Inference of R(0) and transmission heterogeneity from the size distribution of stuttering chains

Emergence failure of early epidemics: A mathematical modeling approach

Epidemic or pathogen emergence is the phenomenon by which a poorly transmissible pathogen finds its evolutionary pathway to become a mutant that can cause an epidemic. Many mathematical models of pathogen emergence rely on branching processes. Here, we discuss pathogen emergence using Markov chains, for a more tractable analysis, generalizing previous work by Kendall and Bartlett about disease invasion. We discuss the probability of emergence failure for early epidemics, when the number of infected individuals is small and the number of the susceptible individuals is virtually unlimited. Our formalism addresses both directly transmitted and vector-borne diseases, in the cases where the original pathogen is 1) one step-mutation away from the epidemic strain, and 2) undergoing a long chain of neutral mutations that do not change the epidemiology. We obtain analytic results for the probabilities of emergence failure and two features transcending the transmission mechanism. First, the reproduction number of the original pathogen is determinant for the probability of pathogen emergence, more important than the mutation rate or the transmissibility of the emerged pathogen. Second, the probability of mutation within infected individuals must be sufficiently high for the pathogen undergoing neutral mutations to start an epidemic, the mutation threshold depending again on the basic reproduction number of the original pathogen. Finally, we discuss the parameterization of models of pathogen emergence, using SARS-CoV1 as an example of zoonotic emergence and HIV as an example for the emergence of drug resistance. We also discuss assumptions of our models and implications for epidemiology.

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.

A beta-Poisson model for infectious disease transmission

Outbreaks of emerging and zoonotic infections represent a substantial threat to human health and well-being. These outbreaks tend to be characterised by highly stochastic transmission dynamics with intense variation in transmission potential between cases. The negative binomial distribution is commonly used as a model for transmission in the early stages of an epidemic as it has a natural interpretation as the convolution of a Poisson contact process and a gamma-distributed infectivity. In this study we expand upon the negative binomial model by introducing a beta-Poisson mixture model in which infectious individuals make contacts at the points of a Poisson process and then transmit infection along these contacts with a beta-distributed probability. We show that the negative binomial distribution is a limit case of this model, as is the zero-inflated Poisson distribution obtained by combining a Poisson-distributed contact process with an additional failure probability. We assess the beta-Poisson model's applicability by fitting it to secondary case distributions (the distribution of the number of subsequent cases generated by a single case) estimated from outbreaks covering a range of pathogens and geographical settings. We find that while the beta-Poisson mixture can achieve a closer to fit to data than the negative binomial distribution, it is consistently outperformed by the negative binomial in terms of Akaike Information Criterion, making it a suboptimal choice on parsimonious grounds. The beta-Poisson performs similarly to the negative binomial model in its ability to capture features of the secondary case distribution such as overdispersion, prevalence of superspreaders, and the probability of a case generating zero subsequent cases. Despite this possible shortcoming, the beta-Poisson distribution may still be of interest in the context of intervention modelling since its structure allows for the simulation of measures which change contact structures while leaving individual-level infectivity unchanged, and vice-versa.

Early underdetected dissemination across countries followed by extensive local transmission propelled 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.

Time-varying overdispersion of SARS-CoV-2 transmission during the periods when different variants of concern were circulating in Japan

Japan has implemented a cluster-based approach for coronavirus disease 2019 (COVID-19) from the pandemic's beginning based on the transmission heterogeneity (overdispersion) of severe acute respiratory coronavirus 2 (SARS-CoV-2). However, studies analyzing overdispersion of transmission among new variants of concerns (VOCs), especially for Omicron, were limited. Thus, we aimed to clarify how the transmission heterogeneity has changed with the emergence of VOCs (Alpha, Delta, and Omicron) using detailed contact tracing data in Yamagata Prefecture, Japan. We estimated the time-varying dispersion parameter ([Formula: see text]) by fitting a negative binomial distribution for each transmission generation. Our results showed that even after the emergence of VOCs, there was transmission heterogeneity of SARS-CoV-2, with changes in [Formula: see text] during each wave. Continuous monitoring of transmission dynamics is vital for implementing appropriate measures. However, a feasible and sustainable epidemiological analysis system should be established to make this possible.

Measles virus transmission patterns and public health responses during Operation Allies Welcome: a descriptive epidemiological study

BACKGROUND

On Aug 29, 2021, Operation Allies Welcome (OAW) was established to support the resettlement of more than 80 000 Afghan evacuees in the USA. After identification of measles among evacuees, incoming evacuee flights were temporarily paused, and mass measles vaccination of evacuees aged 6 months or older was introduced domestically and overseas, with a 21-day quarantine period after vaccination. We aimed to evaluate patterns of measles virus transmission during this outbreak and the impact of control measures.

METHODS

We conducted a measles outbreak investigation among Afghan evacuees who were resettled in the USA as part of OAW. Patients with measles were defined as individuals with an acute febrile rash illness between Aug 29, 2021, and Nov 26, 2021, and either laboratory confirmation of infection or epidemiological link to a patient with measles with laboratory confirmation. We analysed the demographics and clinical characteristics of patients with measles and used epidemiological information and whole-genome sequencing to track transmission pathways. A transmission model was used to evaluate the effects of vaccination and other interventions.

FINDINGS

47 people with measles (attack rate: 0·65 per 1000 evacuees) were reported in six US locations housing evacuees in four states. The median age of patients was 1 year (range 0-26); 33 (70%) were younger than 5 years. The age distribution shifted during the outbreak towards infants younger than 12 months. 20 (43%) patients with wild-type measles virus had rash onset after vaccination. No fatalities or community spread were identified, nor further importations after flight resumption. In a non-intervention scenario, transmission models estimated that a median of 5506 cases (IQR 10-5626) could have occurred. Infection clusters based on epidemiological criteria could be delineated into smaller clusters using phylogenetic analyses; however, sequences with few substitution count differences did not always indicate single lines of transmission.

