Interventions targeting non-symptomatic cases can be important to prevent local outbreaks: SARS-CoV-2 as a case study

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

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

Disease X epidemic control using a stochastic model and a deterministic approximation: Performance comparison with and without parameter uncertainties

BACKGROUND

The spread of infectious diseases can be modeled using deterministic or stochastic models. A deterministic approximation of a stochastic model can be appropriate under some conditions, but is unable to capture the discrete nature of populations. We look into the choice of a model from the perspective of decision making.

METHOD

We consider an emerging disease (Disease X) in a closed population modeled by a stochastic SIR model or its deterministic approximation. The objective of the decision maker is to minimize the cumulative number of symptomatic infected-days over the course of the epidemic by picking a vaccination policy. We consider four decision making scenarios: based on the stochastic model or the deterministic model, and with or without parameter uncertainty. We also consider different sample sizes for uncertain parameter draws and stochastic model runs. We estimate the average performance of decision making in each scenario and for each sample size.

RESULTS

The model used for decision making has an influence on the picked policies. The best achievable performance is obtained with the stochastic model, knowing parameter values, and for a large sample size. For small sample sizes, the deterministic model can outperform the stochastic model due to stochastic effects. Resolving uncertainties may bring more benefit than switching to the stochastic model in our example.

CONCLUSION

This article illustrates the interplay between the choice of a type of model, parameter uncertainties, and sample sizes. It points to issues to be considered when optimizing a stochastic model.

Optimal social distancing in epidemic control: cost prioritization, adherence and insights into preparedness principles

The COVID-19 pandemic experience has highlighted the importance of developing general control principles to inform future pandemic preparedness based on the tension between the different control options, ranging from elimination to mitigation, and related costs. Similarly, during the COVID-19 pandemic, social distancing has been confirmed to be the critical response tool until vaccines become available. Open-loop optimal control of a transmission model for COVID-19 in one of its most aggressive outbreaks is used to identify the best social distancing policies aimed at balancing the direct epidemiological costs of a threatening epidemic with its indirect (i.e., societal level) costs arising from enduring control measures. In particular, we analyse how optimal social distancing varies according to three key policy factors, namely, the degree of prioritization of indirect costs, the adherence to control measures, and the timeliness of intervention. As the prioritization of indirect costs increases, (i) the corresponding optimal distancing policy suddenly switches from elimination to suppression and, finally, to mitigation; (ii) the "effective" mitigation region-where hospitals' overwhelming is prevented-is dramatically narrow and shows multiple control waves; and (iii) a delicate balance emerges, whereby low adherence and lack of timeliness inevitably force ineffective mitigation as the only accessible policy option. The present results show the importance of open-loop optimal control, which is traditionally absent in public health preparedness, for studying the suppression-mitigation trade-off and supplying robust preparedness guidelines.

Exact calculation of end-of-outbreak probabilities using contact tracing data

A key challenge for public health policymakers is determining when an infectious disease outbreak has finished. Following a period without cases, an estimate of the probability that no further cases will occur in future (the end-of-outbreak probability) can be used to inform whether or not to declare an outbreak over. An existing quantitative approach (the Nishiura method), based on a branching process transmission model, allows the end-of-outbreak probability to be approximated from disease incidence time series, the offspring distribution and the serial interval distribution. Here, we show how the end-of-outbreak probability under the same transmission model can be calculated exactly if data describing who-infected-whom (the transmission tree) are also available (e.g. from contact tracing studies). In that scenario, our novel approach (the traced transmission method) is straightforward to use. We demonstrate this by applying the method to data from previous outbreaks of Ebola virus disease and Nipah virus infection. For both outbreaks, the traced transmission method would have determined that the outbreak was over earlier than the Nishiura method. This highlights that collection of contact tracing data and application of the traced transmission method may allow stringent control interventions to be relaxed quickly at the end of an outbreak, with only a limited risk of outbreak resurgence.

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

A practical guide to mathematical methods for estimating infectious disease outbreak risks

Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US

COVID-19, induced by the SARS-CoV-2 infection, has caused an unprecedented pandemic in the world. New variants of the virus have emerged and dominated the virus population. In this paper, we develop a multi-strain model with asymptomatic transmission to study how the asymptomatic or pre-symptomatic infection influences the transmission between different strains and control strategies that aim to mitigate the pandemic. Both analytical and numerical results reveal that the competitive exclusion principle still holds for the model with the asymptomatic transmission. By fitting the model to the COVID-19 case and viral variant data in the US, we show that the omicron variants are more transmissible but less fatal than the previously circulating variants. The basic reproduction number for the omicron variants is estimated to be 11.15, larger than that for the previous variants. Using mask mandate as an example of non-pharmaceutical interventions, we show that implementing it before the prevalence peak can significantly lower and postpone the peak. The time of lifting the mask mandate can affect the emergence and frequency of subsequent waves. Lifting before the peak will result in an earlier and much higher subsequent wave. Caution should also be taken to lift the restriction when a large portion of the population remains susceptible. The methods and results obtained her e may be applied to the study of the dynamics of other infectious diseases with asymptomatic transmission using other control measures.

