Daihai He

Plug-and-play inference for disease dynamics: measles in large and small populations as a case study

Statistical inference for mechanistic models of partially observed dynamic systems is an active area of research. Most existing inference methods place substantial restrictions upon the form of models that can be fitted and hence upon the nature of the scientific hypotheses that can be entertained and the data that can be used to evaluate them. In contrast, the so-called plug-and-play methods require only simulations from a model and are thus free of such restrictions. We show the utility of the plug-and-play approach in the context of an investigation of measles transmission dynamics. Our novel methodology enables us to ask and answer questions that previous analyses have been unable to address. Specifically, we demonstrate that plug-and-play methods permit the development of a modelling and inference framework applicable to data from both large and small populations. We thereby obtain novel insights into the nature of heterogeneity in mixing and comment on the importance of including extra-demographic stochasticity as a means of dealing with environmental stochasticity and model misspecification. Our approach is readily applicable to many other epidemiological and ecological systems.

Prevention and Control of Zika as a Mosquito-Borne and Sexually Transmitted Disease: A Mathematical Modeling Analysis

The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent evidence indicates that ZIKV can also be transmitted via sexual contact with cases of sexually transmitted ZIKV reported in Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and the USA. Yet, the role of sexual transmission on the spread and control of ZIKV infection is not well-understood. We introduce a mathematical model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV and calibrate the model to ZIKV epidemic data from Brazil, Colombia, and El Salvador. Parameter estimates yielded a basic reproduction number 0 = 2.055 (95% CI: 0.523–6.300), in which the percentage contribution of sexual transmission is 3.044% (95% CI: 0.123–45.73). Our sensitivity analyses indicate that 0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Prevention and control efforts against ZIKV should target both the mosquito-borne and sexual transmission routes.

Time series analysis via mechanistic models

The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plug-and-play property. Our work builds on recently developed plug-and-play inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae.

Effects of School Closure on Incidence of Pandemic Influenza in Alberta, Canada

BACKGROUND Control of pandemic influenza by social-distancing measures, such as school closures, is a controversial aspect of pandemic planning. However, investigations of the extent to which these measures actually affect the progression of a pandemic have been limited. OBJECTIVE To examine correlations between the incidence of pandemic H1N1 (pH1N1) influenza in Alberta, Canada, in 2009 and school closures or weather changes, and to estimate the effects of school closures and weather changes on pH1N1 transmission. DESIGN Mathematical transmission models were fit to data that compared the pattern of confirmed pH1N1 cases with the school calendar and weather patterns. SETTING Alberta, Canada, from 19 April 2009 to 2 January 2010. DATA SOURCES 2009 virologic test results, 2006 census data, 2009 daily temperature and humidity data, and 2009 school calendars. MEASUREMENTS Age-specific daily counts of positive results for pH1N1 from the complete database of 35 510 specimens submitted to the Alberta Provincial Laboratory for Public Health for virologic testing from 19 April 2009 to 2 January 2010. RESULTS The ending and restarting of school terms had a major effect in attenuating the first wave and starting the second wave of pandemic influenza cases. Mathematical models suggested that school closure reduced transmission among school-age children by more than 50% and that this was a key factor in interrupting transmission. The models also indicated that seasonal changes in weather had a significant effect on the temporal pattern of the epidemic. LIMITATIONS Data probably represent a small sample of all viral infections. The mathematical models make simplifying assumptions in order to make simulations and analysis feasible. CONCLUSION Analysis of data from unrestricted virologic testing during an influenza pandemic provides compelling evidence that closing schools can have dramatic effects on transmission of pandemic influenza. School closure seems to be an effective strategy for slowing the spread of pandemic influenza in countries with social contact networks similar to those in Canada. PRIMARY FUNDING SOURCE Canadian Institutes of Health Research, Natural Sciences and Engineering Research Council of Canada, and Public Health Agency of Canada.

Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales

Past influenza pandemics appear to be characterized by multiple waves of incidence, but the mechanisms that account for this phenomenon remain unclear. We propose a simple epidemic model, which incorporates three factors that might contribute to the generation of multiple waves: (i) schools opening and closing, (ii) temperature changes during the outbreak, and (iii) changes in human behaviour in response to the outbreak. We fit this model to the reported influenza mortality during the 1918 pandemic in 334 UK administrative units and estimate the epidemiological parameters. We then use information criteria to evaluate how well these three factors explain the observed patterns of mortality. Our results indicate that all three factors are important but that behavioural responses had the largest effect. The parameter values that produce the best fit are biologically reasonable and yield epidemiological dynamics that match the observed data well.

Global Spatio-temporal Patterns of Influenza in the Post-pandemic Era

We study the global spatio-temporal patterns of influenza dynamics. This is achieved by analysing and modelling weekly laboratory confirmed cases of influenza A and B from 138 countries between January 2006 and January 2015. The data were obtained from FluNet, the surveillance network compiled by the the World Health Organization. We report a pattern of skip-and-resurgence behavior between the years 2011 and 2013 for influenza H1N1pdm, the strain responsible for the 2009 pandemic, in Europe and Eastern Asia. In particular, the expected H1N1pdm epidemic outbreak in 2011/12 failed to occur (or “skipped”) in many countries across the globe, although an outbreak occurred in the following year. We also report a pattern of well-synchronized wave of H1N1pdm in early 2011 in the Northern Hemisphere countries, and a pattern of replacement of strain H1N1pre by H1N1pdm between the 2009 and 2012 influenza seasons. Using both a statistical and a mechanistic mathematical model, and through fitting the data of 108 countries, we discuss the mechanisms that are likely to generate these events taking into account the role of multi-strain dynamics. A basic understanding of these patterns has important public health implications and scientific significance.

