Quantifying social distancing arising from pandemic influenza.

Local epidemic curves during the 1918-1919 influenza pandemic were often characterized by multiple epidemic waves. Identifying the underlying cause(s) of such waves may help manage future pandemics. We investigate the hypothesis that these waves were caused by people avoiding potentially infectious contacts-a behaviour termed 'social distancing'. We estimate the effective disease reproduction number and from it infer the maximum degree of social distancing that occurred during the course of the multiple-wave epidemic in Sydney, Australia. We estimate that, on average across the city, people reduced their infectious contact rate by as much as 38%, and that this was sufficient to explain the multiple waves of this epidemic. The basic reproduction number, R0, was estimated to be in the range of 1.6-2.0 with a preferred estimate of 1.8, in line with other recent estimates for the 1918-1919 influenza pandemic. The data are also consistent with a high proportion (more than 90%) of the population being initially susceptible to clinical infection, and the proportion of infections that were asymptomatic (if this occurs) being no higher than approximately 9%. The observed clinical attack rate of 36.6% was substantially lower than the 59% expected based on the estimated value of R0, implying that approximately 22% of the population were spared from clinical infection. This reduction in the clinical attack rate translates to an estimated 260 per 100000 lives having been saved, and suggests that social distancing interventions could play a major role in mitigating the public health impact of future influenza pandemics.     

Estimating reproduction numbers for adults and children from case data

We present a method for estimating reproduction numbers for adults and children from daily onset data, using pandemic influenza A(H1N1) data as a case study. We investigate the impact of different underlying transmission assumptions on our estimates, and identify that asymmetric reproduction matrices are often appropriate. Under-reporting of cases can bias estimates of the reproduction numbers if reporting rates are not equal across the two age groups. However, we demonstrate that the estimate of the higher reproduction number is robust to disproportionate data-thinning. Applying the method to 2009 pandemic influenza H1N1 data from Japan, we demonstrate that the reproduction number for children was considerably higher than that of adults, and that our estimates are insensitive to our choice of reproduction matrix.     

Transmissibility of swine flu at Fort Dix, 1976.

The 1976 outbreak of A/New Jersey/76 influenza in Fort Dix is a rare example of an influenza virus with documented human to human transmission that failed to spread widely. Despite extensive epidemiological investigation, no attempt has been made to quantify the transmissibility of this virus. The World Health Organization and the United States Government view containment of emerging influenza strains as central to combating pandemic influenza. Computational models predict that it may be possible to contain an emergent pandemic influenza if virus transmissibility is low. The A/New Jersey/76 outbreak at the United States Army Training Center at Fort Dix, New Jersey in January 1976 caused 13 hospitalizations, 1 death and an estimated 230 cases. To characterize viral transmission in this epidemic, we estimated the basic reproductive number and serial interval using deterministic epidemic models and stochastic simulations. We estimated the basic reproductive number for this outbreak to be 1.2 (supported interval 1.1-1.4), the serial interval to be 1.9 days (supported interval 1.6-3.8 days), and that the virus had at least six serial human to human transmissions. This places the transmissibility of A/New Jersey/76 virus at the lower end of circulating flu strains, well below the threshold for control.     

Transmission and control of an emerging influenza pandemic in a small-world airline network

The avian influenza virus H5N1 and the 2009 swine flu H1N1 are potentially serious pandemic threats to human health, and air travel readily facilitates the spread of infectious diseases. However, past studies have not yet incorporated the effects of air travel on the transmission of influenza in the construction of mathematical epidemic models. Therefore, this paper focused on the human-to-human transmission of influenza, and investigated the effects of air travel activities on an influenza pandemic in a small-world network. These activities of air travel include passengers’ consolidation, conveyance and distribution in airports and flights. Dynamic transmission models were developed to assess the expected burdens of the pandemic, with and without control measures. This study also investigated how the small-world properties of an air transportation network facilitate the spread of influenza around the globe. The results show that, as soon as the influenza is spread to the top 50 global airports, the transmission is greatly accelerated. Under the constraint of limited resources, a strategy that first applies control measures to the top 50 airports after day 13 and then soon afterwards to all other airports may result in remarkable containment effectiveness. As the infectiousness of the disease increases, it will expand the scale of the pandemic, and move the start time of the pandemic ahead.     

