Potential Impact of Antiviral Drug Use during Influenza Pandemic

Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review

Please cite this paper as: Boëlle P‐Y et al. (2011) Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review. Influenza and Other Respiratory Viruses 5(5), 306–316.

Background  The new influenza virus A/H1N1 (2009), identified in mid‐2009, rapidly spread over the world. Estimating the transmissibility of this new virus was a public health priority.

Methods  We reviewed all studies presenting estimates of the serial interval or generation time and the reproduction number of the A/H1N1 (2009) virus infection.

Results  Thirteen studies documented the serial interval from household or close‐contact studies, with overall mean 3 days (95% CI: 2·4, 3·6); taking into account tertiary transmission reduced this estimate to 2·6 days. Model‐based estimates were more variable, from 1·9 to 6 days. Twenty‐four studies reported reproduction numbers for community‐based epidemics at the town or country level. The range was 1·2–3·1, with larger estimates reported at the beginning of the pandemic. Accounting for under‐reporting in the early period of the pandemic and limiting variation because of the choice of the generation time interval, the reproduction number was between 1·2 and 2·3 with median 1·5.

Discussion  The serial interval of A/H1N1 (2009) flu was typically short, with mean value similar to the seasonal flu. The estimates of the reproduction number were more variable. Compared with past influenza pandemics, the median reproduction number was similar (1968) or slightly smaller (1889, 1918, 1957).

Public health interventions for epidemics: implications for multiple infection waves

BACKGROUND

Epidemics with multiple infection waves have been documented for some human diseases, most notably during past influenza pandemics. While pathogen evolution, co-infection, and behavioural changes have been proposed as possible mechanisms for the occurrence of subsequent outbreaks, the effect of public health interventions remains undetermined.

METHODS

We develop mean-field and stochastic epidemiological models for disease transmission, and perform simulations to show how control measures, such as drug treatment and isolation of ill individuals, can influence the epidemic profile and generate sequences of infection waves with different characteristics.

RESULTS

We demonstrate the impact of parameters representing the effectiveness and adverse consequences of intervention measures, such as treatment and emergence of drug resistance, on the spread of a pathogen in the population. If pathogen resistant strains evolve under drug pressure, multiple outbreaks are possible with variability in their characteristics, magnitude, and timing. In this context, the level of drug use and isolation capacity play an important role in the occurrence of subsequent outbreaks. Our simulations for influenza infection as a case study indicate that the intensive use of these interventions during the early stages of the epidemic could delay the spread of disease, but it may also result in later infection waves with possibly larger magnitudes.

CONCLUSIONS

The findings highlight the importance of intervention parameters in the process of public health decision-making, and in evaluating control measures when facing substantial uncertainty regarding the epidemiological characteristics of an emerging infectious pathogen. Critical factors that influence population health including evolutionary responses of the pathogen under the pressure of different intervention measures during an epidemic should be considered for the design of effective strategies that address short-term targets compatible with long-term disease outcomes.

The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale

BACKGROUND

Computational models play an increasingly important role in the assessment and control of public health crises, as demonstrated during the 2009 H1N1 influenza pandemic. Much research has been done in recent years in the development of sophisticated data-driven models for realistic computer-based simulations of infectious disease spreading. However, only a few computational tools are presently available for assessing scenarios, predicting epidemic evolutions, and managing health emergencies that can benefit a broad audience of users including policy makers and health institutions.

RESULTS

We present "GLEaMviz", a publicly available software system that simulates the spread of emerging human-to-human infectious diseases across the world. The GLEaMviz tool comprises three components: the client application, the proxy middleware, and the simulation engine. The latter two components constitute the GLEaMviz server. The simulation engine leverages on the Global Epidemic and Mobility (GLEaM) framework, a stochastic computational scheme that integrates worldwide high-resolution demographic and mobility data to simulate disease spread on the global scale. The GLEaMviz design aims at maximizing flexibility in defining the disease compartmental model and configuring the simulation scenario; it allows the user to set a variety of parameters including: compartment-specific features, transition values, and environmental effects. The output is a dynamic map and a corresponding set of charts that quantitatively describe the geo-temporal evolution of the disease. The software is designed as a client-server system. The multi-platform client, which can be installed on the user's local machine, is used to set up simulations that will be executed on the server, thus avoiding specific requirements for large computational capabilities on the user side.

CONCLUSIONS

The user-friendly graphical interface of the GLEaMviz tool, along with its high level of detail and the realism of its embedded modeling approach, opens up the platform to simulate realistic epidemic scenarios. These features make the GLEaMviz computational tool a convenient teaching/training tool as well as a first step toward the development of a computational tool aimed at facilitating the use and exploitation of computational models for the policy making and scenario analysis of infectious disease outbreaks.

A note on the use of influenza vaccination strategies when supply is limited

The 2009 A (H1N1) influenza pandemic was rather atypical. It began in North America at the start of the spring and in the following months, as it moved south, efforts to develop a vaccine that would mitigate the potential impact of a second wave were accelerated. The world's limited capacity to produce an adequate vaccine supply over just a few months resulted in the development of public health policies that "had" to optimize the utilization of limited vaccine supplies. Furthermore, even after the vaccine was in production, extensive delays in vaccine distribution were experienced for various reasons. In this note, we use optimal control theory to explore the impact of some of the constraints faced by most nations in implementing a public health policy that tried to meet the challenges that come from having access only to a limited vaccine supply that is never 100% effective.

Healthcare system cost evaluation of antiviral stockpiling for pandemic influenza preparedness

Healthcare workers need to be protected during a severe influenza outbreak; therefore, we evaluated 4 different antiviral strategies: (1) using antiviral medication for outbreak prophylaxis of all hospital employees; (2) using antiviral medication for postexposure prophylaxis (PEP) or treatment of all hospital employees; (3) using a combination of antiviral medication for outbreak prophylaxis of high-risk clinical staff and postexposure prophylaxis or treatment for all other staff; and (4) using antiviral medication for postexposure prophylaxis or treatment of high-risk clinical staff only. Three different purchasing options were applied to each of the 4 antiviral strategies: (1) just-in-time purchase during a severe influenza outbreak, (2) prepandemic stockpiling, or (3) stockpiling through contracts with pharmaceutical manufacturers to reserve a predetermined antiviral supply. Although outbreak prophylaxis of all hospital employees would offer the maximum protection, the large costs associated with such a purchase make this option unrealistic and impractical. In addition, even though postexposure prophylaxis or treatment of only high-risk clinical staff would incur the least expense, the assumed level of protection if these options were offered only to high-risk clinical staff may not be sufficient to maintain routine hospital operations, since needed non-high-risk staff would not be protected. Considering the potential benefits and drawbacks of stockpiling antiviral medication from a cost perspective, it does not appear feasible for hospitals to stockpile antiviral medication in large quantities prior to a severe influenza outbreak. This article focuses on the financial viability of stockpiling antiviral medication, but the potential impact of other factors on the decision to stockpile was also considered and will be explored in future analyses. While legal hurdles related to prescribing, storing, and dispensing antiviral medication can be addressed, unavailability of a suitable vaccine supply may strongly support a decision to stockpile antiviral medication. Other issues to be addressed include antiviral resistance specifically related to the efficacy of oseltamivir, coupled with a high frequency of secondary bacterial infections; uncertainties about the degree of government assistance; potential government seizures of stockpiled assets; and legal and ethical concerns related to fair access to stockpiled medication. These issues may all be perceived as barriers to the feasibility of stockpiling antiviral medication.

