Planning for the control of pandemic influenza A (H1N1) in Los Angeles County and the United States

Probabilistic predictions of SIS epidemics on networks based on population-level observations

We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erdős-Rényi and Barabási-Albert networks. It is known that the contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, in this case at the population-level, contain information about the underlying network. This information, in turn, is useful for predicting the future course of an ongoing epidemic. To exploit this in a prediction framework, the exact high-dimensional stochastic model of an SIS epidemic on a network is approximated by a lower-dimensional surrogate model. The surrogate model is based on a birth-and-death process; the effect of the underlying network is described by a parametric model for the birth rates. We demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. As long as the population-level data is available over a long-enough period, even if not sampled frequently, the model leads to excellent predictions where the underlying network is correctly identified and prediction uncertainty mainly reflects the intrinsic stochasticity of the spreading epidemic. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty. The proposed method relies on minimal data at population-level, which is always likely to be available. This, combined with its numerical efficiency, makes the proposed method attractive to be used either as a standalone inference and prediction scheme or in conjunction with other inference and/or predictive models.

Discrete Stochastic Optimization for Public Health Interventions with Constraints

Many public health threats exist, motivating the need to find optimal intervention strategies. Given the stochastic nature of the threats (e.g., the spread of pandemic influenza, the occurrence of drug overdoses, and the prevalence of alcohol-related threats), deterministic optimization approaches may be inappropriate. In this paper, we implement a stochastic optimization method to address aspects of the 2009 H1N1 and the COVID-19 pandemics, with the spread of disease modeled by the open-source Monte Carlo simulations, FluTE, and Covasim, respectively. Without testing every possible option, the objective of the optimization is to determine the best combination of intervention strategies so as to result in minimal economic loss to society. To reach our objective, this application-oriented paper uses the discrete simultaneous perturbation stochastic approximation method (DSPSA), a recursive simulation-based optimization algorithm, to update the input parameters in the disease simulation software so that the output iteratively approaches minimal economic loss. Assuming that the simulation models for the spread of disease (FluTE for H1N1 and Covasim for COVID-19 in our case) are accurate representations for the population being studied, the simulation-based strategy we present provides decision makers a powerful tool to mitigate potential human and economic losses from any epidemic. The basic approach is also applicable in other public health problems, such as opioid abuse and drunk driving.

Predictive accuracy of particle filtering in dynamic models supporting outbreak projections

BACKGROUND

While a new generation of computational statistics algorithms and availability of data streams raises the potential for recurrently regrounding dynamic models with incoming observations, the effectiveness of such arrangements can be highly subject to specifics of the configuration (e.g., frequency of sampling and representation of behaviour change), and there has been little attempt to identify effective configurations.

METHODS

Combining dynamic models with particle filtering, we explored a solution focusing on creating quickly formulated models regrounded automatically and recurrently as new data becomes available. Given a latent underlying case count, we assumed that observed incident case counts followed a negative binomial distribution. In accordance with the condensation algorithm, each such observation led to updating of particle weights. We evaluated the effectiveness of various particle filtering configurations against each other and against an approach without particle filtering according to the accuracy of the model in predicting future prevalence, given data to a certain point and a norm-based discrepancy metric. We examined the effectiveness of particle filtering under varying times between observations, negative binomial dispersion parameters, and rates with which the contact rate could evolve.

RESULTS

We observed that more frequent observations of empirical data yielded super-linearly improved accuracy in model predictions. We further found that for the data studied here, the most favourable assumptions to make regarding the parameters associated with the negative binomial distribution and changes in contact rate were robust across observation frequency and the observation point in the outbreak.

CONCLUSION

Combining dynamic models with particle filtering can perform well in projecting future evolution of an outbreak. Most importantly, the remarkable improvements in predictive accuracy resulting from more frequent sampling suggest that investments to achieve efficient reporting mechanisms may be more than paid back by improved planning capacity. The robustness of the results on particle filter configuration in this case study suggests that it may be possible to formulate effective standard guidelines and regularized approaches for such techniques in particular epidemiological contexts. Most importantly, the work tentatively suggests potential for health decision makers to secure strong guidance when anticipating outbreak evolution for emerging infectious diseases by combining even very rough models with particle filtering method.

Modelling community-control strategies to protect hospital resources during an influenza pandemic in Ottawa, Canada

BACKGROUND

A novel influenza virus has emerged to produce a global pandemic four times in the past one hundred years, resulting in millions of infections, hospitalizations and deaths. There is substantial uncertainty about when, where and how the next influenza pandemic will occur.