Inferring pandemic growth rates from sequence data

Using sequence data to infer population dynamics is playing an increasing role in the analysis of outbreaks. The most common methods in use, based on coalescent inference, have been widely used but not extensively tested against simulated epidemics. Here, we use simulated data to test the ability of both parametric and non-parametric methods for inference of effective population size (coded in the popular BEAST package) to reconstruct epidemic dynamics. We consider a range of simulations centred on scenarios considered plausible for pandemic influenza, but our conclusions are generic for any exponentially growing epidemic. We highlight systematic biases in non-parametric effective population size estimation. The most prominent such bias leads to the false inference of slowing of epidemic spread in the recent past even when the real epidemic is growing exponentially. We suggest some sampling strategies that could reduce (but not eliminate) some of the biases. Parametric methods can correct for these biases if the infected population size is large. We also explore how some poor sampling strategies (e.g. that over-represent epidemiologically linked clusters of cases) could dramatically exacerbate bias in an uncontrolled manner. Finally, we present a simple diagnostic indicator, based on coalescent density and which can easily be applied to reconstructed phylogenies, that identifies time-periods for which effective population size estimates are less likely to be biased. We illustrate this with an application to the 2009 H1N1 pandemic.     

Forecast the Influenza Pandemic Using Machine Learning

Forecasting future outbreaks can help in minimizing their spread. Influenza is a disease primarily found in animals but transferred to humans through pigs. In 1918, influenza became a pandemic and spread rapidly all over the world becoming the cause behind killing one-third of the human population and killing one-fourth of the pig population. Afterwards, that influenza became a pandemic several times on a local and global levels. In 2009, influenza ‘A’ subtype H1N1 again took many human lives. The disease spread like in a pandemic quickly. This paper proposes a forecasting modeling system for the influenza pandemic using a feed-forward propagation neural network (MSDII-FFNN). This model helps us predict the outbreak, and determines which type of influenza becomes a pandemic, as well as which geographical area is infected. Data collection for the model is done by using IoT devices. This model is divided into 2 phases: The training phase and the validation phase, both being connected through the cloud. In the training phase, the model is trained using FFNN and is updated on the cloud. In the validation phase, whenever the input is submitted through the IoT devices, the system model is updated through the cloud and predicts the pandemic alert. In our dataset, the data is divided into an 85% training ratio and a 15% validation ratio. By applying the proposed model to our dataset, the predicted output precision is 90%.     

A simple criterion to design optimal non-pharmaceutical interventions for mitigating epidemic outbreaks

For mitigating the COVID-19 pandemic, much emphasis is made on implementing non-pharmaceutical interventions to keep the reproduction number below one. However, using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significant economic and societal costs. Here, we derive a simple and mathematically rigorous criterion for designing optimal transitory non-pharmaceutical interventions for mitigating epidemic outbreaks. We find that reducing the reproduction number below one is sufficient but not necessary. Instead, our criterion prescribes the required reduction in the reproduction number according to the desired maximum of disease prevalence and the maximum decrease of disease transmission that the interventions can achieve. We study the implications of our theoretical results for designing non-pharmaceutical interventions in 16 cities and regions during the COVID-19 pandemic. In particular, we estimate the minimal reduction of each region’s contact rate necessary to control the epidemic optimally. Our results contribute to establishing a rigorous methodology to design optimal non-pharmaceutical intervention policies for mitigating epidemic outbreaks.     

A model for the spread and control of pandemic influenza in an isolated geographical region

In the event of an influenza pandemic, the most probable way in which the virus would be introduced to an isolated geographical area is by an infected traveller. We use a mathematical model, structured on the location at which infection occurs and based on published parameters for influenza, to describe an epidemic in a community of one million people. The model is then modified to reflect a variety of control strategies based on social distancing measures, targeted antiviral treatment and antiviral prophylaxis and home quarantine, and the effectiveness of the strategies is compared. The results suggest that the only single strategy that would be successful in preventing an epidemic (with R0=2.0) is targeted antiviral treatment and prophylaxis, and that closing schools combined with either closing work places or home quarantine would only prevent such an epidemic if these strategies were combined with a modest level of antiviral coverage.     

Antiviral treatment for the control of pandemic influenza: some logistical constraints.

