patterns and transmission heterogeneity of MERS and SARS could point to changes in hospital practices since 2003 or differences in transmission mechanisms of these coronaviruses.

Assessing Measles Transmission in the United States Following a Large Outbreak in California

The recent increase in measles cases in California may raise questions regarding the continuing success of measles control. To determine whether the dynamics of measles is qualitatively different in comparison to previous years, we assess whether the 2014-2015 measles outbreak associated with an Anaheim theme park is consistent with subcriticality by calculating maximum-likelihood estimates for the effective reproduction numbe given this year’s outbreak, using the Galton-Watson branching process model. We find that the dynamics after the initial transmission event are consistent with prior transmission, but does not exclude the possibilty that the effective reproduction number has increased.

Characterizing the transmission potential of zoonotic infections from minor outbreaks

The transmission potential of a novel infection depends on both the inherent transmissibility of a pathogen, and the level of susceptibility in the host population. However, distinguishing between these pathogen- and population-specific properties typically requires detailed serological studies, which are rarely available in the early stages of an outbreak. Using a simple transmission model that incorporates age-stratified social mixing patterns, we present a novel method for characterizing the transmission potential of subcritical infections, which have effective reproduction number R<1, from readily available data on the size of outbreaks. We show that the model can identify the extent to which outbreaks are driven by inherent pathogen transmissibility and pre-existing population immunity, and can generate unbiased estimates of the effective reproduction number. Applying the method to real-life infections, we obtained accurate estimates for the degree of age-specific immunity against monkeypox, influenza A(H5N1) and A(H7N9), and refined existing estimates of the reproduction number. Our results also suggest minimal pre-existing immunity to MERS-CoV in humans. The approach we describe can therefore provide crucial information about novel infections before serological surveys and other detailed analyses are available. The methods would also be applicable to data stratified by factors such as profession or location, which would make it possible to measure the transmission potential of emerging infections in a wide range of settings.

The transmission potential of a new infection depends on both the transmissibility of the pathogen and the level of immunity in the host population. However, it can be difficult to measure these properties if there are limited experimental studies of population immunity. By incorporating social contact patterns into a mathematical model of disease transmission, we show that it is possible to estimate both pathogen transmissibility and pre-existing immunity from available data on the size of outbreaks. When an infection does not transmit efficiently between humans, estimates often have to be made using case data from a limited number of small outbreaks. We find that, even with limited data, our technique can accurately evaluate the transmission potential of ‘stuttering’ chains of infection. We use the method to characterise transmission of four real infections: monkeypox, influenza A(H5N1) and A(H7N9) and MERS-CoV.

Modeling infectious disease dynamics in the complex landscape of global health

Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health.

Five challenges for stochastic epidemic models involving global transmission

The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing)? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?

Synthesizing data and models for the spread of MERS-CoV, 2013: key role of index cases and hospital transmission

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Transmission models for the MERS-CoV outbreak during April–October 2013.

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MERS-CoV transmission models with index and secondary cases.

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MERS-CoV transmission models with community and hospital compartments.

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Calibration of MERS-CoV transmission models using MCMC methods.

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Data indicate a strong support for R  < 1 in the first stage of the outbreak in 2013.

The outbreak of Middle East respiratory syndrome coronavirus (MERS-CoV) has caused 209 deaths and 699 laboratory-confirmed cases in the Arabian Peninsula as of June 11, 2014. Preparedness efforts are hampered by considerable uncertainty about the nature and intensity of human-to-human transmission, with previous reproduction number estimates ranging from 0.4 to 1.5. Here we synthesize epidemiological data and transmission models for the MERS-CoV outbreak during April–October 2013 to resolve uncertainties in epidemic risk, while considering the impact of observation bias. We match the progression of MERS-CoV cases in 2013 to a dynamic transmission model that incorporates community and hospital compartments, and distinguishes transmission by zoonotic (index) cases and secondary cases. When observation bias is assumed to account for the fact that all reported zoonotic cases are severe, but only ∼57% of secondary cases are symptomatic, the average reproduction number of MERS-CoV is estimated to be 0.45 (95% CI:0.29–0.61). Alternatively, if these epidemiological observations are taken at face value, index cases are estimated to transmit substantially more effectively than secondary cases, (R_i = 0.84 (0.58-1.20) vs R_s = 0.36 (0.24–0.51)). In both scenarios the relative contribution of hospital-based transmission is over four times higher than that of community transmission, indicating that disease control should be focused on hospitalized patients.