Influenza pandemic waves under various mitigation strategies with 2009 H1N1 as a case study

A significant feature of influenza pandemics is multiple waves of morbidity and mortality over a few months or years. The size of these successive waves depends on intervention strategies including antivirals and vaccination, as well as the effects of immunity gained from previous infection. However, the global vaccine manufacturing capacity is limited. Also, antiviral stockpiles are costly and thus, are limited to very few countries. The combined effect of antivirals and vaccination in successive waves of a pandemic has not been quantified. The effect of acquired immunity from vaccination and previous infection has also not been characterized. In times of a pandemic threat countries must consider the effects of a limited vaccine, limited antiviral use and the effects of prior immunity so as to adopt a pandemic strategy that will best aid the population. We developed a mathematical model describing the first and second waves of an influenza pandemic including drug therapy, vaccination and acquired immunity. The first wave model includes the use of antiviral drugs under different treatment profiles. In the second wave model the effects of antivirals, vaccination and immunity gained from the first wave are considered. The models are used to characterize the severity of infection in a population under different drug therapy and vaccination strategies, as well as school closure, so that public health policies regarding future influenza pandemics are better informed.

The dynamics of an epidemic model with targeted antiviral prophylaxis

Due to the increasing risk of drug resistance and side effects with large-scale antiviral use, it has been suggested to provide antiviral drugs only to susceptibles who have had contacts with infectives. This antiviral distribution strategy is referred to as 'targeted antiviral prophylaxis'. The question of how effective this strategy is in infection control is of great public heath interest. In this paper, we formulate an ordinary differential equation model to describe the transmission dynamics of infectious disease with targeted antiviral prophylaxis, and provide the analysis of dynamical behaviours of the model. The control reproduction number R(c) is derived and shown to govern the disease dynamics, and the stability analysis is carried out. The local bifurcation theory is applied to explore the variety of dynamics of the model. Our theoretical results show that the system undergoes two Hopf bifurcations due to the existence of multiple endemic equilibria and the switch of their stability. Numerical results demonstrate that the system may have more complex dynamical behaviours including multiple periodic solutions and a homoclinic orbit. The results of this study suggest that the possibility of complex disease dynamics can be driven by the use of targeted antiviral prophylaxis, and the critical level of prophylaxis which achieves ℛ(c)=1 is not enough to control the prevalence of a disease.

Global migration dynamics underlie evolution and persistence of human influenza A (H3N2)

The global migration patterns of influenza viruses have profound implications for the evolutionary and epidemiological dynamics of the disease. We developed a novel approach to reconstruct the genetic history of human influenza A (H3N2) collected worldwide over 1998 to 2009 and used it to infer the global network of influenza transmission. Consistent with previous models, we find that China and Southeast Asia lie at the center of this global network. However, we also find that strains of influenza circulate outside of Asia for multiple seasons, persisting through dynamic migration between northern and southern regions. The USA acts as the primary hub of temperate transmission and, together with China and Southeast Asia, forms the trunk of influenza's evolutionary tree. These findings suggest that antiviral use outside of China and Southeast Asia may lead to the evolution of long-term local and potentially global antiviral resistance. Our results might also aid the design of surveillance efforts and of vaccines better tailored to different geographic regions.

Optimal vaccine stockpile design for an eradicated disease: application to polio

Eradication of a disease promises significant health and financial benefits. Preserving those benefits, hopefully in perpetuity, requires preparing for the possibility that the causal agent could re-emerge (unintentionally or intentionally). In the case of a vaccine-preventable disease, creation and planning for the use of a vaccine stockpile becomes a primary concern. Doing so requires consideration of the dynamics at different levels, including the stockpile supply chain and transmission of the causal agent. This paper develops a mathematical framework for determining the optimal management of a vaccine stockpile over time. We apply the framework to the polio vaccine stockpile for the post-eradication era and present examples of solutions to one possible framing of the optimization problem. We use the framework to discuss issues relevant to the development and use of the polio vaccine stockpile, including capacity constraints, production and filling delays, risks associated with the stockpile, dynamics and uncertainty of vaccine needs, issues of funding, location, and serotype dependent behavior, and the implications of likely changes over time that might occur. This framework serves as a helpful context for discussions and analyses related to the process of designing and maintaining a stockpile for an eradicated disease.

Optimal control for pandemic influenza: the role of limited antiviral treatment and isolation

The implementation of optimal control strategies involving antiviral treatment and/or isolation measures can reduce significantly the number of clinical cases of influenza. Pandemic-level control measures must be carefully assessed specially in resource-limited situations. A model for the transmission dynamics of influenza is used to evaluate the impact of isolation and/or antiviral drug delivery measures during an influenza pandemic. Five pre-selected control strategies involving antiviral treatment and isolation are tested under the "unlimited" resource assumption followed by an exploration of the impact of these "optimal" policies when resources are limited in the context of a 1918-type influenza pandemic scenario. The implementation of antiviral treatment at the start of a pandemic tends to reduce the magnitude of epidemic peaks, spreading the maximal impact of an outbreak over an extended window in time. Hence, the controls' timing and intensity can reduce the pressures placed on the health care infrastructure by a pandemic reducing the stress put on the system during epidemic peaks. The role of isolation strategies is highlighted in this study particularly when access to antiviral resources is limited.

Estimating influenza-related excess mortality and reproduction numbers for seasonal influenza in Norway, 1975-2004

Influenza can be a serious, sometimes deadly, disease, especially for people in high-risk groups such as the elderly and patients with underlying, severe disease. In this paper we estimated the influenza-related excess mortality in Norway for 1975-2004, comparing it with dominant virus types and estimates of the reproduction number. Analysis was done using Poisson regression, explaining the weekly all-cause mortality by rates of reported influenza-like illness, together with markers for seasonal and year-to-year variation. The estimated excess mortality was the difference between the observed and predicted mortality, removing the influenza contribution from the prediction. We estimated the overall influenza-related excess mortality as 910 deaths per season, or 2.08% of the overall deaths. Age-grouped analyses indicated that the major part of the excess mortality occurred in the > or =65 years age group, but that there was also a significant contribution to mortality in the 0-4 years age group. Estimates of the reproduction number R, ranged from about 1 to 1.69.