INTERPRETATION

Implementation of control measures limited measles transmission during OAW. Our findings highlight the importance of integration between epidemiological and genetic information in discerning between individual lines of transmission in an elimination setting.

FUNDING

US Centers for Disease Control and Prevention.

Heterogeneity in network structure switches the dominant transmission mode of infectious diseases

Several recent emerging diseases have exhibited both sexual and nonsexual transmission modes (Ebola, Zika, and mpox). In the recent mpox outbreaks, transmission through sexual contacts appears to be the dominant mode of transmission. Motivated by this, we use an SIR-like model to argue that an initially dominant sexual transmission mode can be overtaken by casual transmission at later stages, even if the basic casual reproduction number is less than one. Our results highlight the risk of intervention designs which are informed only by the early dynamics of the disease.

Superspreading, overdispersion and their implications in the SARS-CoV-2 (COVID-19) pandemic: a systematic review and meta-analysis of the literature

BACKGROUND

A recurrent feature of infectious diseases is the observation that different individuals show different levels of secondary transmission. This inter-individual variation in transmission potential is often quantified by the dispersion parameter k. Low values of k indicate a high degree of variability and a greater probability of superspreading events. Understanding k for COVID-19 across contexts can assist policy makers prepare for future pandemics.

METHODS

A literature search following a systematic approach was carried out in PubMed, Embase, Web of Science, Cochrane Library, medRxiv, bioRxiv and arXiv to identify publications containing epidemiological findings on superspreading in COVID-19. Study characteristics, epidemiological data, including estimates for k and R0, and public health recommendations were extracted from relevant records.

RESULTS

The literature search yielded 28 peer-reviewed studies. The mean k estimates ranged from 0.04 to 2.97. Among the 28 studies, 93% reported mean k estimates lower than one, which is considered as marked heterogeneity in inter-individual transmission potential. Recommended control measures were specifically aimed at preventing superspreading events. The combination of forward and backward contact tracing, timely confirmation of cases, rapid case isolation, vaccination and preventive measures were suggested as important components to suppress superspreading.

CONCLUSIONS

Superspreading events were a major feature in the pandemic of SARS-CoV-2. On the one hand, this made outbreaks potentially more explosive but on the other hand also more responsive to public health interventions. Going forward, understanding k is critical for tailoring public health measures to high-risk groups and settings where superspreading events occur.

Monkeypox: a review of epidemiological modelling studies and how modelling has led to mechanistic insight

Human monkeypox (mpox) virus is a viral zoonosis that belongs to the Orthopoxvirus genus of the Poxviridae family, which presents with similar symptoms as those seen in human smallpox patients. Mpox is an increasing concern globally, with over 80,000 cases in non-endemic countries as of December 2022. In this review, we provide a brief history and ecology of mpox, its basic virology, and the key differences in mpox viral fitness traits before and after 2022. We summarize and critique current knowledge from epidemiological mathematical models, within-host models, and between-host transmission models using the One Health approach, where we distinguish between models that focus on immunity from vaccination, geography, climatic variables, as well as animal models. We report various epidemiological parameters, such as the reproduction number, R0, in a condensed format to facilitate comparison between studies. We focus on how mathematical modelling studies have led to novel mechanistic insight into mpox transmission and pathogenesis. As mpox is predicted to lead to further infection peaks in many historically non-endemic countries, mathematical modelling studies of mpox can provide rapid actionable insights into viral dynamics to guide public health measures and mitigation strategies.

Relative role of border restrictions, case finding and contact tracing in controlling SARS-CoV-2 in the presence of undetected transmission: a mathematical modelling study

BACKGROUND

Understanding the overall effectiveness of non-pharmaceutical interventions to control the COVID-19 pandemic and reduce the burden of disease is crucial for future pandemic planning. However, quantifying the effectiveness of specific control measures and the extent of missed infections, in the absence of early large-scale serological surveys or random community testing, has remained challenging.

METHODS

Combining data on notified local COVID-19 cases with known and unknown sources of infections in Singapore with a branching process model, we reconstructed the incidence of missed infections during the early phase of the wild-type SARS-CoV-2 and Delta variant transmission. We then estimated the relative effectiveness of border control measures, case finding and contact tracing when there was no or low vaccine coverage in the population. We compared the risk of ICU admission and death between the wild-type SARS-CoV-2 and the Delta variant in notified cases and all infections.

RESULTS

We estimated strict border control measures were associated with 0.2 (95% credible intervals, CrI 0.04-0.8) missed imported infections per notified case between July and December 2020, a decline from around 1 missed imported infection per notified case in the early phases of the pandemic. Contact tracing was estimated to identify 78% (95% CrI 62-93%) of the secondary infections generated by notified cases before the partial lockdown in Apr 2020, but this declined to 63% (95% CrI 56-71%) during the lockdown and rebounded to 78% (95% CrI 58-94%) during reopening in Jul 2020. The contribution of contact tracing towards overall outbreak control also hinges on ability to find cases with unknown sources of infection: 42% (95% CrI 12-84%) of such cases were found prior to the lockdown; 10% (95% CrI 7-15%) during the lockdown; 47% (95% CrI 17-85%) during reopening, due to increased testing capacity and health-seeking behaviour. We estimated around 63% (95% CrI 49-78%) of the wild-type SARS-CoV-2 infections were undetected during 2020 and around 70% (95% CrI 49-91%) for the Delta variant in 2021.

CONCLUSIONS

Combining models with case linkage data enables evaluation of the effectiveness of different components of outbreak control measures, and provides more reliable situational awareness when some cases are missed. Using such approaches for early identification of the weakest link in containment efforts could help policy makers to better redirect limited resources to strengthen outbreak control.