Modelling the impact of repeat asymptomatic testing policies for staff on SARS-CoV-2 transmission potential

Repeat asymptomatic testing in order to identify and quarantine infectious individuals has become a widely-used intervention to control SARS-CoV-2 transmission. In some workplaces, and in particular health and social care settings with vulnerable patients, regular asymptomatic testing has been deployed to staff to reduce the likelihood of workplace outbreaks. We have developed a model based on data available in the literature to predict the potential impact of repeat asymptomatic testing on SARS-CoV-2 transmission. The results highlight features that are important to consider when modelling testing interventions, including population heterogeneity of infectiousness and correlation with test-positive probability, as well as adherence behaviours in response to policy. Furthermore, the model based on the reduction in transmission potential presented here can be used to parameterise existing epidemiological models without them having to explicitly simulate the testing process. Overall, we find that even with different model paramterisations, in theory, regular asymptomatic testing is likely to be a highly effective measure to reduce transmission in workplaces, subject to adherence. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

The impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants

Introduction

A key feature of the COVID-19 pandemic has been the emergence of SARS-CoV-2 variants with different transmission characteristics. However, when a novel variant arrives in a host population, it will not necessarily lead to many cases. Instead, it may fade out, due to stochastic effects and the level of immunity in the population. Immunity against novel SARS-CoV-2 variants may be influenced by prior exposures to related viruses, such as other SARS-CoV-2 variants and seasonal coronaviruses, and the level of cross-reactive immunity conferred by those exposures.

Methods

Here, we investigate the impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants in a simplified scenario in which a novel SARS-CoV-2 variant is introduced after an antigenically related virus has spread in the population. We use mathematical modelling to explore the risk that the novel variant invades the population and causes a large number of cases, as opposed to fading out with few cases.

Results

We find that, if cross-reactive immunity is complete (i.e. someone infected by the previously circulating virus is not susceptible to the novel variant), the novel variant must be more transmissible than the previous virus to invade the population. However, in a more realistic scenario in which cross-reactive immunity is partial, we show that it is possible for novel variants to invade, even if they are less transmissible than previously circulating viruses. This is because partial cross-reactive immunity effectively increases the pool of susceptible hosts that are available to the novel variant compared to complete cross-reactive immunity. Furthermore, if previous infection with the antigenically related virus assists the establishment of infection with the novel variant, as has been proposed following some experimental studies, then even variants with very limited transmissibility are able to invade the host population.

Discussion

Our results highlight that fast assessment of the level of cross-reactive immunity conferred by related viruses against novel SARS-CoV-2 variants is an essential component of novel variant risk assessments.

Correlation between times to SARS-CoV-2 symptom onset and secondary transmission undermines epidemic control efforts

Severe acute respiratory coronavirus 2 (SARS-CoV-2) infections have been associated with substantial presymptomatic transmission, which occurs when the generation interval-the time between infection of an individual with a pathogen and transmission of the pathogen to another individual-is shorter than the incubation period-the time between infection and symptom onset. We collected a dataset of 257 SARS-CoV-2 transmission pairs in Japan during 2020 and jointly estimated the mean incubation period of infectors (4.8 days, 95 % CrI: 4.4-5.1 days), mean generation interval to when they infect others (4.3 days, 95 % credible interval [CrI]: 4.0-4.7 days), and the correlation (Kendall's tau: 0.5, 95 % CrI: 0.4-0.6) between these two epidemiological parameters. Our finding of a positive correlation and mean generation interval shorter than the mean infector incubation period indicates ample infectiousness before symptom onset and suggests that reliance on isolation of symptomatic COVID-19 cases as a focal point of control efforts is insufficient to address the challenges posed by SARS-CoV-2 transmission dynamics.

Emergence potential of monkeypox in the Western Pacific Region, July 2022

Although new cases of monkeypox have been expected in the Western Pacific Region (WPR) since the virus emerged in Europe earlier this year, there have been only a few reported cases across the WPR (New Zealand 2, Singapore 6, South Korea 1, Taiwan 2), other than a limited number of cases (compared to numbers of cases seen elsewhere in the world) in Australia (33), as of July 15, 2022. In our short communication, we highlight two key reasons for this: i) international travel has still not fully resumed in the WPR following the COVID-19 pandemic, and ii) local public health measures to counter the spread of COVID-19 have not been completely relaxed. We provide supporting evidence for both of these reasons.

