Bayesian Best-Arm Identification for Selecting Influenza Mitigation Strategies

Pandemic influenza has the epidemic potential to kill millions of people. While various preventive measures exist (i.a., vaccination and school closures), deciding on strategies that lead to their most effective and efficient use remains challenging. To this end, individual-based epidemiological models are essential to assist decision makers in determining the best strategy to curb epidemic spread. However, individual-based models are computationally intensive and it is therefore pivotal to identify the optimal strategy using a minimal amount of model evaluations. Additionally, as epidemiological modeling experiments need to be planned, a computational budget needs to be specified a priori. Consequently, we present a new sampling technique to optimize the evaluation of preventive strategies using fixed budget best-arm identification algorithms. We use epidemiological modeling theory to derive knowledge about the reward distribution which we exploit using Bayesian best-arm identification algorithms (i.e., Top-two Thompson sampling and BayesGap). We evaluate these algorithms in a realistic experimental setting and demonstrate that it is possible to identify the optimal strategy using only a limited number of model evaluations, i.e., 2-to-3 times faster compared to the uniform sampling method, the predominant technique used for epidemiological decision making in the literature. Finally, we contribute and evaluate a statistic for Top-two Thompson sampling to inform the decision makers about the confidence of an arm recommendation

The Impact of the Unstructured Contacts Component in Influenza Pandemic Modeling

Individual based models have become a valuable tool for modeling the spatiotemporal dynamics of epidemics, e.g. influenza pandemic, and for evaluating the effectiveness of intervention strategies. While specific contacts among individuals into diverse environments (family, school/workplace) can be modeled in a standard way by employing available socio-demographic data, all the other (unstructured) contacts can be dealt with by adopting very different approaches. This can be achieved for instance by employing distance-based models or by choosing unstructured contacts in the local communities or by employing commuting data.Here we show how diverse choices can lead to different model outputs and thus to a different evaluation of the effectiveness of the containment/mitigation strategies. Sensitivity analysis has been conducted for different values of the first generation index G(0), which is the average number of secondary infections generated by the first infectious individual in a completely susceptible population and by varying the seeding municipality. Among the different considered models, attack rate ranges from 19.1% to 25.7% for G(0) = 1.1, from 47.8% to 50.7% for G(0) = 1.4 and from 62.4% to 67.8% for G(0) = 1.7. Differences of about 15 to 20 days in the peak day have been observed. As regards spatial diffusion, a difference of about 100 days to cover 200 km for different values of G(0) has been observed.To reduce uncertainty in the models it is thus important to employ data, which start being available, on contacts on neglected but important activities (leisure time, sport mall, restaurants, etc.) and time-use data for improving the characterization of the unstructured contacts. Moreover, all the possible effects of different assumptions should be considered for taking public health decisions: not only sensitivity analysis to various model parameters should be performed, but intervention options should be based on the analysis and comparison of different modeling choices

Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees

The spread of infectious diseases crucially depends on the pattern of contacts among individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. Few empirical studies are however available that provide estimates of the number and duration of contacts among social groups. Moreover, their space and time resolution are limited, so that data is not explicit at the person-to-person level, and the dynamical aspect of the contacts is disregarded. Here, we want to assess the role of data-driven dynamic contact patterns among individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population. We consider high resolution data of face-to-face interactions between the attendees of a conference, obtained from the deployment of an infrastructure based on Radio Frequency Identification (RFID) devices that assess mutual face-to-face proximity. The spread of epidemics along these interactions is simulated through an SEIR model, using both the dynamical network of contacts defined by the collected data, and two aggregated versions of such network, in order to assess the role of the data temporal aspects. We show that, on the timescales considered, an aggregated network taking into account the daily duration of contacts is a good approximation to the full resolution network, whereas a homogeneous representation which retains only the topology of the contact network fails in reproducing the size of the epidemic. These results have important implications in understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics

