The outbreak of pneumonia originating in Wuhan, China, has generated 24,500 confirmed cases, including 492 deaths, as of 5 February 2020. The virus (2019-nCoV) has spread elsewhere in China and to 24 countries, including South Korea, Thailand, Japan and USA. Fortunately, there has only been limited human-to-human transmission outside of China. Here, we assess the risk of sustained transmission whenever the coronavirus arrives in other countries. Data describing the times from symptom onset to hospitalisation for 47 patients infected early in the current outbreak are used to generate an estimate for the probability that an imported case is followed by sustained human-to-human transmission. Under the assumptions that the imported case is representative of the patients in China, and that the 2019-nCoV is similarly transmissible to the SARS coronavirus, the probability that an imported case is followed by sustained human-to-human transmission is 0.41 (credible interval [0.27, 0.55]). However, if the mean time from symptom onset to hospitalisation can be halved by intense surveillance, then the probability that an imported case leads to sustained transmission is only 0.012 (credible interval [0, 0.099]). This emphasises the importance of current surveillance efforts in countries around the world, to ensure that the ongoing outbreak will not become a global pandemic.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute ‘Models for an exit strategy’ workshop (11–15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

We assess how presymptomatic infection affects predictability of infectious disease epidemics. We focus on whether or not a major outbreak (i.e. an epidemic that will go on to infect a large number of individuals) can be predicted reliably soon after initial cases of disease have appeared within a population. For emerging epidemics, significant time and effort is spent recording symptomatic cases. Scientific attention has often focused on improving statistical methodologies to estimate disease transmission parameters from these data. Here we show that, even if symptomatic cases are recorded perfectly, and disease spread parameters are estimated exactly, it is impossible to estimate the probability of a major outbreak without ambiguity. Our results therefore provide an upper bound on the accuracy of forecasts of major outbreaks that are constructed using data on symptomatic cases alone. Accurate prediction of whether or not an epidemic will occur requires records of symptomatic individuals to be supplemented with data concerning the true infection status of apparently uninfected individuals. To forecast likely future behavior in the earliest stages of an emerging outbreak, it is therefore vital to develop and deploy accurate diagnostic tests that can determine whether asymptomatic individuals are actually uninfected, or instead are infected but just do not yet show detectable symptoms.

Background:Understanding changes in infectiousness during SARS-COV-2 infections is critical to assess the effectiveness of public health measures such as contact tracing.Methods:Here, we develop a novel mechanistic approach to infer the infectiousness profile of SARS-COV-2-infected individuals using data from known infector–infectee pairs. We compare estimates of key epidemiological quantities generated using our mechanistic method with analogous estimates generated using previous approaches.Results:The mechanistic method provides an improved fit to data from SARS-CoV-2 infector–infectee pairs compared to commonly used approaches. Our best-fitting model indicates a high proportion of presymptomatic transmissions, with many transmissions occurring shortly before the infector develops symptoms.Conclusions:High infectiousness immediately prior to symptom onset highlights the importance of continued contact tracing until effective vaccines have been distributed widely, even if contacts from a short time window before symptom onset alone are traced.Funding:Engineering and Physical Sciences Research Council (EPSRC).

We derive and validate a novel and analytic method for estimating the probability that an epidemic has been eliminated (i.e. that no future local cases will emerge) in real time. When this probability crosses 0.95 an outbreak can be declared over with 95% confidence. Our method is easy to compute, only requires knowledge of the incidence curve and the serial interval distribution, and evaluates the statistical lifetime of the outbreak of interest. Using this approach, we rigorously show how the time-varying under-reporting of infected cases will artificially inflate the inferred probability of elimination, leading to premature (false-positive) end-of-epidemic declarations. Contrastingly, we prove that incorrectly identifying imported cases as local will deceptively decrease this probability, resulting in delayed (false-negative) declarations. Failing to sustain intensive surveillance during the later phases of an epidemic can therefore substantially mislead policymakers on when it is safe to remove travel bans or relax quarantine and social distancing advisories. World Health Organisation guidelines recommend fixed (though disease-specific) waiting times for end-of-epidemic declarations that cannot accommodate these variations. Consequently, there is an unequivocal need for more active and specialised metrics for reliably identifying the conclusion of an epidemic.

One contribution of 16 to a theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. Subject Areas: computational biology, ecology, health and disease and epidemiology, systems biologyThe World Health Organization considers an Ebola outbreak to have ended once 42 days have passed since the last possible exposure to a confirmed case. Benefits of a quick end-of-outbreak declaration, such as reductions in trade/travel restrictions, must be balanced against the chance of flare-ups from undetected residual cases. We show how epidemiological modelling can be used to estimate the surveillance level required for decision-makers to be confident that an outbreak is over. Results from a simple model characterizing an Ebola outbreak suggest that a surveillance sensitivity (i.e. case reporting percentage) of 79% is necessary for 95% confidence that an outbreak is over after 42 days without symptomatic cases. With weaker surveillance, unrecognized transmission may still occur: if the surveillance sensitivity is only 40%, then 62 days must be waited for 95% certainty. By quantifying the certainty in end-of-outbreak declarations, public health decision-makers can plan and communicate more effectively.This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This issue is linked with the earlier theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

The intuitive response to an invading pathogen is to start disease management as rapidly as possible, since this would be expected to minimise the future impacts of disease. However, since more spread data become available as an outbreak unfolds, processes underpinning pathogen transmission can almost always be characterised more precisely later in epidemics. This allows the future progression of any outbreak to be forecast more accurately, and so enables control interventions to be targeted more precisely. There is also the chance that the outbreak might die out without any intervention whatsoever, making prophylactic control unnecessary. Optimal decision-making involves continuously balancing these potential benefits of waiting against the possible costs of further spread. We introduce a generic, extensible data-driven algorithm based on parameter estimation and outbreak simulation for making decisions in real-time concerning when and how to control an invading pathogen. The Control Smart Algorithm (CSA) resolves the trade-off between the competing advantages of controlling as soon as possible and controlling later when more information has become available. We show–using a generic mathematical model representing the transmission of a pathogen of agricultural animals or plants through a population of farms or fields–how the CSA allows the timing and level of deployment of vaccination or chemical control to be optimised. In particular, the algorithm outperforms simpler strategies such as intervening when the outbreak size reaches a pre-specified threshold, or controlling when the outbreak has persisted for a threshold length of time. This remains the case even if the simpler methods are fully optimised in advance. Our work highlights the potential benefits of giving careful consideration to the question of when to start disease management during emerging outbreaks, and provides a concrete framework to allow policy-makers to make this decision.

As a counter measure to the SARS-CoV-2 pandemic there has been swift development and clinical trial assessment of candidate vaccines, with subsequent deployment as part of mass vaccination campaigns. However, the SARS-CoV-2 virus has demonstrated the ability to mutate and develop variants, which can modify epidemiological properties and the potentially also the effectiveness of vaccines. The widespread deployment of highly effective vaccines may rapidly exert selection pressure on the SARS-CoV-2 virus directed towards mutations that escape the vaccine induced immune response. This is particularly concerning whilst infection is widespread. By developing and analysing a mathematical model of two population groupings with differing vulnerability and contact rates, we explore the impact of the deployment of vaccine amongst the population on R, cases, disease abundance and vaccine escape pressure. The results from this model illustrate two insights (i) vaccination aimed at reducing prevalence could be more effective at reducing disease than directly vaccinating the vulnerable; (ii) the highest risk for vaccine escape can occur at intermediate levels of vaccination. This work demonstrates a key principle that the careful targeting of vaccines towards particular population groups could reduce disease as much as possible whilst limiting the risk of vaccine escape.