Quantifying the value of viral genomics when inferring who infected whom in the 2014-16 Ebola virus outbreak in Guinea

Transmission trees can be established through detailed contact histories, statistical or phylogenetic inference, or a combination of methods. Each approach has its limitations, and the extent to which they succeed in revealing a 'true' transmission history remains unclear. In this study, we compared the transmission trees obtained through contact tracing investigations and various inference methods to identify the contribution and value of each approach. We studied eighty-six sequenced cases reported in Guinea between March and November 2015. Contact tracing investigations classified these cases into eight independent transmission chains. We inferred the transmission history from the genetic sequences of the cases (phylogenetic approach), their onset date (epidemiological approach), and a combination of both (combined approach). The inferred transmission trees were then compared to those from the contact tracing investigations. Inference methods using individual data sources (i.e. the phylogenetic analysis and the epidemiological approach) were insufficiently informative to accurately reconstruct the transmission trees and the direction of transmission. The combined approach was able to identify a reduced pool of infectors for each case and highlight likely connections among chains classified as independent by the contact tracing investigations. Overall, the transmissions identified by the contact tracing investigations agreed with the evolutionary history of the viral genomes, even though some cases appeared to be misclassified. Therefore, collecting genetic sequences during outbreak is key to supplement the information contained in contact tracing investigations. Although none of the methods we used could identify one unique infector per case, the combined approach highlighted the added value of mixing epidemiological and genetic information to reconstruct who infected whom.

Superspreading potentials of SARS-CoV-2 Delta variants across different contact settings in Eastern China: A retrospective observational study

OBJECTIVES

As the genetic variants of SARS-CoV-2 continuously pose threats to global health, evaluating superspreading potentials of emerging genetic variants is of importance for region-wide control of COVID-19 outbreaks.

METHODS

By using detailed epidemiological contact tracing data of test-positive COVID-19 cases collected between July and August 2021 in Nanjing and Yangzhou, China, we assessed the superspreading potential of outbreaks seeded by SARS-CoV-2 Delta variants. The transmission chains and case-clusters were constructed according to the individual-based surveillance data. We modelled the disease transmission as a classic branching process with transmission heterogeneity governed by negative binomial models. Subgroup analysis was conducted by different contact settings and age groups.

RESULTS

We reported a considerable heterogeneity in the contact patterns and transmissibility of Delta variants in eastern China. We estimated an expected 14% (95% CI: 11-16%) of the most infectious cases generated 80% of the total transmission.

CONCLUSIONS

Delta variants demonstrated a significant potential of superspreading under strict control measures and active COVID-19 detecting efforts. Enhancing the surveillance on disease transmissibility especially in high-risk settings, along with rapid contact tracing and case isolations would be one of the key factors to mitigate the epidemic caused by the emerging genetic variants of SARS-CoV-2.

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.

A comparison of COVID-19 outbreaks across US Combined Statistical Areas using new methods for estimating R0 and social distancing behaviour

We investigated the initial outbreak rates and subsequent social distancing behaviour over the initial phase of the COVID-19 pandemic across 29 Combined Statistical Areas (CSAs) of the United States. We used the Numerus Model Builder Data and Simulation Analysis (NMB-DASA) web application to fit the exponential phase of a SCLAIV+D (Susceptible, Contact, Latent, Asymptomatic infectious, symptomatic Infectious, Vaccinated, Dead) disease classes model to outbreaks, thereby allowing us to obtain an estimate of the basic reproductive number R₀ for each CSA. Values of R₀ ranged from 1.9 to 9.4, with a mean and standard deviation of 4.5±1.8. Fixing the parameters from the exponential fit, we again used NMB-DASA to estimate a set of social distancing behaviour parameters to compute an epidemic flattening index c_flatten. Finally, we applied hierarchical clustering methods using this index to divide CSA outbreaks into two clusters: those presenting a social distancing response that was either weaker or stronger. We found c_flatten to be more influential in the clustering process than R₀. Thus, our results suggest that the behavioural response after a short initial exponential growth phase is likely to be more determinative of the rise of an epidemic than R₀ itself.

The effect of spatial dynamics on the behaviour of an environmentally transmitted disease

Understanding the spread of pathogens through the environment is critical to a fuller comprehension of disease dynamics. However, many mathematical models of disease dynamics ignore spatial effects. We seek to expand knowledge around the interaction between the bare-nosed wombat (Vombatus ursinus) and sarcoptic mange (etiologic agent Sarcoptes scabiei), by extending an aspatial mathematical model to include spatial variation. S. scabiei was found to move through our modelled region as a spatio-temporal travelling wave, leaving behind pockets of localized host extinction, consistent with field observations. The speed of infection spread was also comparable with field research. Our model predicts that the inclusion of spatial dynamics leads to the survival and recovery of affected wombat populations when an aspatial model predicts extinction. Collectively, this research demonstrates how environmentally transmitted S. scabiei can result in travelling wave dynamics, and that inclusion of spatial variation reveals a more resilient host population than aspatial modelling approaches.

Forecasting COVID-19 cases by assessing control-intervention effects in Republic of Korea: A statistical modeling approach

The Coronavirus disease of 2019 (COVID-19) is an ongoing public health concern worldwide. COVID-19 infections continue to occur and thus, it is important to assess the effects of various public health measures. This study aims to forecast COVID-19 cases by geographical area in Korea, based on the effects of different control-intervention intensities (CII). Methods involved estimating the effective reproduction number (Rt) by Korean geographical area using the SEIHR model, and the instantaneous reproduction number using statistical model, comparing the epidemic curves and high-, intermediate-, and low-intensity control interventions. Here, short-term four-week forecasts by geographical area were conducted. The mean of delayed instantaneous reproduction number was estimated at 1.36, 1.03, and 0.93 for the low-, intermediate-, and high-intensity control interventions, respectively, in the capital area of Korea from July 16, 2020, to March 4, 2021. The COVID-19 cases were forecasted with an accuracy rate of 11.28%, 13.62%, and 20.19% MAPE in Korea, including both the capital and non-capital areas. High-intensity control measures significantly reduced the reproduction number to be less than one. The proposed model forecasted COVID-19 transmission dynamics with good accuracy and interpretability. High-intensity control intervention, active case detection, and isolation efforts should be maintained to control the pandemic.