The Waiting Time for Inter-Country Spread of Pandemic Influenza

BACKGROUND: The time delay between the start of an influenza pandemic and its subsequent initiation in other countries is highly relevant to preparedness planning. We quantify the distribution of this random time in terms of the separate components of this delay, and assess how the delay may be extended by non-pharmaceutical interventions. METHODS AND FINDINGS: The model constructed for this time delay accounts for: (i) epidemic growth in the source region, (ii) the delay until an infected individual from the source region seeks to travel to an at-risk country, (iii) the chance that infected travelers are detected by screening at exit and entry borders, (iv) the possibility of in-flight transmission, (v) the chance that an infected arrival might not initiate an epidemic, and (vi) the delay until infection in the at-risk country gathers momentum. Efforts that reduce the disease reproduction number in the source region below two and severe travel restrictions are most effective for delaying a local epidemic, and under favourable circumstances, could add several months to the delay. On the other hand, the model predicts that border screening for symptomatic infection, wearing a protective mask during travel, promoting early presentation of cases arising among arriving passengers and moderate reduction in travel volumes increase the delay only by a matter of days or weeks. Elevated in-flight transmission reduces the delay only minimally. CONCLUSIONS: The delay until an epidemic of pandemic strain influenza is imported into an at-risk country is largely determined by the course of the epidemic in the source region and the number of travelers attempting to enter the at-risk country, and is little affected by non-pharmaceutical interventions targeting these travelers. Short of preventing international travel altogether, eradicating a nascent pandemic in the source region appears to be the only reliable method of preventing country-to-country spread of a pandemic strain of influenza

Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility

On 11 June the World Health Organization officially raised the phase of pandemic alert (with regard to the new H1N1 influenza strain) to level 6. We use a global structured metapopulation model integrating mobility and transportation data worldwide in order to estimate the transmission potential and the relevant model parameters we used the data on the chronology of the 2009 novel influenza A(H1N1). The method is based on the maximum likelihood analysis of the arrival time distribution generated by the model in 12 countries seeded by Mexico by using 1M computationally simulated epidemics. An extended chronology including 93 countries worldwide seeded before 18 June was used to ascertain the seasonality effects. We found the best estimate R0 = 1.75 (95% CI 1.64 to 1.88) for the basic reproductive number. Correlation analysis allows the selection of the most probable seasonal behavior based on the observed pattern, leading to the identification of plausible scenarios for the future unfolding of the pandemic and the estimate of pandemic activity peaks in the different hemispheres. We provide estimates for the number of hospitalizations and the attack rate for the next wave as well as an extensive sensitivity analysis on the disease parameter values. We also studied the effect of systematic therapeutic use of antiviral drugs on the epidemic timeline. The analysis shows the potential for an early epidemic peak occurring in October/November in the Northern hemisphere, likely before large-scale vaccination campaigns could be carried out. We suggest that the planning of additional mitigation policies such as systematic antiviral treatments might be the key to delay the activity peak inorder to restore the effectiveness of the vaccination programs.Comment: Paper: 29 Pages, 3 Figures and 5 Tables. Supplementary Information: 29 Pages, 5 Figures and 7 Tables. Print version: http://www.biomedcentral.com/1741-7015/7/4

Controlling Pandemic Flu: The Value of International Air Travel Restrictions

BACKGROUND: Planning for a possible influenza pandemic is an extremely high priority, as social and economic effects of an unmitigated pandemic would be devastating. Mathematical models can be used to explore different scenarios and provide insight into potential costs, benefits, and effectiveness of prevention and control strategies under consideration. METHODS AND FINDINGS: A stochastic, equation-based epidemic model is used to study global transmission of pandemic flu, including the effects of travel restrictions and vaccination. Economic costs of intervention are also considered. The distribution of First Passage Times (FPT) to the United States and the numbers of infected persons in metropolitan areas worldwide are studied assuming various times and locations of the initial outbreak. International air travel restrictions alone provide a small delay in FPT to the U.S. When other containment measures are applied at the source in conjunction with travel restrictions, delays could be much longer. If in addition, control measures are instituted worldwide, there is a significant reduction in cases worldwide and specifically in the U.S. However, if travel restrictions are not combined with other measures, local epidemic severity may increase, because restriction-induced delays can push local outbreaks into high epidemic season. The per annum cost to the U.S. economy of international and major domestic air passenger travel restrictions is minimal: on the order of 0.8% of Gross National Product. CONCLUSIONS: International air travel restrictions may provide a small but important delay in the spread of a pandemic, especially if other disease control measures are implemented during the afforded time. However, if other measures are not instituted, delays may worsen regional epidemics by pushing the outbreak into high epidemic season. This important interaction between policy and seasonality is only evident with a global-scale model. Since the benefit of travel restrictions can be substantial while their costs are minimal, dismissal of travel restrictions as an aid in dealing with a global pandemic seems premature