METHODS

We developed a novel mathematical model to chart the evolution of an influenza pandemic. We estimate the likely burden of future influenza pandemics through health and economic endpoints. An important component of this is the adequacy of existing hospital-resource capacity. Using a simulated population reflective of Ottawa, Canada, we model the potential impact of a future influenza pandemic under different combinations of pharmaceutical and non-pharmaceutical interventions.

RESULTS

There was substantial variation in projected pandemic impact and outcomes across intervention scenarios. In a population of 1.2 million, the illness attack rate ranged from 8.4% (all interventions) to 54.5% (no interventions); peak acute care hospital capacity ranged from 0.2% (all interventions) to 13.8% (no interventions); peak ICU capacity ranged from 1.1% (all interventions) to 90.2% (no interventions); and mortality ranged from 11 (all interventions) to 363 deaths (no interventions). Associated estimates of economic burden ranged from CAD $115 million to over $2 billion when extended mass school closure was implemented.

DISCUSSION

Children accounted for a disproportionate number of pandemic infections, particularly in household settings. Pharmaceutical interventions effectively reduced peak and total pandemic burden without affecting timing, while non-pharmaceutical measures delayed and attenuated pandemic wave progression. The timely implementation of a layered intervention bundle appeared likely to protect hospital resource adequacy in Ottawa. The adaptable nature of this model provides value in informing pandemic preparedness policy planning in situations of uncertainty, as scenarios can be updated in real time as more data become available. However-given the inherent uncertainties of model assumptions-results should be interpreted with caution.

A framework for evaluating epidemic forecasts

Background

Over the past few decades, numerous forecasting methods have been proposed in the field of epidemic forecasting. Such methods can be classified into different categories such as deterministic vs. probabilistic, comparative methods vs. generative methods, and so on. In some of the more popular comparative methods, researchers compare observed epidemiological data from the early stages of an outbreak with the output of proposed models to forecast the future trend and prevalence of the pandemic. A significant problem in this area is the lack of standard well-defined evaluation measures to select the best algorithm among different ones, as well as for selecting the best possible configuration for a particular algorithm.

Results

In this paper we present an evaluation framework which allows for combining different features, error measures, and ranking schema to evaluate forecasts. We describe the various epidemic features (Epi-features) included to characterize the output of forecasting methods and provide suitable error measures that could be used to evaluate the accuracy of the methods with respect to these Epi-features. We focus on long-term predictions rather than short-term forecasting and demonstrate the utility of the framework by evaluating six forecasting methods for predicting influenza in the United States. Our results demonstrate that different error measures lead to different rankings even for a single Epi-feature. Further, our experimental analyses show that no single method dominates the rest in predicting all Epi-features when evaluated across error measures. As an alternative, we provide various Consensus Ranking schema that summarize individual rankings, thus accounting for different error measures. Since each Epi-feature presents a different aspect of the epidemic, multiple methods need to be combined to provide a comprehensive forecast. Thus we call for a more nuanced approach while evaluating epidemic forecasts and we believe that a comprehensive evaluation framework, as presented in this paper, will add value to the computational epidemiology community.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-017-2365-1) contains supplementary material, which is available to authorized users.

Extrapolating theoretical efficacy of inactivated influenza A/H5N1 virus vaccine from human immunogenicity studies

Influenza A virus subtype H5N1 has been a public health concern for almost 20years due to its potential ability to become transmissible among humans. Phase I and II clinical trials have assessed safety, reactogenicity and immunogenicity of inactivated influenza A/H5N1 virus vaccines. A shortage of vaccine is likely to occur during the first months of a pandemic. Hence, determining whether to give one dose to more people or two doses to fewer people to best protect the population is essential. We use hemagglutination-inhibition antibody titers as an immune correlate for avian influenza vaccines. Using an established relationship to obtain a theoretical vaccine efficacy from immunogenicity data from thirteen arms of six phase I and phase II clinical trials of inactivated influenza A/H5N1 virus vaccines, we assessed: (1) the proportion of theoretical vaccine efficacy achieved after a single dose (defined as primary response level), and (2) whether theoretical efficacy increases after a second dose, with and without adjuvant. Participants receiving vaccine with AS03 adjuvant had higher primary response levels (range: 0.48-0.57) compared to participants receiving vaccine with MF59 adjuvant (range: 0.32-0.47), with no observed trends in primary response levels by antigen dosage. After the first and second doses, vaccine with AS03 at dosage levels 3.75, 7.5 and 15mcg had the highest estimated theoretical vaccine efficacy: Dose (1) 45% (95% CI: 36-57%), 53% (95% CI: 42-63%) and 55% (95% CI: 44-64%), respectively and Dose (2) 93% (95% CI: 89-96%), 97% (95% CI: 95-98%) and 97% (95% CI: 96-100%), respectively. On average, the estimated theoretical vaccine efficacy of lower dose adjuvanted vaccines (AS03 and MF59) was 17% higher than that of higher dose unadjuvanted vaccines, suggesting that including an adjuvant is dose-sparing. These data indicate adjuvanted inactivated influenza A/H5N1 virus vaccine produces high theoretical efficacy after two doses to protect individuals against a potential avian influenza pandemic.