The shifting demographic landscape of pandemic influenza

BACKGROUND

As Pandemic (H1N1) 2009 influenza spreads around the globe, it strikes school-age children more often than adults. Although there is some evidence of pre-existing immunity among older adults, this alone may not explain the significant gap in age-specific infection rates.

METHODS AND FINDINGS

Based on a retrospective analysis of pandemic strains of influenza from the last century, we show that school-age children typically experience the highest attack rates in primarily naive populations, with the burden shifting to adults during the subsequent season. Using a parsimonious network-based mathematical model which incorporates the changing distribution of contacts in the susceptible population, we demonstrate that new pandemic strains of influenza are expected to shift the epidemiological landscape in exactly this way.

CONCLUSIONS

Our analysis provides a simple demographic explanation for the age bias observed for H1N1/09 attack rates, and suggests that this bias may shift in coming months. These results have significant implications for the allocation of public health resources for H1N1/09 and future influenza pandemics.

Absolute humidity and the seasonal onset of influenza in the continental United States

Much of the observed wintertime increase of mortality in temperate regions is attributed to seasonal influenza. A recent reanalysis of laboratory experiments indicates that absolute humidity strongly modulates the airborne survival and transmission of the influenza virus. Here, we extend these findings to the human population level, showing that the onset of increased wintertime influenza-related mortality in the United States is associated with anomalously low absolute humidity levels during the prior weeks. We then use an epidemiological model, in which observed absolute humidity conditions temper influenza transmission rates, to successfully simulate the seasonal cycle of observed influenza-related mortality. The model results indicate that direct modulation of influenza transmissibility by absolute humidity alone is sufficient to produce this observed seasonality. These findings provide epidemiological support for the hypothesis that absolute humidity drives seasonal variations of influenza transmission in temperate regions.

Estimates of the transmissibility of the 1968 (Hong Kong) influenza pandemic: evidence of increased transmissibility between successive waves

The transmissibility of the strain of influenza virus which caused the 1968 influenza pandemic is poorly understood. Increases in outbreak size between the first and second waves suggest that it may even have increased between successive waves. The authors estimated basic and effective reproduction numbers for both waves of the 1968 influenza pandemic. Epidemic curves and overall attack rates for the 1968 pandemic, based on clinical and serologic data, were retrieved from published literature. The basic and effective reproduction numbers were estimated from 46 and 17 data sets for the first and second waves, respectively, based on the growth rate and/or final size of the epidemic. Estimates of the basic reproduction number (R₀) were in the range of 1.06–2.06 for the first wave and, assuming cross-protection, 1.21–3.58 in the second. Within each wave, there was little geographic variation in transmissibility. In the 10 settings for which data were available for both waves, R₀ was estimated to be higher during the second wave than during the first. This might partly explain the larger outbreaks in the second wave as compared with the first. This potential for change in viral behavior may have consequences for future pandemic mitigation strategies.

Nurses' contacts and potential for infectious disease transmission

These data can help predict staff availability and provide information for pandemic preparedness planning.

Nurses’ contacts with potentially infectious persons probably place them at higher risk than the general population for infectious diseases. During an influenza pandemic, illness among nurses might result in staff shortage. We aimed to show the value of individual data from the healthcare sector for mathematical modeling of infectious disease transmission. Using a paper diary approach, we compared nurses’ daily contacts (2-way conversation with >2 words or skin-to-skin contact) with those of matched controls from a representative population survey. Nurses (n = 129) reported a median of 40 contacts (85% work related), and controls (n = 129) reported 12 contacts (33% work related). For nurses, 51% of work-related contacts were with patients (74% involving skin-to-skin contact, and 63% lasted <15 minutes); 40% were with staff members (29% and 36%, respectively). Our data, used with simulation models, can help predict staff availability and provide information for pandemic preparedness planning.

Absolute Humidity and the Seasonal Onset of Influenza in the Continental US

Much of the observed wintertime increase of mortality in temperate regions is attributed to seasonal influenza. A recent re-analysis of laboratory experiments indicates that absolute humidity strongly modulates the airborne survival and transmission of the influenza virus. Here we extend these findings to the human population level, showing that the onset of increased wintertime influenza-related mortality in the United States is associated with anomalously low absolute humidity levels during the prior weeks. We then use an epidemiological model, in which observed absolute humidity conditions temper influenza transmission rates, to successfully simulate the seasonal cycle of observed influenza-related mortality. The model results indicate that direct modulation of influenza transmissibility by absolute humidity alone is sufficient to produce this observed seasonality. These findings provide epidemiological support for the hypothesis that absolute humidity drives seasonal variations of influenza transmission in temperate regions.

Modeling the critical care demand and antibiotics resources needed during the Fall 2009 wave of influenza A(H1N1) pandemic

While the H1N1 pandemic is reaching high levels of influenza activity in the Northern Hemisphere, the attention focuses on the ability of national health systems to respond to the expected massive influx of additional patients. Given the limited capacity of health care providers and hospitals and the limited supplies of antibiotics, it is important to predict the potential demand on critical care to assist planning for the management of resources and plan for additional stockpiling. We develop a disease model that considers the development of influenza-associated complications and incorporate it into a global epidemic model to assess the expected surge in critical care demands due to viral and bacterial pneumonia. Based on the most recent estimates of complication rates, we predict the expected peak number of intensive care unit beds and the stockpile of antibiotic courses needed for the current pandemic wave. The effects of dynamic vaccination campaigns, and of variations of the relative proportion of bacterial co-infection in complications and different length of staying in the intensive care unit are explored.

Post-exposure prophylaxis during pandemic outbreaks

BACKGROUND

With the rise of the second pandemic wave of the novel influenza A (H1N1) virus in the current season in the Northern Hemisphere, pandemic plans are being carefully re-evaluated, particularly for the strategic use of antiviral drugs. The recent emergence of oseltamivir-resistant in treated H1N1 patients has raised concerns about the prudent use of neuraminidase inhibitors for both treatment of ill individuals and post-exposure prophylaxis of close contacts.

METHODS

We extended an established population dynamical model of pandemic influenza with treatment to include post-exposure prophylaxis of close contacts. Using parameter estimates published in the literature, we simulated the model to evaluate the combined effect of treatment and prophylaxis in minimizing morbidity and mortality of pandemic infections in the context of transmissible drug resistance.