Patterns of spread of influenza A in Canada

Understanding spatial patterns of influenza transmission is important for designing control measures. We investigate spatial patterns of laboratory-confirmed influenza A across Canada from October 1999 to August 2012. A statistical analysis (generalized linear model) of the seasonal epidemics in this time period establishes a clear spatio-temporal pattern, with influenza emerging earlier in western provinces. Early emergence is also correlated with low temperature and low absolute humidity in the autumn. For the richer data from the 2009 pandemic, a mechanistic mathematical analysis, based on a transmission model, shows that both school terms and weather had important effects on pandemic influenza transmission.

Seasonality of Influenza A(H7N9) Virus in China-Fitting Simple Epidemic Models to Human Cases.

Background Three epidemic waves of influenza A(H7N9) (hereafter ‘H7N9’) human cases have occurred between March 2013 and July 2015 in China. However, the underlying transmission mechanism remains unclear. Our main objective is to use mathematical models to study how seasonality, secular changes and environmental transmission play a role in the spread of H7N9 in China. Methods Data on human cases and chicken cases of H7N9 infection were downloaded from the EMPRES-i Global Animal Disease Information System. We modelled on chicken-to-chicken transmission, assuming a constant ratio of 10−6 human case per chicken case, and compared the model fit with the observed human cases. We developed three different modified Susceptible-Exposed-Infectious-Recovered-Susceptible models: (i) a non-periodic transmission rate model with an environmental class, (ii) a non-periodic transmission rate model without an environmental class, and (iii) a periodic transmission rate model with an environmental class. We then estimated the key epidemiological parameters and compared the model fit using Akaike Information Criterion and Bayesian Information Criterion. Results Our results showed that a non-periodic transmission rate model with an environmental class provided the best model fit to the observed human cases in China during the study period. The estimated parameter values were within biologically plausible ranges. Conclusions This study highlighted the importance of considering secular changes and environmental transmission in the modelling of human H7N9 cases. Secular changes were most likely due to control measures such as Live Poultry Markets closures that were implemented during the initial phase of the outbreaks in China. Our results suggested that environmental transmission via viral shedding of infected chickens had contributed to the spread of H7N9 human cases in China.

Impact of the 2009 H1N1 Pandemic on Age-Specific Epidemic Curves of Other Respiratory Viruses: A Comparison of Pre-Pandemic, Pandemic and Post-Pandemic Periods in a Subtropical City.

Background The 2009 H1N1 influenza pandemic caused offseason peaks in temperate regions but coincided with the summer epidemic of seasonal influenza and other common respiratory viruses in subtropical Hong Kong. This study was aimed to investigate the impact of the pandemic on age-specific epidemic curves of other respiratory viruses. Methods Weekly laboratory-confirmed cases of influenza A (subtypes seasonal A(H1N1), A(H3N2), pandemic virus A(H1N1)pdm09), influenza B, respiratory syncytial virus (RSV), adenovirus and parainfluenza were obtained from 2004 to 2013. Age-specific epidemic curves of viruses other than A(H1N1)pdm09 were compared between the pre-pandemic (May 2004 – April 2009), pandemic (May 2009 – April 2010) and post-pandemic periods (May 2010 – April 2013). Results There were two peaks of A(H1N1)pdm09 in Hong Kong, the first in September 2009 and the second in February 2011. The infection rate was found highest in young children in both waves, but markedly fewer cases in school children were recorded in the second wave than in the first wave. Positive proportions of viruses other than A(H1N1)pdm09 markedly decreased in all age groups during the first pandemic wave. After the first wave of the pandemic, the positive proportion of A(H3N2) increased, but those of B and RSV remained slightly lower than their pre-pandemic proportions. Changes in seasonal pattern and epidemic peak time were also observed, but inconsistent across virus-age groups. Conclusion Our findings provide some evidence that age distribution, seasonal pattern and peak time of other respiratory viruses have changed since the pandemic. These changes could be the result of immune interference and changing health seeking behavior, but the mechanism behind still needs further investigations.

Age-specific epidemic waves of influenza and respiratory syncytial virus in a subtropical city.

Both influenza and respiratory syncytial virus (RSV) are active throughout the year in subtropical or tropical regions, but few studies have reported on age-specific seasonal patterns of these viruses. We examined the age-specific epidemic curves of laboratory-confirmed cases of influenza A (subtyped into seasonal A(H1N1), A(H3N2), and pandemic virus A(H1N1)pdm09), influenza B and respiratory syncytial virus (RSV), in subtropical city Hong Kong from 2004 to 2013. We found that different types and subtypes of influenza showed similar two-peak patterns across age groups, with one peak in winter and another in spring/summer. Age differences were found in epidemic onset time and duration, but none could reach statistical significance (p > 0.05). Age synchrony was found in epidemic peak time for both cool and warm seasons. RSV showed less clear seasonal patterns and non-synchronized epidemic curves across age. In conclusion, age synchrony was found in influenza seasonal epidemics and the 2009 pandemic, but not in RSV. None of the age groups consistently appear as the driving force for seasonal epidemics of influenza and RSV in Hong Kong.