Modeling and Predicting Human Infectious Diseases

The spreading of infectious diseases has dramatically shaped our history and society. The quest to understand and prevent their spreading dates more than two centuries. Over the years, advances in Medicine, Biology, Mathematics, Physics, Network Science, Computer Science, and Technology in general contributed to the development of modern epidemiology. In this chapter, we present a summary of different mathematical and computational approaches aimed at describing, modeling, and forecasting the diffusion of viruses. We start from the basic concepts and models in an unstructured population and gradually increase the realism by adding the effects of realistic contact structures within a population as well as the effects of human mobility coupling different subpopulations. Building on these concepts we present two realistic data-driven epidemiological models able to forecast the spreading of infectious diseases at different geographical granularities. We conclude by introducing some recent developments in diseases modeling rooted in the big-data revolution.

Responding to vaccine safety signals during pandemic influenza: a modeling study

Background

Managing emerging vaccine safety signals during an influenza pandemic is challenging. Federal regulators must balance vaccine risks against benefits while maintaining public confidence in the public health system.

Methods

We developed a multi-criteria decision analysis model to explore regulatory decision-making in the context of emerging vaccine safety signals during a pandemic. We simulated vaccine safety surveillance system capabilities and used an age-structured compartmental model to develop potential pandemic scenarios. We used an expert-derived multi-attribute utility function to evaluate potential regulatory responses by combining four outcome measures into a single measure of interest: 1) expected vaccination benefit from averted influenza; 2) expected vaccination risk from vaccine-associated febrile seizures; 3) expected vaccination risk from vaccine-associated Guillain-Barre Syndrome; and 4) expected change in vaccine-seeking behavior in future influenza seasons.

Results

Over multiple scenarios, risk communication, with or without suspension of vaccination of high-risk persons, were the consistently preferred regulatory responses over no action or general suspension when safety signals were detected during a pandemic influenza. On average, the expert panel valued near-term vaccine-related outcomes relative to long-term projected outcomes by 3∶1. However, when decision-makers had minimal ability to influence near-term outcomes, the response was selected primarily by projected impacts on future vaccine-seeking behavior.

Conclusions

The selected regulatory response depends on how quickly a vaccine safety signal is identified relative to the peak of the pandemic and the initiation of vaccination. Our analysis suggested two areas for future investment: efforts to improve the size and timeliness of the surveillance system and behavioral research to understand changes in vaccine-seeking behavior.

Efficiency of points of dispensing for influenza A(H1N1)pdm09 vaccination, Los Angeles County, California, USA, 2009

During October 23-December 8, 2009, the Los Angeles County Department of Public Health used points of dispensing (PODs) to improve access to and increase the number of vaccinations against influenza A(H1N1)pdm09. We assessed the efficiency of these units and access to vaccines among ethnic groups. An average of 251 persons per hour (SE 65) were vaccinated at the PODs; a 10% increase in use of live-attenuated monovalent vaccines reduced that rate by 23 persons per hour (SE 7). Vaccination rates were highest for Asians (257/10,000 persons), followed by Hispanics (114/10,000), whites (75/100,000), and African Americans (37/10,000). Average distance traveled to a POD was highest for whites (6.6 miles; SD 6.5) and lowest for Hispanics (4.7 miles; SD ±5.3). Placing PODs in areas of high population density could be an effective strategy to reach large numbers of persons for mass vaccination, but additional PODs may be needed to improve coverage for specific populations.