RESULTS

We demonstrated that, when transmissible resistant strains are present, post-exposure prophylaxis can promote the spread of resistance, especially when combined with aggressive treatment. For a given treatment level, there is an optimal coverage of prophylaxis that minimizes the total number of infections (final size) and this coverage decreases as a higher proportion of infected individuals are treated. We found that, when treatment is maintained at intermediate levels, limited post-exposure prophylaxis provides an optimal strategy for reducing the final size of the pandemic while minimizing the total number of deaths. We tested our results by performing a sensitivity analysis over a range of key model parameters and observed that the incidence of infection depends strongly on the transmission fitness of resistant strains.

CONCLUSION

Our findings suggest that, in the presence of transmissible drug resistance, strategies that prioritize the treatment of only ill individuals, rather than the prophylaxis of those suspected of being exposed, are most effective in reducing the morbidity and mortality of the pandemic. The impact of post-exposure prophylaxis depends critically on the treatment level and the transmissibility of resistant strains and, therefore, enhanced surveillance and clinical monitoring for resistant mutants constitutes a key component of any comprehensive plan for antiviral drug use during an influenza pandemic.

Influenza--insights from mathematical modelling

BACKGROUND

When the first cases of a new infectious disease appear, questions arise about the further course of the epidemic and about the appropriate interventions to be taken to protect individuals and the public as a whole. Mathematical models can help answer these questions. In this article, the authors describe basic concepts in the mathematical modelling of infectious diseases, illustrate their use with a simple example, and present the results of influenza models.

METHOD

Description of the mathematical modelling of infectious diseases and selective review of the literature.

RESULTS

The two fundamental concepts of mathematical modelling of infectious diseases-the basic reproduction number and the generation time-allow a better understanding of the course of an epidemic. Modelling studies based on past influenza epidemics suggest that the rise of the epidemic curve can be slowed at the beginning of the epidemic by isolating ill persons and giving prophylactic medications to their contacts. Later on in the course of the epidemic, restricting the number of contacts (e.g., by closing schools) may mitigate the epidemic but will only have a limited effect on the total number of persons who contract the disease.

CONCLUSION

Mathematical modelling is a valuable tool for understanding the dynamics of an epidemic and for planning and evaluating interventions.

Modeling vaccination campaigns and the Fall/Winter 2009 activity of the new A(H1N1) influenza in the Northern Hemisphere

The unfolding of pandemic influenza A(H1N1) for Fall 2009 in the Northern Hemisphere is still uncertain. Plans for vaccination campaigns and vaccine trials are underway, with the first batches expected to be available early October. Several studies point to the possibility of an anticipated pandemic peak that could undermine the effectiveness of vaccination strategies. Here, we use a structured global epidemic and mobility metapopulation model to assess the effectiveness of massive vaccination campaigns for the Fall/Winter 2009. Mitigation effects are explored depending on the interplay between the predicted pandemic evolution and the expected delivery of vaccines. The model is calibrated using recent estimates on the transmissibility of the new A(H1N1) influenza. Results show that if additional intervention strategies were not used to delay the time of pandemic peak, vaccination may not be able to considerably reduce the cumulative number of cases, even when the mass vaccination campaign is started as early as mid-October. Prioritized vaccination would be crucial in slowing down the pandemic evolution and reducing its burden.

The shifting demographic landscape of influenza

BACKGROUND

As Pandemic (H1N1) 2009 influenza spreads around the globe, it strikes school-age children more often than adults. Although there is some evidence of pre-existing immunity among older adults, this alone may not explain the significant gap in age-specific infection rates.

METHODS & FINDINGS

Based on a retrospective analysis of pandemic strains of influenza from the last century, we show that school-age children typically experience the highest attack rates in primarily naive populations, with the burden shifting to adults during the subsequent season. Using a parsimonious network-based mathematical model which incorporates the changing distribution of contacts in the susceptible population, we demonstrate that new pandemic strains of influenza are expected to shift the epidemiological landscape in exactly this way.

CONCLUSIONS

Our results provide a simple demographic explanation for the age bias observed for H1N1/09 attack rates, and a prediction that this bias will shift in coming months. These results also have significant implications for the allocation of public health resources including vaccine distribution policies.

The representativeness of sentinel practice networks

BACKGROUND

The representativeness of practice networks is important when using the information obtained to guide health policy.

AIM

To develop a model for examining the representativeness of practice networks.

METHODS

Comparison of surveyed population, practice structure and prescribing characteristics with the national data using the Weekly Returns Service (WRS) for 2006 as an example of practice network. The population monitored was compared with the national PCT population. The practice postcode was linked to the Index of Multiple Deprivation and the distribution compared with the national equivalents. Doctor and practice-specific structural data (obtained by questionnaire) and practice-prescribing data were compared with the national equivalents. The significance of differences was evaluated using non-parametric tests.

RESULTS

The WRS population was closely matched with the national data by age, gender and deprivation index. Compared with the national equivalents, WRS practices, included more younger GPs, had a larger average list per GP and fewer practices with a list of less than 1499 per GP. Prescribing patterns were similar to their PCT equivalents excepting for small reductions of antibacterial prescribing (items 7% and cost 5%).

CONCLUSION

We demonstrate a low-cost model methodology for examining the representativeness of practice networks using independent data with minimum practice input.

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

BACKGROUND

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. As of 19 July, 137,232 cases of the H1N1 influenza strain have been officially confirmed in 142 different countries, and the pandemic unfolding in the Southern hemisphere is now under scrutiny to gain insights about the next winter wave in the Northern hemisphere. A major challenge is pre-emptied by the need to estimate the transmission potential of the virus and to assess its dependence on seasonality aspects in order to be able to use numerical models capable of projecting the spatiotemporal pattern of the pandemic.

METHODS

In the present work, we use a global structured metapopulation model integrating mobility and transportation data worldwide. The model considers data on 3,362 subpopulations in 220 different countries and individual mobility across them. The model generates stochastic realizations of the epidemic evolution worldwide considering 6 billion individuals, from which we can gather information such as prevalence, morbidity, number of secondary cases and number and date of imported cases for each subpopulation, all with a time resolution of 1 day. 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 1 million computationally simulated epidemics. An extended chronology including 93 countries worldwide seeded before 18 June was used to ascertain the seasonality effects.

RESULTS

We found the best estimate R0 = 1.75 (95% confidence interval (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.

CONCLUSION

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. The baseline results refer to a worst-case scenario in which additional mitigation policies are not considered. We suggest that the planning of additional mitigation policies such as systematic antiviral treatments might be the key to delay the activity peak in order to restore the effectiveness of the vaccination programs.