The role of super-spreaders in modeling of SARS-CoV-2

In stochastic modeling of infectious diseases, it has been established that variations in infectivity affect the probability of a major outbreak, but not the shape of the curves during a major outbreak, which is predicted by deterministic models (Diekmann et al., 2012). However, such conclusions are derived under idealized assumptions such as the population size tending to infinity, and the individual degree of infectivity only depending on variations in the infectiousness period. In this paper we show that the same conclusions hold true in a finite population representing a medium size city, where the degree of infectivity is determined by the offspring distribution, which we try to make as realistic as possible for SARS-CoV-2. In particular, we consider distributions with fat tails, to incorporate the existence of super-spreaders. We also provide new theoretical results on convergence of stochastic models which allows to incorporate any offspring distribution with a finite variance.

Atypical and Unique Transmission of Monkeypox Virus during the 2022 Outbreak: An Overview of the Current State of Knowledge

An ongoing monkeypox outbreak in non-endemic countries has resulted in the declaration of a public health emergency of international concern by the World Health Organization (WHO). Though monkeypox has long been endemic in regions of sub-Saharan Africa, relatively little is known about its ecology, epidemiology, and transmission. Here, we consider the relevant research on both monkeypox and smallpox, a close relative, to make inferences about the current outbreak. Undetected circulation combined with atypical transmission and case presentation, including mild and asymptomatic disease, have facilitated the spread of monkeypox in non-endemic regions. A broader availability of diagnostics, enhanced surveillance, and targeted education, combined with a better understanding of the routes of transmission, are critical to identify at-risk populations and design science-based countermeasures to control the current outbreak.

Basic reproduction number of the COVID-19 Delta variant: Estimation from multiple transmission datasets

The basic reproduction number, $ R_0 $, plays a central role in measuring the transmissibility of an infectious disease, and it thus acts as the fundamental index for planning control strategies. In the present study, we apply a branching process model to meticulously observed contact tracing data from Wakayama Prefecture, Japan, obtained in early 2020 and mid-2021. This allows us to efficiently estimate $ R_0 $ and the dispersion parameter $ k $ of the wild-type COVID-19, as well as the relative transmissibility of the Delta variant and relative transmissibility among fully vaccinated individuals, from a very limited data. $ R_0 $ for the wild type of COVID-19 is estimated to be 3.78 (95% confidence interval [CI]: 3.72-3.83), with $ k = 0.236 $ (95% CI: 0.233-0.240). For the Delta variant, the relative transmissibility to the wild type is estimated to be 1.42 (95% CI: 0.94-1.90), which gives $ R_0 = 5.37 $ (95% CI: 3.55-7.21). Vaccine effectiveness, determined by the reduction in the number of secondary transmissions among fully vaccinated individuals, is estimated to be 91% (95% CI: 85%-97%). The present study highlights that basic reproduction numbers can be accurately estimated from the distribution of minor outbreak data, and these data can provide further insightful epidemiological estimates including the dispersion parameter and vaccine effectiveness regarding the prevention of transmission.

Simulation applications to support teaching and research in epidemiological dynamics

BACKGROUND

An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP ^Ⓡ (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.

RESULTS

We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that 'burn' through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R₀, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R₀>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.

CONCLUSION

Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

Estimating the potential to prevent locally acquired HIV infections in a UNAIDS Fast-Track City, Amsterdam

Background:

More than 300 cities including the city of Amsterdam in the Netherlands have joined the UNAIDS Fast-Track Cities initiative, committing to accelerate their HIV response and end the AIDS epidemic in cities by 2030. To support this commitment, we aimed to estimate the number and proportion of Amsterdam HIV infections that originated within the city, from Amsterdam residents. We also aimed to estimate the proportion of recent HIV infections during the 5-year period 2014–2018 in Amsterdam that remained undiagnosed.

Methods:

We located diagnosed HIV infections in Amsterdam using postcode data (PC4) at time of registration in the ATHENA observational HIV cohort, and used HIV sequence data to reconstruct phylogeographically distinct, partially observed Amsterdam transmission chains. Individual-level infection times were estimated from biomarker data, and used to date the phylogenetically observed transmission chains as well as to estimate undiagnosed proportions among recent infections. A Bayesian Negative Binomial branching process model was used to estimate the number, size, and growth of the unobserved Amsterdam transmission chains from the partially observed phylogenetic data.

Results:

Between 1 January 2014 and 1 May 2019, there were 846 HIV diagnoses in Amsterdam residents, of whom 516 (61%) were estimated to have been infected in 2014–2018. The rate of new Amsterdam diagnoses since 2014 (104 per 100,000) remained higher than the national rates excluding Amsterdam (24 per 100,000), and in this sense Amsterdam remained a HIV hotspot in the Netherlands. An estimated 14% [12–16%] of infections in Amsterdan MSM in 2014–2018 remained undiagnosed by 1 May 2019, and 41% [35–48%] in Amsterdam heterosexuals, with variation by region of birth. An estimated 67% [60–74%] of Amsterdam MSM infections in 2014–2018 had an Amsterdam resident as source, and 56% [41–70%] in Amsterdam heterosexuals, with heterogeneity by region of birth. Of the locally acquired infections, an estimated 43% [37–49%] were in foreign-born MSM, 41% [35–47%] in Dutch-born MSM, 10% [6–18%] in foreign-born heterosexuals, and 5% [2–9%] in Dutch-born heterosexuals. We estimate the majority of Amsterdam MSM infections in 2014–2018 originated in transmission chains that pre-existed by 2014.

Conclusions:

This combined phylogenetic, epidemiologic, and modelling analysis in the UNAIDS Fast-Track City Amsterdam indicates that there remains considerable potential to prevent HIV infections among Amsterdam residents through city-level interventions. The burden of locally acquired infection remains concentrated in MSM, and both Dutch-born and foreign-born MSM would likely benefit most from intensified city-level interventions.

Funding:

This study received funding as part of the H-TEAM initiative from Aidsfonds (project number P29701). The H-TEAM initiative is being supported by Aidsfonds (grant number: 2013169, P29701, P60803), Stichting Amsterdam Dinner Foundation, Bristol-Myers Squibb International Corp. (study number: AI424-541), Gilead Sciences Europe Ltd (grant number: PA-HIV-PREP-16-0024), Gilead Sciences (protocol numbers: CO-NL-276-4222, CO-US-276-1712, CO-NL-985-6195), and M.A.C AIDS Fund.

Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model

Countries such as New Zealand, Australia and Taiwan responded to the Covid-19 pandemic with an elimination strategy. This involves a combination of strict border controls with a rapid and effective response to eliminate border-related re-introductions. An important question for decision makers is, when there is a new re-introduction, what is the right threshold at which to implement strict control measures designed to reduce the effective reproduction number below 1. Since it is likely that there will be multiple re-introductions, responding at too low a threshold may mean repeatedly implementing controls unnecessarily for outbreaks that would self-eliminate even without control measures. On the other hand, waiting for too high a threshold to be reached creates a risk that controls will be needed for a longer period of time, or may completely fail to contain the outbreak. Here, we use a highly idealised branching process model of small border-related outbreaks to address this question. We identify important factors that affect the choice of threshold in order to minimise the expect time period for which control measures are in force. We find that the optimal threshold for introducing controls decreases with the effective reproduction number, and increases with overdispersion of the offspring distribution and with the effectiveness of control measures. Our results are not intended as a quantitative decision-making algorithm. However, they may help decision makers understand when a wait-and-see approach is likely to be preferable over an immediate response.

Modeling scenarios for mitigating outbreaks in congregate settings

The explosive outbreaks of COVID-19 seen in congregate settings such as prisons and nursing homes, has highlighted a critical need for effective outbreak prevention and mitigation strategies for these settings. Here we consider how different types of control interventions impact the expected number of symptomatic infections due to outbreaks. Introduction of disease into the resident population from the community is modeled as a stochastic point process coupled to a branching process, while spread between residents is modeled via a deterministic compartmental model that accounts for depletion of susceptible individuals. Control is modeled as a proportional decrease in the number of susceptible residents, the reproduction number, and/or the proportion of symptomatic infections. This permits a range of assumptions about the density dependence of transmission and modes of protection by vaccination, depopulation and other types of control. We find that vaccination or depopulation can have a greater than linear effect on the expected number of cases. For example, assuming a reproduction number of 3.0 with density-dependent transmission, we find that preemptively reducing the size of the susceptible population by 20% reduced overall disease burden by 47%. In some circumstances, it may be possible to reduce the risk and burden of disease outbreaks by optimizing the way a group of residents are apportioned into distinct residential units. The optimal apportionment may be different depending on whether the goal is to reduce the probability of an outbreak occurring, or the expected number of cases from outbreak dynamics. In other circumstances there may be an opportunity to implement reactive disease control measures in which the number of susceptible individuals is rapidly reduced once an outbreak has been detected to occur. Reactive control is most effective when the reproduction number is not too high, and there is minimal delay in implementing control. We highlight the California state prison system as an example for how these findings provide a quantitative framework for understanding disease transmission in congregate settings. Our approach and accompanying interactive website (https://phoebelu.shinyapps.io/DepopulationModels/) provides a quantitative framework to evaluate the potential impact of policy decisions governing infection control in outbreak settings.

Characterizing superspreading potential of infectious disease: Decomposition of individual transmissibility

In the context of infectious disease transmission, high heterogeneity in individual infectiousness indicates that a few index cases can generate large numbers of secondary cases, a phenomenon commonly known as superspreading. The potential of disease superspreading can be characterized by describing the distribution of secondary cases (of each seed case) as a negative binomial (NB) distribution with the dispersion parameter, k. Based on the feature of NB distribution, there must be a proportion of individuals with individual reproduction number of almost 0, which appears restricted and unrealistic. To overcome this limitation, we generalized the compound structure of a Poisson rate and included an additional parameter, and divided the reproduction number into independent and additive fixed and variable components. Then, the secondary cases followed a Delaporte distribution. We demonstrated that the Delaporte distribution was important for understanding the characteristics of disease transmission, which generated new insights distinct from the NB model. By using real-world dataset, the Delaporte distribution provides improvements in describing the distributions of COVID-19 and SARS cases compared to the NB distribution. The model selection yielded increasing statistical power with larger sample sizes as well as conservative type I error in detecting the improvement in fitting with the likelihood ratio (LR) test. Numerical simulation revealed that the control strategy-making process may benefit from monitoring the transmission characteristics under the Delaporte framework. Our findings highlighted that for the COVID-19 pandemic, population-wide interventions may control disease transmission on a general scale before recommending the high-risk-specific control strategies.

Superspreading is one of the key transmission features of many infectious diseases and is considered a consequence of the heterogeneity in infectiousness of individual cases. To characterize the superspreading potential, we divided individual infectiousness into two independent and additive components, including a fixed baseline and a variable part. Such decomposition produced an improvement in the fit of the model explaining the distribution of real-world datasets of COVID-19 and SARS that can be captured by the classic statistical tests. Disease control strategies may be developed by monitoring the characteristics of superspreading. For the COVID-19 pandemic, population-wide interventions are suggested first to limit the transmission at a scale of general population, and then high-risk-specific control strategies are recommended subsequently to lower the risk of superspreading.

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, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R$$\end{document}R, 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.

Assessing the risk of human-to-wildlife pathogen transmission for conservation and public health

The SARS‐CoV‐2 pandemic has led to increased concern over transmission of pathogens from humans to animals, and its potential to threaten conservation and public health. To assess this threat, we reviewed published evidence of human‐to‐wildlife transmission events, with a focus on how such events could threaten animal and human health. We identified 97 verified examples, involving a wide range of pathogens; however, reported hosts were mostly non‐human primates or large, long‐lived captive animals. Relatively few documented examples resulted in morbidity and mortality, and very few led to maintenance of a human pathogen in a new reservoir or subsequent “secondary spillover” back into humans. We discuss limitations in the literature surrounding these phenomena, including strong evidence of sampling bias towards non‐human primates and human‐proximate mammals and the possibility of systematic bias against reporting human parasites in wildlife, both of which limit our ability to assess the risk of human‐to‐wildlife pathogen transmission. We outline how researchers can collect experimental and observational evidence that will expand our capacity for risk assessment for human‐to‐wildlife pathogen transmission.