Efficiency of points of dispensing for influenza A(H1N1)pdm09 vaccination, Los Angeles County, California, USA, 2009

During October 23–December 8, 2009, the Los Angeles County Department of Public Health used points of dispensing (PODs) to improve access to and increase the number of vaccinations against influenza A(H1N1)pdm09. We assessed the efficiency of these units and access to vaccines among ethnic groups. An average of 251 persons per hour (SE 65) were vaccinated at the PODs; a 10% increase in use of live-attenuated monovalent vaccines reduced that rate by 23 persons per hour (SE 7). Vaccination rates were highest for Asians (257/10,000 persons), followed by Hispanics (114/10,000), whites (75/100,000), and African Americans (37/10,000). Average distance traveled to a POD was highest for whites (6.6 miles; SD 6.5) and lowest for Hispanics (4.7 miles; SD ±5.3). Placing PODs in areas of high population density could be an effective strategy to reach large numbers of persons for mass vaccination, but additional PODs may be needed to improve coverage for specific populations.

Modelling the epidemic spread of an H1N1 influenza outbreak in a rural university town

Knowledge of mechanisms of infection in vulnerable populations is needed in order to prepare for future outbreaks. Here, using a unique dataset collected during a 2009 outbreak of influenza A(H1N1)pdm09 in a university town, we evaluated mechanisms of infection and identified that an epidemiological model containing partial protection of susceptibles best describes H1N1 dynamics in a rural university environment. We found that the protected group was over 14 times less susceptible to H1N1 infection than unprotected susceptibles. Our estimates show that the basic reproductive rate, R 0, was 5·96 (95% confidence interval 5·83-6·61), and, importantly, R 0 could be decreased to below 1 and similar epidemics could be avoided by increasing the proportion of the initial protected group. Moreover, several weeks into the epidemic, this protected group generated more new infections than the unprotected susceptible group, and thus, such protected groups should be taken into account while studying influenza epidemics in similar settings.

The effects of school closures on influenza outbreaks and pandemics: systematic review of simulation studies

BACKGROUND

School closure is a potential intervention during an influenza pandemic and has been investigated in many modelling studies.

OBJECTIVES

To systematically review the effects of school closure on influenza outbreaks as predicted by simulation studies.

METHODS

We searched Medline and Embase for relevant modelling studies published by the end of October 2012, and handsearched key journals. We summarised the predicted effects of school closure on the peak and cumulative attack rates and the duration of the epidemic. We investigated how these predictions depended on the basic reproduction number, the timing and duration of closure and the assumed effects of school closures on contact patterns.

RESULTS

School closures were usually predicted to be most effective if they caused large reductions in contact, if transmissibility was low (e.g. a basic reproduction number <2), and if attack rates were higher in children than in adults. The cumulative attack rate was expected to change less than the peak, but quantitative predictions varied (e.g. reductions in the peak were frequently 20-60% but some studies predicted >90% reductions or even increases under certain assumptions). This partly reflected differences in model assumptions, such as those regarding population contact patterns.

CONCLUSIONS

Simulation studies suggest that school closure can be a useful control measure during an influenza pandemic, particularly for reducing peak demand on health services. However, it is difficult to accurately quantify the likely benefits. Further studies of the effects of reactive school closures on contact patterns are needed to improve the accuracy of model predictions.

INDIVIDUAL-BASED COMPUTATIONAL MODEL USED TO EXPLAIN 2009 PANDEMIC H1N1 IN RURAL CAMPUS COMMUNITY

In the beginning of fall semester 2009, over 2,000 students contacted the student health service at Washington State University to report symptoms of influenza. The epidemic in Pullman, WA made national news, and many speculated on the severity and extent of the disease spread. Analysis of data from the influenza A(H1N1)pdm09 epidemic in Pullman, WA offers an opportunity to gain insights into characteristics of this rural campus community outbreak. In this study, an individual-based stochastic epidemic simulation model was used with the data to estimate infection parameters and make projections of the number of symptomatic individuals that would result given a variety of plausible scenarios. The parameters that were estimated include the number of individuals initially infected and the basic reproductive ratio (R0). The model was then used to predict the magnitude of infection with vaccination, isolation and quarantine. The results show that the best single intervention strategy is vaccination, and the reduction in infection is greatest when vaccination, isolation and quarantine are used simultaneously.