Population-Wide Emergence of Antiviral Resistance during Pandemic Influenza

Background: The emergence of neuraminidase inhibitor resistance has raised concerns about the prudent use of antiviral drugs in response to the next influenza pandemic. While resistant strains may initially emerge with compromised viral fitness, mutations that largely compensate for this impaired fitness can arise. Understanding the extent to which these mutations affect the spread of disease in the population can have important implications for developing pandemic plans. Methodology/Principal Findings: By employing a deterministic mathematical model, we investigate possible scenarios for the emergence of population-wide resistance in the presence of antiviral drugs. The results show that if the treatment level (the fraction of clinical infections which receives treatment) is maintained constant during the course of the outbreak, there is an optimal level that minimizes the final size of the pandemic. However, aggressive treatment above the optimal level can substantially promote the spread of highly transmissible resistant mutants and increase the total number of infections. We demonstrate that resistant outbreaks can occur more readily when the spread of disease is further delayed by applying other curtailing measures, even if treatment levels are kept modest. However, by changing treatment levels over the course of the pandemic, it is possible to reduce the final size of the pandemic below the minimum achieved at the optimal constant level. This reduction can occur with low treatment levels during the early stages of the pandemic, followed by a sharp increase in drug-use before the virus becomes widely spread. Conclusions/Significance: Our findings suggest that an adaptive antiviral strategy with conservative initial treatment levels, followed by a timely increase in the scale of drug-use, can minimize the final size of a pandemic while preventing large outbreaks of resistant infections

Estimating the impact of school closure on social mixing behaviour and the transmission of close contact infections in eight European countries

BACKGROUND: Mathematical modelling of infectious disease is increasingly used to help guide public health policy. As directly transmitted infections, such as influenza and tuberculosis, require contact between individuals, knowledge about contact patterns is a necessary pre-requisite of accurate model predictions. Of particular interest is the potential impact of school closure as a means of controlling pandemic influenza (and potentially other pathogens). METHODS: This paper uses a population-based prospective survey of mixing patterns in eight European countries to study the relative change in the basic reproduction number (R0--the average number of secondary cases from a typical primary case in a fully susceptible population) on weekdays versus weekends and during regular versus holiday periods. The relative change in R0 during holiday periods and weekends gives an indication of the impact collective school closures (and prophylactic absenteeism) may have during a pandemic. RESULTS: Social contact patterns differ substantially when comparing weekdays to the weekend and regular to holiday periods mainly due to the reduction in work and/or school contacts. For most countries the basic reproduction number decreases from the week to weekends and regular to holiday periods by about 21% and 17%, respectively. However for other countries no significant decrease was observed. CONCLUSION: We use a large-scale social contact survey in eight different European countries to gain insights in the relative change in the basic reproduction number on weekdays versus weekends and during regular versus holiday periods. The resulting estimates indicate that school closure can have a substantial impact on the spread of a newly emerging infectious disease that is transmitted via close (non sexual) contacts

Age groups and spread of influenza: implications for vaccination strategy

<p>Abstract</p> <p>Background</p> <p>The unpredictable nature of the potentially devastating impact of 2009 pH1N1 influenza pandemic highlights the need for pandemic preparedness planning, where modeling studies could be most useful for simulations of possible future scenarios.</p> <p>Methods</p> <p>A compartmental model with pre-symptomatic and asymptomatic influenza infections is proposed which incorporates age groups as well as intervention measures such as age-specific vaccination, in order to study spread of influenza in a community.</p> <p>Results</p> <p>We derive the basic reproduction number and other effective reproduction numbers under various intervention measures. For illustration, we make use of the Pneumonia and Influenza (P&I) mortality data and vaccination data of the very young (age 0-2) and the very old (age >64) during 2004-2005 Taiwan winter influenza season to fit our model and to compute the relevant reproduction numbers. The reproduction number for this winter flu season is estimated to be slightly above one (~1.0001).</p> <p>Conclusions</p> <p>Comparatively large errors in fitting the P&I mortality data of the elderly (>64) were observed shortly after winter school closings in January, which may indicate the impact of younger, more active age groups transmitting influenza to other age groups outside of the school settings; in particular, to the elderly in the households. Pre-symptomatic infections seemed to have little effect on the model fit, while asymptomatic infection by asymptomatic infectives has a more pronounced impact on the model fit for the elderly mortality, perhaps indicating a larger role in disease transmission by asymptomatic infection. Simulations indicate that the impact of vaccination on the disease incidence might not be fully revealed in the change (or the lack thereof) in the effective reproduction number with interventions, but could still be substantial. The estimated per contact transmission probability for susceptible elderly is significantly higher than that of any other age group, perhaps highlighting the vulnerability of the elderly due to close contacts with their caretakers from other age groups. The relative impact of targeting the very young and the very old for vaccination was weakened by their relative inactivity, thus giving evidence of the lack of impact of vaccinating these two groups on the overall transmissibility of the disease in the community. This further underscores the need for morbidity-based strategy to prevent elderly mortality.</p