Qualitative analysis of the level of cross-protection between epidemic waves of the 1918-1919 influenza pandemic

The 1918-1919 influenza pandemic was composed of multiple waves within a period of nine months in several regions of the world. Increasing our understanding of the mechanisms responsible for this multi-wave profile has important public health implications. We model the transmission dynamics of two strains of influenza interacting via cross-immunity to simulate two temporal waves of influenza and explore the impact of the basic reproduction number, as a measure of transmissibility associated to each influenza strain, cross-immunity and the timing of the onset of the second influenza epidemic on the pandemic profile. We use time series of case notifications during the 1918 influenza pandemic in Geneva, Switzerland, for illustration. We calibrate our mathematical model to the initial wave of infection to estimate the basic reproduction number of the first wave and the corresponding timing of onset of the second influenza variant. We use this information to explore the impact of cross-immunity levels on the dynamics of the second wave of influenza. Our results for the 1918 pandemic in Geneva, Switzerland, indicate that a second wave can occur whenever R 01 < 1.5 or when cross-immunity levels are less than 0.58 for our estimated R 02 of 2.4. We also explore qualitatively profiles of two-wave pandemics and compare them with real temporal profiles of the 1918 influenza pandemic in other regions of the world including several Scandinavian cities, New York City, England and Wales, and Sydney, Australia. Pandemic profiles are classified into three broad categories namely "right-handed", "left-handed", and "M-shape". Our results indicate that avoiding a second influenza epidemic is plausible given sufficient levels of cross-protection are attained via natural infection during an early (herald) wave of infection or vaccination campaigns prior to a second wave. Furthermore, interventions aimed at mitigating the first pandemic wave may be counterproductive by increasing the chances of a second wave of infection that could potentially be more virulent than the first.

A comparative evaluation of modelling strategies for the effect of treatment and host interactions on the spread of drug resistance

The evolutionary responses of infectious pathogens often have ruinous consequences for the control of disease spread in the population. Drug resistance is a well-documented instance that is generally driven by the selective pressure of drugs on both the replication of the pathogen within hosts and its transmission between hosts. Management of drug resistance therefore requires the development of treatment strategies that can impede the emergence and spread of resistance in the population. This study evaluates various treatment strategies for influenza infection as a case study by comparing the long-term epidemiological outcomes predicted by deterministic and stochastic versions of a homogeneously mixing (mean-field) model and those predicted by a heterogeneous model that incorporates spatial pair-wise correlation. We discuss the importance of three major parameters in our evaluation: the basic reproduction number, the population level of treatment, and the degree of clustering as a key parameter determining the structure of heterogeneous interactions. The results show that, as a common feature in all models, high treatment levels during the early stages of disease outset can result in large resistant outbreaks, with the possibility of a second wave of infection appearing in the pair-approximation model. Our simulations demonstrate that, if the basic reproduction number exceeds a threshold value, the population-wide spread of the resistant pathogen emerges more rapidly in the pair-approximation model with significantly lower treatment levels than in the homogeneous models. We tested an antiviral strategy that delays the onset of aggressive treatment for a certain amount of time after the onset of the outbreak. The findings indicate that the overall disease incidence is reduced as the degree of clustering increases, and a longer delay should be considered for implementing the large-scale treatment.

Models of epidemics: when contact repetition and clustering should be included

BACKGROUND

The spread of infectious disease is determined by biological factors, e.g. the duration of the infectious period, and social factors, e.g. the arrangement of potentially contagious contacts. Repetitiveness and clustering of contacts are known to be relevant factors influencing the transmission of droplet or contact transmitted diseases. However, we do not yet completely know under what conditions repetitiveness and clustering should be included for realistically modelling disease spread.

METHODS

We compare two different types of individual-based models: One assumes random mixing without repetition of contacts, whereas the other assumes that the same contacts repeat day-by-day. The latter exists in two variants, with and without clustering. We systematically test and compare how the total size of an outbreak differs between these model types depending on the key parameters transmission probability, number of contacts per day, duration of the infectious period, different levels of clustering and varying proportions of repetitive contacts.

RESULTS

The simulation runs under different parameter constellations provide the following results: The difference between both model types is highest for low numbers of contacts per day and low transmission probabilities. The number of contacts and the transmission probability have a higher influence on this difference than the duration of the infectious period. Even when only minor parts of the daily contacts are repetitive and clustered can there be relevant differences compared to a purely random mixing model.

CONCLUSION

We show that random mixing models provide acceptable estimates of the total outbreak size if the number of contacts per day is high or if the per-contact transmission probability is high, as seen in typical childhood diseases such as measles. In the case of very short infectious periods, for instance, as in Norovirus, models assuming repeating contacts will also behave similarly as random mixing models. If the number of daily contacts or the transmission probability is low, as assumed for MRSA or Ebola, particular consideration should be given to the actual structure of potentially contagious contacts when designing the model.

Simple models for containment of a pandemic

Stochastic simulations of network models have become the standard approach to studying epidemics. We show that many of the predictions of these models can also be obtained from simple classical deterministic compartmental models. We suggest that simple models may be a better way to plan for a threatening pandemic with location and parameters as yet unknown, reserving more detailed network models for disease outbreaks already underway in localities where the social networks are well identified.We formulate compartmental models to describe outbreaks of influenza and attempt to manage a disease outbreak by vaccination or antiviral treatment. The models give an important prediction that may not have been noticed in other models, namely that the number of doses of antiviral treatment required is extremely sensitive to the number of initial infectives. This suggests that the actual number of doses needed cannot be estimated with any degree of reliability. The model is applicable to pre-epidemic vaccination, such as annual vaccination programs in anticipation of an 'ordinary' influenza outbreak with limited drift, and as a combination of treatment both before and during an epidemic.

Pandemic potential of a strain of influenza A (H1N1): early findings

A novel influenza A (H1N1) virus has spread rapidly across the globe. Judging its pandemic potential is difficult with limited data, but nevertheless essential to inform appropriate health responses. By analyzing the outbreak in Mexico, early data on international spread, and viral genetic diversity, we make an early assessment of transmissibility and severity. Our estimates suggest that 23,000 (range 6000 to 32,000) individuals had been infected in Mexico by late April, giving an estimated case fatality ratio (CFR) of 0.4% (range: 0.3 to 1.8%) based on confirmed and suspected deaths reported to that time. In a community outbreak in the small community of La Gloria, Veracruz, no deaths were attributed to infection, giving an upper 95% bound on CFR of 0.6%. Thus, although substantial uncertainty remains, clinical severity appears less than that seen in the 1918 influenza pandemic but comparable with that seen in the 1957 pandemic. Clinical attack rates in children in La Gloria were twice that in adults (<15 years of age: 61%; >/=15 years: 29%). Three different epidemiological analyses gave basic reproduction number (R0) estimates in the range of 1.4 to 1.6, whereas a genetic analysis gave a central estimate of 1.2. This range of values is consistent with 14 to 73 generations of human-to-human transmission having occurred in Mexico to late April. Transmissibility is therefore substantially higher than that of seasonal flu, and comparable with lower estimates of R0 obtained from previous influenza pandemics.