A systematic review of studies on forecasting the dynamics of influenza outbreaks

Forecasting the dynamics of influenza outbreaks could be useful for decision-making regarding the allocation of public health resources. Reliable forecasts could also aid in the selection and implementation of interventions to reduce morbidity and mortality due to influenza illness. This paper reviews methods for influenza forecasting proposed during previous influenza outbreaks and those evaluated in hindsight. We discuss the various approaches, in addition to the variability in measures of accuracy and precision of predicted measures. PubMed and Google Scholar searches for articles on influenza forecasting retrieved sixteen studies that matched the study criteria. We focused on studies that aimed at forecasting influenza outbreaks at the local, regional, national, or global level. The selected studies spanned a wide range of regions including USA, Sweden, Hong Kong, Japan, Singapore, United Kingdom, Canada, France, and Cuba. The methods were also applied to forecast a single measure or multiple measures. Typical measures predicted included peak timing, peak height, daily/weekly case counts, and outbreak magnitude. Due to differences in measures used to assess accuracy, a single estimate of predictive error for each of the measures was difficult to obtain. However, collectively, the results suggest that these diverse approaches to influenza forecasting are capable of capturing specific outbreak measures with some degree of accuracy given reliable data and correct disease assumptions. Nonetheless, several of these approaches need to be evaluated and their performance quantified in real-time predictions.

Containing the accidental laboratory escape of potential pandemic influenza viruses

BACKGROUND

The recent work on the modified H5N1 has stirred an intense debate on the risk associated with the accidental release from biosafety laboratory of potential pandemic pathogens. Here, we assess the risk that the accidental escape of a novel transmissible influenza strain would not be contained in the local community.

METHODS

We develop here a detailed agent-based model that specifically considers laboratory workers and their contacts in microsimulations of the epidemic onset. We consider the following non-pharmaceutical interventions: isolation of the laboratory, laboratory workers' household quarantine, contact tracing of cases and subsequent household quarantine of identified secondary cases, and school and workplace closure both preventive and reactive.

RESULTS

Model simulations suggest that there is a non-negligible probability (5% to 15%), strongly dependent on reproduction number and probability of developing clinical symptoms, that the escape event is not detected at all. We find that the containment depends on the timely implementation of non-pharmaceutical interventions and contact tracing and it may be effective (>90% probability per event) only for pathogens with moderate transmissibility (reproductive number no larger than R₀ = 1.5). Containment depends on population density and structure as well, with a probability of giving rise to a global event that is three to five times lower in rural areas.

CONCLUSIONS

Results suggest that controllability of escape events is not guaranteed and, given the rapid increase of biosafety laboratories worldwide, this poses a serious threat to human health. Our findings may be relevant to policy makers when designing adequate preparedness plans and may have important implications for determining the location of new biosafety laboratories worldwide.

Apollo: giving application developers a single point of access to public health models using structured vocabularies and Web services

This paper describes the Apollo Web Services and Apollo-SV, its related ontology. The Apollo Web Services give an end-user application a single point of access to multiple epidemic simulators. An end user can specify an analytic problem-which we define as a configuration and a query of results-exactly once and submit it to multiple epidemic simulators. The end user represents the analytic problem using a standard syntax and vocabulary, not the native languages of the simulators. We have demonstrated the feasibility of this design by implementing a set of Apollo services that provide access to two epidemic simulators and two visualizer services.

A Simulation Optimization Approach to Epidemic Forecasting

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area.

Forecasting peaks of seasonal influenza epidemics

We present a framework for near real-time forecast of influenza epidemics using a simulation optimization approach. The method combines an individual-based model and a simple root finding optimization method for parameter estimation and forecasting. In this study, retrospective forecasts were generated for seasonal influenza epidemics using web-based estimates of influenza activity from Google Flu Trends for 2004-2005, 2007-2008 and 2012-2013 flu seasons. In some cases, the peak could be forecasted 5-6 weeks ahead. This study adds to existing resources for influenza forecasting and the proposed method can be used in conjunction with other approaches in an ensemble framework.

Real-time numerical forecast of global epidemic spreading: case study of 2009 A/H1N1pdm

BACKGROUND

Mathematical and computational models for infectious diseases are increasingly used to support public-health decisions; however, their reliability is currently under debate. Real-time forecasts of epidemic spread using data-driven models have been hindered by the technical challenges posed by parameter estimation and validation. Data gathered for the 2009 H1N1 influenza crisis represent an unprecedented opportunity to validate real-time model predictions and define the main success criteria for different approaches.