A Cluster-based Method to Quantify Individual Heterogeneity in Tuberculosis Transmission

BACKGROUND

Recent evidence suggests transmission of Mycobacterium tuberculosis (Mtb) may be characterized by extreme individual heterogeneity in secondary cases (i.e., few cases account for the majority of transmission). Such heterogeneity implies outbreaks are rarer but more extensive and has profound implications in infectious disease control. However, discrete person-to-person transmission events in tuberculosis (TB) are often unobserved, precluding our ability to directly quantify individual heterogeneity in TB epidemiology.

METHODS

We used a modified negative binomial branching process model to quantify the extent of individual heterogeneity using only observed transmission cluster size distribution data (i.e., the simple sum of all cases in a transmission chain) without knowledge of individual-level transmission events. The negative binomial parameter k quantifies the extent of individual heterogeneity (generally, indicates extensive heterogeneity, and as transmission becomes more homogenous). We validated the robustness of the inference procedure considering common limitations affecting cluster size data. Finally, we demonstrate the epidemiologic utility of this method by applying it to aggregate US molecular surveillance data from the US Centers for Disease Control and Prevention.

RESULTS

The cluster-based method reliably inferred k using TB transmission cluster data despite a high degree of bias introduced into the model. We found that the TB transmission in the United States was characterized by a high propensity for extensive outbreaks (; 95% confidence interval = 0.09, 0.10).

CONCLUSIONS

The proposed method can accurately quantify critical parameters that govern TB transmission using simple, more easily obtainable cluster data to improve our understanding of TB epidemiology.

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.

Secondary transmission of SARS-CoV-2 during the first two waves in Japan: Demographic characteristics and overdispersion

Objectives

Super-spreading events caused by overdispersed secondary transmission are crucial in the transmission of COVID-19. However, the exact level of overdispersion, demographics, and other factors associated with secondary transmission remain elusive. In this study, we aimed to elucidate the frequency and patterns of secondary transmission of SARS-CoV-2 in Japan.

Methods

We analyzed 16,471 cases between January 2020 and August 2020. We generated the number of secondary cases distribution and estimated the dispersion parameter (k) by fitting the negative binomial distribution in each phase. The frequencies of the secondary transmission were compared by demographic and clinical characteristics, calculating the odds ratio using logistic regression models.

Results

We observed that 76.7% of the primary cases did not generate secondary cases with an estimated dispersion parameter k of 0.23. The demographic patterns of primary-secondary cases differed between phases, with 20–69 years being the predominant age group. There were higher proportions of secondary transmissions among older individuals, symptomatic patients, and patients with 2 days or more between onset and confirmation.

Conclusions

The study showed the estimation of the frequency of secondary transmission of SARS-CoV-2 and the characteristics of people who generated the secondary transmission.

Early warning signal reliability varies with COVID-19 waves

Early warning signals (EWSs) aim to predict changes in complex systems from phenomenological signals in time series data. These signals have recently been shown to precede the emergence of disease outbreaks, offering hope that policymakers can make predictive rather than reactive management decisions. Here, using a novel, sequential analysis in combination with daily COVID-19 case data across 24 countries, we suggest that composite EWSs consisting of variance, autocorrelation and skewness can predict nonlinear case increases, but that the predictive ability of these tools varies between waves based upon the degree of critical slowing down present. Our work suggests that in highly monitored disease time series such as COVID-19, EWSs offer the opportunity for policymakers to improve the accuracy of urgent intervention decisions but best characterize hypothesized critical transitions.

Maintenance of measles elimination status in the United States for 20 years despite increasing challenges

BACKGROUND

Measles elimination (interruption of endemic measles virus transmission) in the United States was declared in 2000; however, the number of cases and outbreaks have increased in recent years. We characterized the epidemiology of measles outbreaks and measles transmission patterns post-elimination to identify potential gaps in the U.S. measles control program.

METHODS

We analyzed national measles notification data from January 1, 2001-December 31, 2019. We defined measles infection clusters as single cases (isolated cases not linked to additional cases), 2-case clusters, or outbreaks with 3 or more linked cases. We calculated the effective reproduction number (R) to assess changes in transmissibility and reviewed molecular epidemiology data.

RESULTS

During 2001-2019, 3,873 measles cases, including 747 international importations, were reported in the United States; 29% of importations were associated with outbreaks. Among 871 clusters, 69% were single cases and 72% had no spread. Larger and longer clusters were reported since 2013, including seven outbreaks with >50 cases lasting >2 months, 5 of which occurred in known underimmunized, close-knit communities. No measles lineage circulated in a single transmission chain for >12 months. Higher estimates of R were noted in recent years, although R remained below the epidemic threshold of 1.

CONCLUSIONS

Current epidemiology continues to support the interruption of endemic measles virus transmission in the United States. However, larger and longer outbreaks in recent post-elimination years and emerging trends of increased transmission in underimmunized communities emphasize the need for targeted approaches to close existing immunity gaps and maintain measles elimination.

Challenges in modeling the emergence of novel pathogens

The emergence of infectious agents with pandemic potential present scientific challenges from detection to data interpretation to understanding determinants of risk and forecasts. Mathematical models could play an essential role in how we prepare for future emergent pathogens. Here, we describe core directions for expansion of the existing tools and knowledge base, including: using mathematical models to identify critical directions and paths for strengthening data collection to detect and respond to outbreaks of novel pathogens; expanding basic theory to identify infectious agents and contexts that present the greatest risks, over both the short and longer term; by strengthening estimation tools that make the most use of the likely range and uncertainties in existing data; and by ensuring modelling applications are carefully communicated and developed within diverse and equitable collaborations for increased public health benefit.