Epidemic patch models applied to pandemic influenza: contact matrix, stochasticity, robustness of predictions

Due to the recent emergence of H5N1 virus, the modelling of pandemic influenza has become a relevant issue. Here we present an SEIR model formulated to simulate a possible outbreak in Italy, analysing its structure and, more generally, the effect of including specific details into a model. These details regard population heterogeneities, such as age and spatial distribution, as well as stochasticity, that regulates the epidemic dynamics when the number of infectives is low. We discuss and motivate the specific modelling choices made when building the model and investigate how the model details influence the predicted dynamics. Our analysis may help in deciding which elements of complexity are worth including in the design of a deterministic model for pandemic influenza, in a balance between, on the one hand, keeping the model computationally efficient and the number of parameters low and, on the other hand, maintaining the necessary realistic features.

Antiviral resistance during pandemic influenza: implications for stockpiling and drug use

Background

The anticipated extent of antiviral use during an influenza pandemic can have adverse consequences for the development of drug resistance and rationing of limited stockpiles. The strategic use of drugs is therefore a major public health concern in planning for effective pandemic responses.

Methods

We employed a mathematical model that includes both sensitive and resistant strains of a virus with pandemic potential, and applies antiviral drugs for treatment of clinical infections. Using estimated parameters in the published literature, the model was simulated for various sizes of stockpiles to evaluate the outcome of different antiviral strategies.

Results

We demonstrated that the emergence of highly transmissible resistant strains has no significant impact on the use of available stockpiles if treatment is maintained at low levels or the reproduction number of the sensitive strain is sufficiently high. However, moderate to high treatment levels can result in a more rapid depletion of stockpiles, leading to run-out, by promoting wide-spread drug resistance. We applied an antiviral strategy that delays the onset of aggressive treatment for a certain amount of time after the onset of the outbreak. Our results show that if high treatment levels are enforced too early during the outbreak, a second wave of infections can potentially occur with a substantially larger magnitude. However, a timely implementation of wide-scale treatment can prevent resistance spread in the population, and minimize the final size of the pandemic.

Conclusion

Our results reveal that conservative treatment levels during the early stages of the outbreak, followed by a timely increase in the scale of drug-use, will offer an effective strategy to manage drug resistance in the population and avoid run-out. For a 1918-like strain, the findings suggest that pandemic plans should consider stockpiling antiviral drugs to cover at least 20% of the population.

Fragment-based quantitative structure-activity relationship (FB-QSAR) for fragment-based drug design

In cooperation with the fragment-based design a new drug design method, the so-called "fragment-based quantitative structure-activity relationship" (FB-QSAR) is proposed. The essence of the new method is that the molecular framework in a family of drug candidates are divided into several fragments according to their substitutes being investigated. The bioactivities of molecules are correlated with the physicochemical properties of the molecular fragments through two sets of coefficients in the linear free energy equations. One coefficient set is for the physicochemical properties and the other for the weight factors of the molecular fragments. Meanwhile, an iterative double least square (IDLS) technique is developed to solve the two sets of coefficients in a training data set alternately and iteratively. The IDLS technique is a feedback procedure with machine learning ability. The standard Two-dimensional quantitative structure-activity relationship (2D-QSAR) is a special case, in the FB-QSAR, when the whole molecule is treated as one entity. The FB-QSAR approach can remarkably enhance the predictive power and provide more structural insights into rational drug design. As an example, the FB-QSAR is applied to build a predictive model of neuraminidase inhibitors for drug development against H5N1 influenza virus.

Antiviral resistance and the control of pandemic influenza: the roles of stochasticity, evolution and model details

Antiviral drugs, most notably the neuraminidase inhibitors, are an important component of control strategies aimed to prevent or limit any future influenza pandemic. The potential large-scale use of antiviral drugs brings with it the danger of drug resistance evolution. A number of recent studies have shown that the emergence of drug-resistant influenza could undermine the usefulness of antiviral drugs for the control of an epidemic or pandemic outbreak. While these studies have provided important insights, the inherently stochastic nature of resistance generation and spread, as well as the potential for ongoing evolution of the resistant strain have not been fully addressed. Here, we study a stochastic model of drug resistance emergence and consecutive evolution of the resistant strain in response to antiviral control during an influenza pandemic. We find that taking into consideration the ongoing evolution of the resistant strain does not increase the probability of resistance emergence; however, it increases the total number of infecteds if a resistant outbreak occurs. Our study further shows that taking stochasticity into account leads to results that can differ from deterministic models. Specifically, we find that rapid and strong control cannot only contain a drug sensitive outbreak, it can also prevent a resistant outbreak from occurring. We find that the best control strategy is early intervention heavily based on prophylaxis at a level that leads to outbreak containment. If containment is not possible, mitigation works best at intermediate levels of antiviral control. Finally, we show that the results are not very sensitive to the way resistance generation is modeled.

Energy and public health: the challenge of peak petroleum

Petroleum is a unique and essential energy source, used as the principal fuel for transportation, in producing many chemicals, and for numerous other purposes. Global petroleum production is expected to reach a maximum in the near future and to decline thereafter, a phenomenon known as "peak petroleum." This article reviews petroleum geology and uses, describes the phenomenon of peak petroleum, and reviews the scientific literature on the timing of this transition. It then discusses how peak petroleum may affect public health and health care, by reference to four areas: medical supplies and equipment, transportation, energy generation, and food production. Finally, it suggests strategies for anticipating and preparing for peak petroleum, both general public health preparedness strategies and actions specific to the four expected health system impacts.

Responding to simulated pandemic influenza in San Antonio, Texas

OBJECTIVE

To describe the results of a simulation study of the spread of pandemic influenza, the effects of public health measures on the simulated pandemic, and the resultant adequacy of the surge capacity of the hospital infrastructure and to investigate the adequacy of key elements of the national pandemic influenza plan to reduce the overall attack rate so that surge capacity would not be overwhelmed.

DESIGN

We used 2 discrete-event simulation models: the first model simulates the contact and disease transmission process, as affected by public health interventions, to produce a stream of arriving patients, and the second model simulates the diagnosis and treatment process and determines patient outcomes.