METHODS

We used the Global Epidemic and Mobility Model to generate stochastic simulations of epidemic spread worldwide, yielding (among other measures) the incidence and seeding events at a daily resolution for 3,362 subpopulations in 220 countries. Using a Monte Carlo Maximum Likelihood analysis, the model provided an estimate of the seasonal transmission potential during the early phase of the H1N1 pandemic and generated ensemble forecasts for the activity peaks in the northern hemisphere in the fall/winter wave. These results were validated against the real-life surveillance data collected in 48 countries, and their robustness assessed by focusing on 1) the peak timing of the pandemic; 2) the level of spatial resolution allowed by the model; and 3) the clinical attack rate and the effectiveness of the vaccine. In addition, we studied the effect of data incompleteness on the prediction reliability.

RESULTS

Real-time predictions of the peak timing are found to be in good agreement with the empirical data, showing strong robustness to data that may not be accessible in real time (such as pre-exposure immunity and adherence to vaccination campaigns), but that affect the predictions for the attack rates. The timing and spatial unfolding of the pandemic are critically sensitive to the level of mobility data integrated into the model.

CONCLUSIONS

Our results show that large-scale models can be used to provide valuable real-time forecasts of influenza spreading, but they require high-performance computing. The quality of the forecast depends on the level of data integration, thus stressing the need for high-quality data in population-based models, and of progressive updates of validated available empirical knowledge to inform these models.

Sensitivity analysis of an individual-based model for simulation of influenza epidemics

Individual-based epidemiology models are increasingly used in the study of influenza epidemics. Several studies on influenza dynamics and evaluation of intervention measures have used the same incubation and infectious period distribution parameters based on the natural history of influenza. A sensitivity analysis evaluating the influence of slight changes to these parameters (in addition to the transmissibility) would be useful for future studies and real-time modeling during an influenza pandemic.

In this study, we examined individual and joint effects of parameters and ranked parameters based on their influence on the dynamics of simulated epidemics. We also compared the sensitivity of the model across synthetic social networks for Montgomery County in Virginia and New York City (and surrounding metropolitan regions) with demographic and rural-urban differences. In addition, we studied the effects of changing the mean infectious period on age-specific epidemics. The research was performed from a public health standpoint using three relevant measures: time to peak, peak infected proportion and total attack rate. We also used statistical methods in the design and analysis of the experiments.

The results showed that: (i) minute changes in the transmissibility and mean infectious period significantly influenced the attack rate; (ii) the mean of the incubation period distribution appeared to be sufficient for determining its effects on the dynamics of epidemics; (iii) the infectious period distribution had the strongest influence on the structure of the epidemic curves; (iv) the sensitivity of the individual-based model was consistent across social networks investigated in this study and (v) age-specific epidemics were sensitive to changes in the mean infectious period irrespective of the susceptibility of the other age groups. These findings suggest that small changes in some of the disease model parameters can significantly influence the uncertainty observed in real-time forecasting and predicting of the characteristics of an epidemic.

Critical immune and vaccination thresholds for determining multiple influenza epidemic waves

Previous influenza pandemics (1918, 1957, and 1968) have all had multiple waves. The 2009 pandemic influenza A (H1N1) (pandemic H1N1) started in April 2009 and was followed, in the United States (US) and temperate Northern Hemisphere, by a second wave during the fall of 2009. The ratio of susceptible and immune individuals in a population at the end of a wave determines the potential and magnitude of a subsequent wave. As influenza vaccines are not completely protective, there was a combined immunity in the population at the beginning of 2010 (due to vaccination and due to previous natural infection), and it was uncertain if this mixture of herd immunity was enough to prevent a third wave of pandemic influenza during the winter of 2010. Motivated by this problem, we developed a mathematical deterministic two-group epidemic model with vaccination and calibrated it for the 2009 pandemic H1N1. Then, applying methods from mathematical epidemiology we developed a scheme that allowed us to determine critical thresholds for vaccine-induced and natural immunity that would prevent the spread of influenza. Finally, we estimated the level of combined immunity in the US during winter 2010. Our results suggest that a third wave was unlikely if the basic reproduction number R(0) were below 1.6, plausible if the original R(0) was 1.6, and likely if the original R(0) was 1.8 or higher. Given that the estimates for the basic reproduction number for pandemic influenza place it in the range between 1.4 and 1.6 (Bacaer and Ait Dads, 2011; Fraser et al., 2009; Munayco et al., 2009; Pourbohloul et al., 2009; Tuite et al., 2010; White et al., 2009; Yang et al., 2009), our approach accurately predicted the absence of a third wave of influenza in the US during the winter of 2010. We also used this scheme to accurately predict the second wave of pandemic influenza in London and the West Midlands, UK during the fall of 2009.