Quantifying superspreading for COVID-19 using Poisson mixture distributions

The number of secondary cases, i.e. the number of new infections generated by an infectious individual, is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the distribution of the number of secondary cases is skewed and often modeled using a negative binomial distribution. However, this may not always be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the mean and variance of this distribution when the data generating distribution is different from the one used for inference. We also analyze COVID-19 data from Hong Kong, India, and Rwanda, and quantify the proportion of cases responsible for 80% of transmission, [Formula: see text], while acknowledging the variation arising from the assumed offspring distribution. In a simulation study, we find that variance estimates may be biased when there is a substantial amount of heterogeneity, and that selection of the most accurate distribution from a set of distributions is important. In addition we find that the number of secondary cases for two of the three COVID-19 datasets is better described by a Poisson-lognormal distribution.

Mitigating outbreaks in congregate settings by decreasing the size of the susceptible population

While many transmission models have been developed for community spread of respiratory pathogens, less attention has been given to modeling the interdependence of disease introduction and spread seen in congregate settings, such as prisons or nursing homes. As demonstrated by the explosive outbreaks of COVID-19 seen in congregate settings, the need for effective outbreak prevention and mitigation strategies for these settings is critical. Here we consider how interventions that decrease the size of the susceptible populations, such as vaccination or depopulation, impact the expected number of infections due to outbreaks. Introduction of disease into the resident population from the community is modeled as a branching process, while spread between residents is modeled via a compartmental model. Control is modeled as a proportional decrease in both the number of susceptible residents and the reproduction number. We find that vaccination or depopulation can have a greater than linear effect on anticipated infections. For example, assuming a reproduction number of 3.0 for density-dependent COVID-19 transmission, we find that reducing the size of the susceptible population by 20% reduced overall disease burden by 47%. We highlight the California state prison system as an example for how these findings provide a quantitative framework for implementing infection control in congregate settings. Additional applications of our modeling framework include optimizing the distribution of residents into independent residential units, and comparison of preemptive versus reactive vaccination strategies.

Comparison of Estimated Effectiveness of Case-Based and Population-Based Interventions on COVID-19 Containment in Taiwan

IMPORTANCE

Taiwan is one of the few countries with initial success in COVID-19 control without strict lockdown or school closure. The reasons remain to be fully elucidated.

OBJECTIVE

To compare and evaluate the effectiveness of case-based (including contact tracing and quarantine) and population-based (including social distancing and facial masking) interventions for COVID-19 in Taiwan.

DESIGN, SETTING, AND PARTICIPANTS

This comparative effectiveness study used a stochastic branching process model using COVID-19 epidemic data from Taiwan, an island nation of 23.6 million people, with no locally acquired cases of COVID-19 reported for 253 days between April and December 2020.

MAIN OUTCOMES AND MEASURES

Effective reproduction number of COVID-19 cases (the number of secondary cases generated by 1 primary case) and the probability of outbreak extinction (0 new cases within 20 generations). For model development and calibration, an estimation of the incubation period (interval from exposure to symptom onset), serial interval (time between symptom onset in an infector-infectee pair), and the statistical distribution of the number of any subsequent infections generated by 1 primary case was calculated.

RESULTS

This study analyzed data from 158 confirmed COVID-19 cases (median age, 45 years; interquartile range, 25-55 years; 84 men [53%]). An estimated 55% (95% credible interval [CrI], 41%-68%) of transmission events occurred during the presymptomatic stage. In our estimated analysis, case detection, contact tracing, and 14-day quarantine of close contacts (regardless of symptoms) was estimated to decrease the reproduction number from the counterfactual value of 2.50 to 1.53 (95% CrI, 1.50-1.57), which would not be sufficient for epidemic control, which requires a value of less than 1. In our estimated analysis, voluntary population-based interventions, if used alone, were estimated to have reduced the reproduction number to 1.30 (95% CrI, 1.03-1.58). Combined case-based and population-based interventions were estimated to reduce the reproduction number to below unity (0.85; 95% CrI, 0.78-0.89). Results were similar for additional analyses with influenza data and sensitivity analyses.

CONCLUSIONS AND RELEVANCE

In this comparative effectiveness research study, the combination of case-based and population-based interventions (with wide adherence) may explain the success of COVID-19 control in Taiwan in 2020. Either category of interventions alone would have been insufficient, even in a country with an effective public health system and comprehensive contact tracing program. Mitigating the COVID-19 pandemic requires the collaborative effort of public health professionals and the general public.

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.

o2geosocial: Reconstructing who-infected-whom from routinely collected surveillance data

Reconstructing the history of individual transmission events between cases is key to understanding what factors facilitate the spread of an infectious disease. Since conducting extended contact-tracing investigations can be logistically challenging and costly, statistical inference methods have been developed to reconstruct transmission trees from onset dates and genetic sequences. However, these methods are not as effective if the mutation rate of the virus is very slow, or if sequencing data is sparse. We developed the package o2geosocial to combine variables from routinely collected surveillance data with a simple transmission process model. The model reconstructs transmission trees when full genetic sequences are unavailable, or uninformative. Our model incorporates the reported age-group, onset date, location and genotype of infected cases to infer probabilistic transmission trees. The package also includes functions to summarise and visualise the inferred cluster size distribution. The results generated by o2geosocial can highlight regions where importations repeatedly caused large outbreaks, which may indicate a higher regional susceptibility to infections. It can also be used to generate the individual number of secondary transmissions, and show the features associated with individuals involved in high transmission events. The package is available for download from the Comprehensive R Archive Network (CRAN) and GitHub.