Disease control programmes for an influenza pandemic will rely initially on the deployment of antiviral drugs such as Tamiflu, until a vaccine becomes available. However, such control programmes may be severely hampered by logistical constraints such as a finite stockpile of drugs and a limit on the distribution rate. We study the effects of such constraints using a compartmental modelling approach.We find that the most aggressive possible antiviral programme minimizes the final epidemic size, even if this should lead to premature stockpile run-out. Moreover, if the basic reproductive number R(0) is not too high, such a policy can avoid run-out altogether. However, where run-out would occur, such benefits must be weighed against the possibility of a higher epidemic peak than if a more conservative policy were followed.Where there is a maximum number of treatment courses that can be dispensed per day, reflecting a manpower limit on antiviral distribution, our results suggest that such a constraint is unlikely to have a significant impact (i.e. increasing the final epidemic size by more than 10%), as long as drug courses sufficient to treat at least 6% of the population can be dispensed per day.     

Strategies for mitigating an influenza pandemic with pre-pandemic H5N1 vaccines

The recent worldwide spread of the swine-origin H1N1 2009 influenza outbreak has resulted in its designation as a pandemic by the World Health Organization. While it appears to result in mild symptoms, concern still exists that a more severe influenza pandemic with a high case fatality ratio might arise by reassortment or mutation of the currently circulating avian influenza (H5N1) virus. Given that recently developed candidate pre-pandemic H5N1 vaccines have shown potential for cross-strain protection, we investigated alternative vaccination strategies that exploit such vaccines using an agent-based simulation model of an actual community of approximately 30 000 people in a developed country. Assuming that a two-dose vaccination regimen would be required, we examined three vaccination strategies: pre-emptive, with vaccination applied prior to emergence of human-transmissible H5N1 influenza; reactive, where vaccination was initiated immediately after the first cases in the community were diagnosed; and a ‘split’ strategy where the first dose was administered pre-emptively during the pre-pandemic phase, with the second dose administered reactively. We showed that by effectively moving the delay between first and second doses into the pre-pandemic period, the split vaccination strategy achieved a substantially better attack rate reduction than the reactive strategy. Our results for an influenza strain with a reproduction number of 1.5 suggest reactive vaccination strategies that may be applicable to the current H1N1 2009 pandemic.     

The impact of prophylaxis of healthcare workers on influenza pandemic burden.

Several models have rationalized the use of antiviral drugs as an early control measure for delaying the progression and limiting the size of outbreaks during an influenza pandemic. However, the strategy for use of these drugs is still under debate. We evaluated the impact of prophylaxis of healthcare workers (HCWs) through a mathematical model that considers attack rates in a range of 25-35% in the general population and 25-50% among HCWs. Simulations and uncertainty analysis using the demographics of the province of Ontario, Canada show that increasing prophylaxis coverage of HCWs has little impact on reducing the reproduction number of disease transmission and may not prevent the occurrence of an outbreak if expected. However, it does enable a high level of treatment, which substantially reduces morbidity and mortality in the population as a whole. Therefore, prophylaxis of HCWs should be considered an important part of public health efforts for minimizing influenza pandemic burden and its socio-economic disruption.     

Inferring the reproduction number using the renewal equation in heterogeneous epidemics

Real-time estimation of the reproduction number has become the focus of modelling groups around the world as the SARS-CoV-2 pandemic unfolds. One of the most widely adopted means of inference of the reproduction number is via the renewal equation, which uses the incidence of infection and the generation time distribution. In this paper, we derive a multi-type equivalent to the renewal equation to estimate a reproduction number which accounts for heterogeneity in transmissibility including through asymptomatic transmission, symptomatic isolation and vaccination. We demonstrate how use of the renewal equation that misses these heterogeneities can result in biased estimates of the reproduction number. While the bias is small with symptomatic isolation, it can be much larger with asymptomatic transmission or transmission from vaccinated individuals if these groups exhibit substantially different generation time distributions to unvaccinated symptomatic transmitters, whose generation time distribution is often well defined. The bias in estimate becomes larger with greater population size or transmissibility of the poorly characterized group. We apply our methodology to Ebola in West Africa in 2014 and the SARS-CoV-2 in the UK in 2020–2021.     

Spatial dynamics of the 1918 influenza pandemic in England,Wales and the United States

There is still limited understanding of key determinants of spatial spread of influenza. The 1918 pandemic provides an opportunity to elucidate spatial determinants of spread on a large scale.To better characterize the spread of the 1918 major wave, we fitted a range of city-to-city transmission models to mortality data collected for 246 population centres in England and Wales and 47 cities in the US. Using a gravity model for city-to-city contacts, we explored the effect of population size and distance on the spread of disease and tested assumptions regarding density dependence in connectivity between cities. We employed Bayesian Markov Chain Monte Carlo methods to estimate parameters of the model for population, infectivity, distance and density dependence. We inferred the most likely transmission trees for both countries.For England and Wales, a model that estimated the degree of density dependence in connectivity between cities was preferable by deviance information criterion comparison. Early in the major wave, long distance infective interactions predominated, with local infection events more likely as the epidemic became widespread. For the US, with fewer more widely dispersed cities, statistical power was lacking to estimate population size dependence or the degree of density dependence, with the preferred model depending on distance only. We find that parameters estimated from the England and Wales dataset can be applied to the US data with no likelihood penalty.     