A direct comparison of methods for assessing the threat from emerging infectious diseases in seasonally varying environments

Seasonal variations in environmental conditions lead to changing infectious disease epidemic risks at different times of year. The probability that early cases initiate a major epidemic depends on the season in which the pathogen enters the population. The instantaneous epidemic risk (IER) can be tracked. This quantity is straightforward to calculate, and corresponds to the probability of a major epidemic starting from a single case introduced at time t=t₀, assuming that environmental conditions remain identical from that time onwards (i.e. for all t≥t₀). However, the threat when a pathogen enters the population in fact depends on changes in environmental conditions occurring within the timescale of the initial phase of the outbreak. For that reason, we compare the IER with a different metric: the case epidemic risk (CER). The CER corresponds to the probability of a major epidemic starting from a single case entering the population at time t=t₀, accounting for changes in environmental conditions after that time. We show how the IER and CER can be calculated using different epidemiological models (the stochastic Susceptible-Infectious-Removed model and a stochastic host-vector model that is parameterised using temperature data for Miami) in which transmission parameters vary temporally. While the IER is always easy to calculate numerically, the adaptable method we provide for calculating the CER for the host-vector model can also be applied easily and solved using widely available software tools. In line with previous research, we demonstrate that if a pathogen is likely to either invade the population or fade out on a fast timescale compared to changes in environmental conditions, the IER closely matches the CER. However, if this is not the case, the IER and the CER can be significantly different, and so the CER should be used. This demonstrates the need to consider future changes in environmental conditions carefully when assessing the risk posed by emerging pathogens.

Estimating local outbreak risks and the effects of non-pharmaceutical interventions in age-structured populations: SARS-CoV-2 as a case study

During the COVID-19 pandemic, non-pharmaceutical interventions (NPIs) including school closures, workplace closures and social distancing policies have been employed worldwide to reduce transmission and prevent local outbreaks. However, transmission and the effectiveness of NPIs depend strongly on age-related factors including heterogeneities in contact patterns and pathophysiology. Here, using SARS-CoV-2 as a case study, we develop a branching process model for assessing the risk that an infectious case arriving in a new location will initiate a local outbreak, accounting for the age distribution of the host population. We show that the risk of a local outbreak depends on the age of the index case, and we explore the effects of NPIs targeting individuals of different ages. Social distancing policies that reduce contacts outside of schools and workplaces and target individuals of all ages are predicted to reduce local outbreak risks substantially, whereas school closures have a more limited impact. In the scenarios considered here, when different NPIs are used in combination the risk of local outbreaks can be eliminated. We also show that heightened surveillance of infectious individuals reduces the level of NPIs required to prevent local outbreaks, particularly if enhanced surveillance of symptomatic cases is combined with efforts to find and isolate nonsymptomatic infected individuals. Our results reflect real-world experience of the COVID-19 pandemic, during which combinations of intense NPIs have reduced transmission and the risk of local outbreaks. The general modelling framework that we present can be used to estimate local outbreak risks during future epidemics of a range of pathogens, accounting fully for age-related factors.

Impact of the first superspreading outbreak of COVID-19 related to a nightlife establishment in Andalusia, Spain

INTRODUCTION AND AIM OF THE STUDY

A notable proportion of COVID outbreaks are generated by "super-spreading events", where a few subjects transmit the pathogen to many secondary cases, increasing contact networks and the spread of the pathogen. We conducted a description of a COVID-19 superspreading event in Córdoba during July 2020, linked to a nightlife establishment.

MATERIAL AND METHODS

Retrospective observational study describing characteristics of person, time, PCR result and contact network of confirmed cases. PCR results in Córdoba during July and August and information collected in surveillance systems were analyzed.

RESULTS

935 individuals associated with the outbreak were included; 120 (12.83%) became confirmed cases. July 17 was the day with the highest incidence, with 27 new cases (22.5% of the total). People under 25 years old represented 69.2% of the cases. The average number of close contacts per person was 10.7, with a decrease as age raised. During the outbreak, incidence increased at the provincial level compared to previous weeks; at the end, incidence did not return to initial values but remained high with a relevant percentage of cases having unknown epidemiological association.

CONCLUSIONS

A greater transmission capacity of SARS-CoV-2 was observed in a closed, crowded space, and among young people that tended to report a greater number of social contacts and may present little or no symptoms. Developing preventive measures in scenarios that combine these factors and early detection of cases are essential to avoid an increase in the spread of the virus.

The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions

Background

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed.

Methods

Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel.

Results

We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility.

Conclusions

Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high.

The effectiveness of public health measures against COVID-19 has varied between countries, with some experiencing many infections and others containing transmission successfully. As vaccines are deployed, an important challenge is deciding when to relax measures. Here, we consider locations with few cases, and investigate whether vaccination can ever eliminate the risk of COVID-19 outbreaks completely, allowing measures to be removed risk-free. Using a mathematical model, we demonstrate that there is still a risk that imported cases initiate outbreaks when measures are removed, even if most of the population is fully vaccinated. This highlights the need for continued vigilance in low prevalence settings to prevent imported cases leading to local transmission. Until case numbers are reduced globally, so that SARS-CoV-2 spread between countries is less likely, the risk of outbreaks in low prevalence settings will remain.

Sachak-Patwa et al. estimate the risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions and other non-pharmaceutical interventions, with the Isle of Man and Israel as case studies. Using a branching process mathematical model, the authors show that even after a large proportion of the population is vaccinated, there remains a risk of local outbreaks from imported cases.