Transmission Dynamics, Heterogeneity and Controllability of SARS-CoV-2: A Rural-Urban Comparison

Few studies have examined the transmission dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in rural areas and clarified rural-urban differences. Moreover, the effectiveness of non-pharmaceutical interventions (NPIs) relative to vaccination in rural areas is uncertain. We addressed this knowledge gap through using an improved statistical stochastic method based on the Galton-Watson branching process, considering both symptomatic and asymptomatic cases. Data included 1136 SARS-2-CoV infections of the rural outbreak in Hebei, China, and 135 infections of the urban outbreak in Tianjin, China. We reconstructed SARS-CoV-2 transmission chains and analyzed the effectiveness of vaccination and NPIs by simulation studies. The transmission of SARS-CoV-2 showed strong heterogeneity in urban and rural areas, with the dispersion parameters k = 0.14 and 0.35, respectively (k < 1 indicating strong heterogeneity). Although age group and contact-type distributions significantly differed between urban and rural areas, the average reproductive number (R) and k did not. Further, simulation results based on pre-control parameters (R = 0.81, k = 0.27) showed that in the vaccination scenario (80% efficacy and 55% coverage), the cumulative secondary infections will be reduced by more than half; however, NPIs are more effective than vaccinating 65% of the population. These findings could inform government policies regarding vaccination and NPIs in rural and urban areas.

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.

Localized end-of-outbreak determination for coronavirus disease 2019 (COVID-19): examples from clusters in Japan

OBJECTIVES

End-of-outbreak declarations are an important component of outbreak response because they indicate that public health and social interventions may be relaxed or lapsed. Our study aimed to assess end-of-outbreak probabilities for clusters of coronavirus disease 2019 (COVID-19) cases detected during the first wave of the COVID-19 pandemic in Japan.

METHODS

A statistical model for end-of-outbreak determination, which accounted for reporting delays for new cases, was computed. Four clusters, representing different social contexts and time points during the first wave of the epidemic, were selected and their end-of-outbreak probabilities were evaluated.

RESULTS

The speed of end-of-outbreak determination was most closely tied to outbreak size. Notably, accounting underascertainment of cases led to later end-of-outbreak determinations. In addition, end-of-outbreak determination was closely related to estimates of case dispersionk and the effective reproduction number Re. Increasing local transmission (Re>1) leads to greater uncertainty in the probability estimates.

CONCLUSIONS

When public health measures are effective, lowerRe (less transmission on average) and larger k (lower risk of superspreading) will be in effect, and end-of-outbreak determinations can be declared with greater confidence. The application of end-of-outbreak probabilities can help distinguish between local extinction and low levels of transmission, and communicating these end-of-outbreak probabilities can help inform public health decision making with regard to the appropriate use of resources.

Bayesian Inference in Y-Linked Two-Sex Branching Processes with Mutations: ABC Approach

A Y-linked two-sex branching process with mutations and blind choice of males is a suitable model for analyzing the evolution of the number of carriers of a Y-linked allele and its mutations. Such a model considers a two-sex monogamous population in which each female chooses her partner from among the male population without caring about his type (i.e., the allele he carries). In this work, we deal with the problem of estimating the main parameters of these models by developing Bayesian inference in a parametric framework. First, we consider as a sample scheme the observation of the total number of females and males up to some generation as well as the number of males of each genotype in the last generation. Subsequently, we introduce the information on the mutated males in only the last generation, obtaining in this way a second sample scheme. For both samples, we apply the Approximate Bayesian Computation (ABC) method to approximate the posterior distributions of the main parameters of the model. The accuracy of the procedure based on these samples is illustrated and discussed by way of simulated examples.

A Framework to Monitor Changes in Transmission and Epidemiology of Emerging Pathogens: Lessons From Nipah Virus

It is of uttermost importance that the global health community develops the surveillance capability to effectively monitor emerging zoonotic pathogens that constitute a major and evolving threat for human health. In this study, we propose a comprehensive framework to measure changes in (1) spillover risk, (2) interhuman transmission, and (3) morbidity/mortality associated with infections based on 6 epidemiological key indicators derived from routine surveillance. We demonstrate the indicators' value for the retrospective or real-time assessment of changes in transmission and epidemiological characteristics using data collected through a long-standing, systematic, hospital-based surveillance system for Nipah virus in Bangladesh. We show that although interhuman transmission and morbidity/mortality indicators were stable, the number and geographic extent of spillovers varied significantly over time. This combination of systematic surveillance and active tracking of transmission and epidemiological indicators should be applied to other high-risk emerging pathogens to prevent public health emergencies.

Inferencing superspreading potential using zero-truncated negative binomial model: exemplification with COVID-19

Background

In infectious disease transmission dynamics, the high heterogeneity in individual infectiousness indicates that few index cases generate large numbers of secondary cases, which is commonly known as superspreading events. The heterogeneity in transmission can be measured by describing the distribution of the number of secondary cases as a negative binomial (NB) distribution with dispersion parameter, k. However, such inference framework usually neglects the under-ascertainment of sporadic cases, which are those without known epidemiological link and considered as independent clusters of size one, and this may potentially bias the estimates.

Methods

In this study, we adopt a zero-truncated likelihood-based framework to estimate k. We evaluate the estimation performance by using stochastic simulations, and compare it with the baseline non-truncated version. We exemplify the analytical framework with three contact tracing datasets of COVID-19.

Results

We demonstrate that the estimation bias exists when the under-ascertainment of index cases with 0 secondary case occurs, and the zero-truncated inference overcomes this problem and yields a less biased estimator of k. We find that the k of COVID-19 is inferred at 0.32 (95%CI: 0.15, 0.64), which appears slightly smaller than many previous estimates. We provide the simulation codes applying the inference framework in this study.

Conclusions

The zero-truncated framework is recommended for less biased transmission heterogeneity estimates. These findings highlight the importance of individual-specific case management strategies to mitigate COVID-19 pandemic by lowering the transmission risks of potential super-spreaders with priority.

Quantifying superspreading for COVID-19 using Poisson mixture distributions

The number of secondary cases is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the number of secondary cases is often modelled using a negative binomial distribution. However, this may not be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the offspring mean and its overdispersion when the data generating distribution is different from the one used for inference. We find that overdispersion estimates may be biased when there is a substantial amount of heterogeneity, and that the use of other distributions besides the negative binomial should be considered. We revisit three previously analysed COVID-19 datasets and quantify the proportion of cases responsible for 80% of transmission, p 80% , while acknowledging the variation arising from the assumed offspring distribution. We find that the number of secondary cases for these datasets is better described by a Poisson-lognormal distribution.

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.