The pluses and minuses of R0.

The concept of the basic reproduction number (R0) occupies a central place in epidemic theory. The value of R0 determines the proportion of the population that becomes infected over the course of a (modelled) epidemic. In many models, (i) an endemic infection can persist only if R0>1, (ii) the value of R0 provides a direct measure of the control effort required to eliminate the infection, and (iii) pathogens evolve to maximize their value of R0. These three statements are not universally true. In this paper, some exceptions to them are discussed, based on the extensions of the SIR model.     

The ideal reporting interval for an epidemic to objectively interpret the epidemiological time course

The reporting interval of infectious diseases is often determined as a time unit in the calendar regardless of the epidemiological characteristics of the disease. No guidelines have been proposed to choose the reporting interval of infectious diseases. The present study aims at translating coarsely reported epidemic data into the reproduction number and clarifying the ideal reporting interval to offer detailed insights into the time course of an epidemic. We briefly revisit the dispersibility ratio, i.e. ratio of cases in successive reporting intervals, proposed by Clare Oswald Stallybrass, detecting technical flaws in the historical studies. We derive a corrected expression for this quantity and propose simple algorithms to estimate the effective reproduction number as a function of time, adjusting the reporting interval to the generation time of a disease and demonstrating a clear relationship among the generation-time distribution, reporting interval and growth rate of an epidemic. Our exercise suggests that an ideal reporting interval is the mean generation time, so that the ratio of cases in successive intervals can yield the reproduction number. When it is impractical to report observations every mean generation time, we also present an alternative method that enables us to obtain straightforward estimates of the reproduction number for any reporting interval that suits the practical purpose of infection control.     

Joint modelling of serological and hospitalization data reveals that high levels of pre-existing immunity and school holidays shaped the influenza A pandemic of 2009 in The Netherlands

Obtaining a quantitative understanding of the transmission dynamics of influenza A is important for predicting healthcare demand and assessing the likely impact of intervention measures. The pandemic of 2009 provides an ideal platform for developing integrative analyses as it has been studied intensively, and a wealth of data sources is available. Here, we analyse two complementary datasets in a disease transmission framework: cross-sectional serological surveys providing data on infection attack rates, and hospitalization data that convey information on the timing and duration of the pandemic. We estimate key epidemic determinants such as infection and hospitalization rates, and the impact of a school holiday. In contrast to previous approaches, our novel modelling of serological data with mixture distributions provides a probabilistic classification of individual samples (susceptible, immune and infected), propagating classification uncertainties to the transmission model and enabling serological classifications to be informed by hospitalization data. The analyses show that high levels of immunity among persons 20 years and older provide a consistent explanation of the skewed attack rates observed during the pandemic and yield precise estimates of the probability of hospitalization per infection (1–4 years: 0.00096 (95%CrI: 0.00078–0.0012); 5–19 years: 0.00036 (0.00031–0.0044); 20–64 years: 0.0015 (0.00091–0.0020); 65+ years: 0.0084 (0.0028–0.016)). The analyses suggest that in The Netherlands, the school holiday period reduced the number of infectious contacts between 5- and 9-year-old children substantially (estimated reduction: 54%; 95%CrI: 29–82%), thereby delaying the unfolding of the pandemic in The Netherlands by approximately a week.     

Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study

This paper presents new computational and modelling tools for studying the dynamics of an epidemic in its initial stages that use both available incidence time series and data describing the population''s infection network structure. The work is motivated by data collected at the beginning of the H1N1 pandemic outbreak in Israel in the summer of 2009. We formulated a new discrete-time stochastic epidemic SIR (susceptible-infected-recovered) model that explicitly takes into account the disease''s specific generation-time distribution and the intrinsic demographic stochasticity inherent to the infection process. Moreover, in contrast with many other modelling approaches, the model allows direct analytical derivation of estimates for the effective reproductive number (R_e) and of their credible intervals, by maximum likelihood and Bayesian methods. The basic model can be extended to include age–class structure, and a maximum likelihood methodology allows us to estimate the model''s next-generation matrix by combining two types of data: (i) the incidence series of each age group, and (ii) infection network data that provide partial information of ‘who-infected-who’. Unlike other approaches for estimating the next-generation matrix, the method developed here does not require making a priori assumptions about the structure of the next-generation matrix. We show, using a simulation study, that even a relatively small amount of information about the infection network greatly improves the accuracy of estimation of the next-generation matrix. The method is applied in practice to estimate the next-generation matrix from the Israeli H1N1 pandemic data. The tools developed here should be of practical importance for future investigations of epidemics during their initial stages. However, they require the availability of data which represent a random sample of the real epidemic process. We discuss the conditions under which reporting rates may or may not influence our estimated quantities and the effects of bias.     

Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands

An increasing number of avian flu cases in humans, arising primarily from direct contact with poultry, in several regions of the world have prompted the urgency to develop pandemic preparedness plans worldwide. Leading recommendations in these plans include basic public health control measures for minimizing transmission in hospitals and communities, the use of antiviral drugs and vaccination. This paper presents a mathematical model for the evaluation of the pandemic flu preparedness plans of the United States (US), the United Kingdom (UK) and the Netherlands. The model is used to assess single and combined interventions. Using data from the US, we show that hospital and community transmission control measures alone can be highly effective in reducing the impact of a potential flu pandemic. We further show that while the use of antivirals alone could lead to very significant reductions in the burden of a pandemic, the combination of transmission control measures, antivirals and vaccine gives the most 'optimal' result. However, implementing such an optimal strategy at the onset of a pandemic may not be realistic. Thus, it is important to consider other plausible alternatives. An optimal preparedness plan is largely dependent on the availability of resources; hence, it is country-specific. We show that countries with limited antiviral stockpiles should emphasize their use therapeutically (rather than prophylactically). However, countries with large antiviral stockpiles can achieve greater reductions in disease burden by implementing them both prophylactically and therapeutically. This study promotes alternative strategies that may be feasible and attainable for the US, UK and the Netherlands. It emphasizes the role of hospital and community transmission control measures in addition to the timely administration of antiviral treatment in reducing the burden of a flu pandemic. The latter is consistent with the preparedness plans of the UK and the Netherlands. Our results indicate that for low efficacy and coverage levels of antivirals and vaccine, the use of a vaccine leads to the greatest reduction in morbidity and mortality compared with the singular use of antivirals. However, as these efficacy and coverage levels are increased, the use of antivirals is more effective.     

The relation between fit and prediction for alternative forms of learning curves and relearning curves

Learning-curve models fitted to initial data are used to predict subsequent performance; however, the model that fits the initial data best may not predict best in future periods - a paradox documented in applications of other prediction models. Little evidence exists about the magnitude of the problem in the domain of learning curves and relearning curves. Using laboratory data, the authors examine the predictive ability of alternative models, examine the strength of the relation between goodness-of-fit and predictive ability, and test whether this relation is the same for both learning curves and relearning curves. Although the correlations between measures of goodness-of-fit and predictive ability are not high, one curve (a log-log-linear model recently introduced to the literature) tended to dominate the rankings on the basis of predictive ability for both learning curves and relearning curves. This curve also tended to provide the best fit in the estimation period as a relearning curve, and the second-best fit as a learning curve.     

It wasn't supposed to be a coronavirus: The quest for an influenza A(H5N1)-derived vaccine and the limits of pandemic preparedness

The COVID-19 pandemic has raised questions about what efforts were made across the world to prepare governments and healthcare systems for such an event. This spotlight article looks at developments made in “pre-pandemic preparedness planning” following a number of outbreaks of influenza type A virus in 1997. At that time, a specific avian influenza subtype, referred to as A(H5N1), wreaked havoc among fowl but also infected humans through direct transmission. The potential for slight genetic mutations that could make A(H5N1) more infectious, allowing human-to-human transmission, presented the threat of a deadly influenza pandemic. As a result, the U.S. government (and others coordinating through the World Health Organization) launched a pandemic preparation plan, including strategies to develop vaccines against A(H5N1) and its genetic lineages each year. This spotlight article discusses the events that led to the specific concern about A(H5N1) among public health officials, as well as early efforts to derive and stockpile an appropriate vaccine to protect against a possible pandemic. This perspective presents the challenges the world has faced, in recent history, in striving to keep one step ahead of pandemic threats.