SETTING

Hypothetical scenarios were based on the response plans, infrastructure, and demographic data of the population of San Antonio, Texas.

RESULTS

Use of a mix of strategies, including social distancing, antiviral medications, and targeted vaccination, may limit the overall attack rate so that demand for care would not exceed the capacity of the infrastructure. Additional simulations to assess social distancing as a sole mitigation strategy suggest that a reduction of infectious community contacts to half of normal levels would have to occur within approximately 7 days.

CONCLUSIONS

Under ideal conditions, the mix of strategies may limit demand, which can then be met by community surge capacity. Given inadequate supplies of vaccines and antiviral medications, aggressive social distancing alone might allow for the control of a local epidemic without reliance on outside support.

Management of drug resistance in the population: influenza as a case study

The rise of drug resistance remains a major impediment to the treatment of some diseases caused by fast-evolving pathogens that undergo genetic mutations. Models describing the within-host infectious dynamics suggest that the resistance is unlikely to emerge if the pathogen-specific immune responses are maintained above a certain threshold during therapy. However, emergence of resistance in the population involves both within-host and between-host infection mechanisms. Here, we employ a mathematical model to identify an effective treatment strategy for the management of drug resistance in the population. We show that, in the absence of pre-existing immunity, the population-wide spread of drug-resistant pathogen strains can be averted if a sizable portion of susceptible hosts is depleted before drugs are used on a large scale. The findings, based on simulations for influenza infection as a case study, suggest that the initial prevalence of the drug-sensitive strain under low pressure of drugs, followed by a timely implementation of intensive treatment, can minimize the total number of infections while preventing outbreaks of drug-resistant infections.

Household structure and infectious disease transmission

One of the central tenets of modern infectious disease epidemiology is that an understanding of heterogeneities, both in host demography and transmission, allows control to be efficiently optimized. Due to the strong interactions present, households are one of the most important heterogeneities to consider, both in terms of predicting epidemic severity and as a target for intervention. We consider these effects in the context of pandemic influenza in Great Britain, and find that there is significant local (ward-level) variation in the basic reproductive ratio, with some regions predicted to suffer 50% faster growth rate of infection than the mean. Childhood vaccination was shown to be highly effective at controlling an epidemic, generally outperforming random vaccination and substantially reducing the variation between regions; only nine out of over 10 000 wards did not obey this rule and these can be identified as demographically atypical regions. Since these benefits of childhood vaccination are a product of correlations between household size and number of dependent children in the household, our results are qualitatively robust for a variety of disease scenarios.

Neuraminidase activity provides a practical read-out for a high throughput influenza antiviral screening assay

BACKGROUND

The emergence of influenza strains that are resistant to commonly used antivirals has highlighted the need to develop new compounds that target viral gene products or host mechanisms that are essential for effective virus replication. Existing assays to identify potential antiviral compounds often use high throughput screening assays that target specific viral replication steps. To broaden the search for antivirals, cell-based replication assays can be performed, but these are often labor intensive and have limited throughput.

RESULTS

We have adapted a traditional virus neutralization assay to develop a practical, cell-based, high throughput screening assay. This assay uses viral neuraminidase (NA) as a read-out to quantify influenza replication, thereby offering an assay that is both rapid and sensitive. In addition to identification of inhibitors that target either viral or host factors, the assay allows simultaneous evaluation of drug toxicity. Antiviral activity was demonstrated for a number of known influenza inhibitors including amantadine that targets the M2 ion channel, zanamivir that targets NA, ribavirin that targets IMP dehydrogenase, and bis-indolyl maleimide that targets protein kinase A/C. Amantadine-resistant strains were identified by comparing IC50 with that of the wild-type virus.

CONCLUSION

Antivirals with specificity for a broad range of targets are easily identified in an accelerated viral inhibition assay that uses NA as a read-out of replication. This assay is suitable for high throughput screening to identify potential antivirals or can be used to identify drug-resistant influenza strains.

Rapid molecular detection of the H275Y oseltamivir resistance gene mutation in circulating influenza A (H1N1) viruses

In early 2008, drug susceptibility surveillance of influenza viruses in Europe revealed that some influenza A viruses (subtype H1N1) circulating during the winter season of 2007 and 2008 were resistant to the neuraminidase inhibitor, oseltamivir. This resistance arises due to a histidine to tyrosine substitution in the neuraminidase active site (H275Y in N1 nomenclature). Current methods to detect this mutation involve an end-point reverse transcription polymerase chain reaction followed by nucleotide sequencing. While accurate, this approach has the limitation of being time-consuming, labour-intensive and expensive. Herein we describe a one-step allelic discrimination assay which rapidly (2 h) detects this resistance mutation. The sensitivity of the assay was as low as 10 copies per reaction and is capable of detecting the antiviral resistance mutation in a mixture of wild type H275 and mutant H275Y targets.

In vitro evaluation of neuraminidase inhibitors using the neuraminidase-dependent release assay of hemagglutinin-pseudotyped viruses

For the treatment of influenza virus infections, neuraminidase inhibitors (NAIs) that prevent the release of virus particles have been effective against most influenza strains. Several neuraminidase (NA) assays are available for the evaluation of NAIs. To understand the NAI functions under physiological conditions, assays mimicking viral particle release should be useful. We have constructed retrovirus-based reporter viruses that are pseudotyped with hemagglutinin (HA) glycoprotein by transfection of producer cells using plasmids expressing retroviral gag-pol, influenza HA, NA, and firefly luciferase genes. Similarly to the life cycle of influenza viruses, the release of pseudotype viruses also requires neuraminidase functions. This requirement was used to develop an assay to evaluate NAI activities by measuring inhibition of pseudotype virus production at different NAI concentrations. The pseudotype virus release assay was used to determine the IC(50) values of Oseltamivir carboxylate, Zanamivir, and the novel phosphonate congeners of Oseltamivir against N1 group neuraminidases and their H274Y Oseltamivir carboxylate-resistant mutants. The deduced IC(50) values obtained using the release assay correlated with those determined using the fluorogenic substrate 2'-(4-methylumbelliferyl)-alpha-d-N-acetylneuraminic acid (MUNANA) and also correlated with the infectivity results.

Surveillance for neuraminidase-inhibitor-resistant influenza viruses in Japan, 1996–2007

Background

High usage of the neuraminidase inhibitor (NAI) oseltamivir in Japan since 2003 led the Neuraminidase Inhibitor Susceptibility Network to assess the susceptibility of community isolates of influenza viruses to oseltamivir and zanamivir.

Methods

Isolates were tested by the enzyme inhibition assay and by neuraminidase (NA) sequence analysis.