Adjusting previously published estimates for observation bias confirms a strong support for the average R < 1 in the first stage of the outbreak in 2013 and thus, transmissibility of secondary cases of MERS-CoV remained well below the epidemic threshold. More information on the observation process is needed to clarify whether MERS-CoV is intrinsically weakly transmissible between people or whether existing control measures have contributed meaningfully to reducing the transmissibility of secondary cases. Our results could help evaluate the progression of MERS-CoV in recent months in response to changes in disease surveillance, control interventions, or viral adaptation.

Detecting differential transmissibilities that affect the size of self-limited outbreaks

Our ability to respond appropriately to infectious diseases is enhanced by identifying differences in the potential for transmitting infection between individuals. Here, we identify epidemiological traits of self-limited infections (i.e. infections with an effective reproduction number satisfying [0 < R eff < 1) that correlate with transmissibility. Our analysis is based on a branching process model that permits statistical comparison of both the strength and heterogeneity of transmission for two distinct types of cases. Our approach provides insight into a variety of scenarios, including the transmission of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in the Arabian peninsula, measles in North America, pre-eradication smallpox in Europe, and human monkeypox in the Democratic Republic of the Congo. When applied to chain size data for MERS-CoV transmission before 2014, our method indicates that despite an apparent trend towards improved control, there is not enough statistical evidence to indicate that R eff has declined with time. Meanwhile, chain size data for measles in the United States and Canada reveal statistically significant geographic variation in R eff, suggesting that the timing and coverage of national vaccination programs, as well as contact tracing procedures, may shape the size distribution of observed infection clusters. Infection source data for smallpox suggests that primary cases transmitted more than secondary cases, and provides a quantitative assessment of the effectiveness of control interventions. Human monkeypox, on the other hand, does not show evidence of differential transmission between animals in contact with humans, primary cases, or secondary cases, which assuages the concern that social mixing can amplify transmission by secondary cases. Lastly, we evaluate surveillance requirements for detecting a change in the human-to-human transmission of monkeypox since the cessation of cross-protective smallpox vaccination. Our studies lay the foundation for future investigations regarding how infection source, vaccination status or other putative transmissibility traits may affect self-limited transmission.

Nine challenges in modelling the emergence of novel pathogens

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We summarize key challenges in modeling the emergence of novel infectious agents.

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We focus on connections to data, including epidemiologic and genetic data.

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Zoonoses are emphasized, because they are the source of most new human pathogens.

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Challenges span reservoir dynamics, cross-species spillover, and outbreak dynamics.

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Estimation of fatality rates and overall risk assessment are also addressed.

Studying the emergence of novel infectious agents involves many processes spanning host species, spatial scales, and scientific disciplines. Mathematical models play an essential role in combining insights from these investigations and drawing robust inferences from field and experimental data. We describe nine challenges in modelling the emergence of novel pathogens, emphasizing the interface between models and data.

Identifying postelimination trends for the introduction and transmissibility of measles in the United States

The continued elimination of measles requires accurate assessment of its epidemiology and a critical evaluation of how its incidence is changing with time. National surveillance of measles in the United States between 2001 and 2011 provides data on the number of measles introductions and the size of the resulting transmission chains. These data allow inference of the effective reproduction number, Reff, and the probability of an outbreak occurring. Our estimate of 0.52 (95% confidence interval: 0.44, 0.60) for Reff is smaller than prior results. Our findings are relatively insensitive to the possibility that as few as 75% of cases were detected. Although we confirm that measles remains eliminated, we identify an increasing trend in the number of measles cases with time. We show that this trend is likely attributable to an increase in the number of disease introductions rather than a change in the transmissibility of measles. However, we find that transmissibility may increase substantially if vaccine coverage drops by as little as 1%. Our general approach of characterizing the case burden of measles is applicable to the epidemiologic assessment of other weakly transmitting or vaccine-controlled pathogens that are either at risk of emerging or on the brink of elimination.