Results

Among 1,141 A(H3N2) viruses and 171 type B viruses collected in Japan during the 2003–2004 season, 3 (0.3%) A(H3N2) isolates showed high 50% inhibitory concentrations (IC50) to oseltamivir. Each possessed a known resistance NA mutation at R292K or E119V. During the 2004–2005 season, no resistance was found among 567 influenza A(H3N2) or 60 A(H1N1) isolates, but 1 of 58 influenza B isolates had an NAI resistance mutation (D197N). Sequence analysis found that 4 (3%) of 132 A(H1N1) viruses from 2005–2006 had known NA resistance mutations (all H274Y), but no additional resistant isolates were detected from that or the subsequent 2006–2007 season. Concurrent testing of a selection of 500 influenza B viruses from 2000 to 2006 showed significant variations between seasons in both oseltamivir and zanamivir IC50 values, but no persistent increases over this period.

Conclusions

Our findings suggested possible low-level transmission of resistant variants from oseltamivir-treated patients in several seasons in Japan but no sustained reductions in NAI susceptibility or consistently increased frequency of detecting resistant variants for any strain or subtype, despite high levels of drug use. In particular, although oseltamivir-resistant A(H1N1) viruses with the H274Y mutation spread globally in 2007–2008, we found little evidence for increasing levels of resistant A(H1N1) variants in Japan in preceding years.

Epidemic models with heterogeneous mixing and treatment

We consider a two-group epidemic model with treatment and establish a final size relation that gives the extent of the epidemic. This relation can be established with arbitrary mixing between the groups even though it may not be feasible to determine the reproduction number for the model. If the mixing of the two groups is proportionate, there is an explicit expression for the reproductive number and the final size relation is expressible in terms of the components of the reproduction number. We also extend the results to a two-group influenza model with proportionate mixing. Some numerical simulations suggest that (i) the assumption of no disease deaths is a good approximation if the disease death rate is small and (ii) a one-group model is a close approximation to a two-group model but a two-group model is necessary for comparing targeted treatment strategies.

Protecting residential care facilities from pandemic influenza

It is widely believed that protecting health care facilities against outbreaks of pandemic influenza requires pharmaceutical resources such as antivirals and vaccines. However, early in a pandemic, vaccines will not likely be available and antivirals will probably be of limited supply. The containment of pandemic influenza within acute-care hospitals anywhere is problematic because of open connections with communities. However, other health care institutions, especially those providing care for the disabled, can potentially control community access. We modeled a residential care facility by using a stochastic compartmental model to address the question of whether conditions exist under which nonpharmaceutical interventions (NPIs) alone might prevent the introduction of a pandemic virus. The model projected that with currently recommended staff-visitor interactions and social distancing practices, virus introductions are inevitable in all pandemics, accompanied by rapid internal propagation. The model identified staff reentry as the critical pathway of contagion, and provided estimates of the reduction in risk required to minimize the probability of a virus introduction. By using information on latency for historical and candidate pandemic viruses, we developed NPIs that simulated notions of protective isolation for staff away from the facility that reduced the probability of bringing the pandemic infection back to the facility to levels providing protection over a large range of projected pandemic severities. The proposed form of protective isolation was evaluated for social plausibility by collaborators who operate residential facilities. It appears unavoidable that NPI combinations effective against pandemics more severe than mild imply social disruption that increases with severity.

A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of R0

We present a novel SEIR (susceptible-exposure-infective-recovered) model that is suitable for modeling the eradication of diseases by mass vaccination or control of diseases by case isolation combined with contact tracing, incorporating the vaccine efficacy or the control efficacy into the model. Moreover, relying on this novel SEIR model and some probabilistic arguments, we have found four formulas that are suitable for estimating the basic reproductive numbers R(0) in terms of the ratio of the mean infectious period to the mean latent period of a disease. The ranges of R(0) for most known diseases, that are calculated by our formulas, coincide very well with the values of R(0) estimated by the usual method of fitting the models to observed data.

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.

Virtual epidemic in a virtual city: simulating the spread of influenza in a US metropolitan area

A wide variety of biologic, physiologic, social, economic, and geographic factors may affect the transmission, spread, and impact of influenza. Recent concerns about an impending influenza epidemic have generated a need for predictive computer simulation models to forecast the spread of influenza and the effectiveness of prevention and control strategies. We designed an agent-based computer simulation of a theoretical influenza epidemic in Norfolk, Va, that included extensive city-level details and computer representations of every Norfolk citizen, including their expected behavior and social interactions. The simulation introduced 200 infected cases on November 27, 2002 (day 87), and tracked the progress of the epidemic. On average, the prevalence peaked on day 178 (12.2% of the population). Our model showed a cyclical variation in influenza cases by day of the week with fewer people being exposed on weekends, differences in emergency room and clinic visits by day of the week, an earlier peak in influenza cases, and persistent high prevalence among people age 65 or older and the daily prevalence of infection among health-care workers. The level of detail included in our simulation model made these findings possible. Compared with other existing models, our model has a very extensive and detailed social network, which may be important because individuals with more social interactions and extensive social networks may be more likely to spread influenza. Our simulation may serve as a virtual laboratory to better understand the way different factors and interventions affect the spread of influenza.

Seasonal influenza in the United States, France, and Australia: transmission and prospects for control

Recurrent epidemics of influenza are observed seasonally around the world with considerable health and economic consequences. A key quantity for the control of infectious diseases is the reproduction number, which measures the transmissibility of a pathogen and determines the magnitude of public health interventions necessary to control epidemics. Here we applied a simple epidemic model to weekly indicators of influenza mortality to estimate the reproduction numbers of seasonal influenza epidemics spanning three decades in the United States, France, and Australia. We found similar distributions of reproduction number estimates in the three countries, with mean value 1.3 and important year-to-year variability (range 0.9-2.1). Estimates derived from two different mortality indicators (pneumonia and influenza excess deaths and influenza-specific deaths) were in close agreement for the United States (correlation=0.61, P60%) in healthy individuals who respond well to vaccine, in addition to periodic re-vaccination due to evolving viral antigens and waning population immunity.

Optimal allocation of pandemic influenza vaccine depends on age, risk and timing

The limited production capacity for vaccines raises the question what the best strategy is for allocating the vaccine to mitigate an influenza pandemic. We developed an age-structured model for spread of an influenza pandemic and validated it against observations from the Asian flu pandemic. Two strategies were evaluated: vaccination can be implemented at the start of the influenza pandemic, or vaccination will be implemented near the peak of it. Our results suggest prioritizing individuals with a high-risk of complications if a vaccine becomes available during a pandemic. If available at the start, vaccinating school children might be considered since this results in slightly lower expected number of deaths.