Babak Pourbohloul

Network theory and SARS: predicting outbreak diversity.

Abstract Many infectious diseases spread through populations via the networks formed by physical contacts among individuals. The patterns of these contacts tend to be highly heterogeneous. Traditional “compartmental” modeling in epidemiology, however, assumes that population groups are fully mixed, that is, every individual has an equal chance of spreading the disease to every other. Applications of compartmental models to Severe Acute Respiratory Syndrome (SARS) resulted in estimates of the fundamental quantity called the basic reproductive number R 0 —the number of new cases of SARS resulting from a single initial case—above one, implying that, without public health intervention, most outbreaks should spark large-scale epidemics. Here we compare these predictions to the early epidemiology of SARS. We apply the methods of contact network epidemiology to illustrate that for a single value of R 0 , any two outbreaks, even in the same setting, may have very different epidemiological outcomes. We offer quantitative insight into the heterogeneity of SARS outbreaks worldwide, and illustrate the utility of this approach for assessing public health strategies.

The Unexpected Impact of a Chlamydia trachomatis Infection Control Program on Susceptibility to Reinfection

BACKGROUND After the introduction of a program to control Chlamydia trachomatis infection in British Columbia, Canada, case rates fell from 216 cases/100,000 population in 1991 to 104 cases/100,000 population in 1997. Since 1998, rates have increased, and case counts now exceed those recorded before the intervention. METHODS We used Cox proportional-hazards survival analysis and developed a compartmental mathematical model to investigate the cause of resurgence in chlamydia cases. RESULTS Cox proportional-hazards survival analysis showed that the relative risk of C. trachomatis reinfection has increased 4.6% per year since 1989, with the increased risk greatest among the young and greater among women than men. A compartmental mathematical model of C. trachomatis transmission showed that a control strategy based on shortening the average duration of infection results in an early reduction in prevalence followed by a rebound in prevalence, reproducing the observed trends. CONCLUSIONS We speculate that a C. trachomatis infection control program based on early case identification and treatment interferes with the effects of immunity on population susceptibility to infection and that, in the absence of strategies to alter sexual networks, a vaccine will be needed to halt the spread of infection at the population level.

Estimated epidemiologic parameters and morbidity associated with pandemic H1N1 influenza

Background: In the face of an influenza pandemic, accurate estimates of epidemiologic parameters are required to help guide decision-making. We sought to estimate epidemiologic parameters for pandemic H1N1 influenza using data from initial reports of laboratory-confirmed cases. Methods: We obtained data on laboratory-confirmed cases of pandemic H1N1 influenza reported in the province of Ontario, Canada, with dates of symptom onset between Apr. 13 and June 20, 2009. Incubation periods and duration of symptoms were estimated and fit to parametric distributions. We used competing-risk models to estimate risk of hospital admission and case-fatality rates. We used a Markov Chain Monte Carlo model to simulate disease transmission. Results: The median incubation period was 4 days and the duration of symptoms was 7 days. Recovery was faster among patients less than 18 years old than among older patients (hazard ratio 1.23, 95% confidence interval 1.06–1.44). The risk of hospital admission was 4.5% (95% CI 3.8%–5.2%) and the case-fatality rate was 0.3% (95% CI 0.1%–0.5%). The risk of hospital admission was highest among patients less than 1 year old and those 65 years or older. Adults more than 50 years old comprised 7% of cases but accounted for 7 of 10 initial deaths (odds ratio 28.6, 95% confidence interval 7.3–111.2). From the simulation models, we estimated the following values (and 95% credible intervals): a mean basic reproductive number (R0, the number of new cases created by a single primary case in a susceptible population) of 1.31 (1.25–1.38), a mean latent period of 2.62 (2.28–3.12) days and a mean duration of infectiousness of 3.38 (2.06–4.69) days. From these values we estimated a serial interval (the average time from onset of infectiousness in a case to the onset of infectiousness in a person infected by that case) of 4–5 days. Interpretation: The low estimates for R0 indicate that effective mitigation strategies may reduce the final epidemic impact of pandemic H1N1 influenza.

Initial human transmission dynamics of the pandemic (H1N1) 2009 virus in North America.

Background  Between 5 and 25 April 2009, pandemic (H1N1) 2009 caused a substantial, severe outbreak in Mexico, and subsequently developed into the first global pandemic in 41 years. We determined the reproduction number of pandemic (H1N1) 2009 by analyzing the dynamics of the complete case series in Mexico City during this early period.

A Comparative Analysis of Influenza Vaccination Programs

Background The threat of avian influenza and the 2004–2005 influenza vaccine supply shortage in the United States have sparked a debate about optimal vaccination strategies to reduce the burden of morbidity and mortality caused by the influenza virus. Methods and Findings We present a comparative analysis of two classes of suggested vaccination strategies: mortality-based strategies that target high-risk populations and morbidity-based strategies that target high-prevalence populations. Applying the methods of contact network epidemiology to a model of disease transmission in a large urban population, we assume that vaccine supplies are limited and then evaluate the efficacy of these strategies across a wide range of viral transmission rates and for two different age-specific mortality distributions. We find that the optimal strategy depends critically on the viral transmission level (reproductive rate) of the virus: morbidity-based strategies outperform mortality-based strategies for moderately transmissible strains, while the reverse is true for highly transmissible strains. These results hold for a range of mortality rates reported for prior influenza epidemics and pandemics. Furthermore, we show that vaccination delays and multiple introductions of disease into the community have a more detrimental impact on morbidity-based strategies than mortality-based strategies. Conclusions If public health officials have reasonable estimates of the viral transmission rate and the frequency of new introductions into the community prior to an outbreak, then these methods can guide the design of optimal vaccination priorities. When such information is unreliable or not available, as is often the case, this study recommends mortality-based vaccination priorities.

The dynamic nature of contact networks in infectious disease epidemiology.

Although contact network models have yielded important insights into infectious disease transmission and control throughout the last decade, researchers have just begun to explore the dynamic nature of contact patterns and their epidemiological significance. Most network models have assumed that contacts are static through time. Developing more realistic models of the social interactions that underlie the spread of infectious diseases thus remains an important challenge for both data gatherers and modelers. In this article, we review some recent data-driven and process-driven approaches that capture the dynamics of human contact, and discuss future challenges for the field.

Modeling Control Strategies of Respiratory Pathogens

Contact network epidemiology can provide quantitative input even before pathogen is fully characterized.

Targeted mass treatment for syphilis with oral azithromycin

From mid 1997 to end of 1999, there was a sexually-transmitted infectious syphilis outbreak mainly in heterosexual people in British Columbia, Canada, that was concentrated in Vancouver. The rate across the province increased from less than 0.5 to 3.4 per 100000, and the rate in Vancouver reached 12.9 per 100000. We aimed to eliminate the syphillis outbreak by treating people at risk of infection. In 2000, a targeted mass treatment programme provided azithromycin (1.8 g orally) to 4384 at-risk residents in this city. After the programme, syphilis frequency fell significantly for 6 months (p=0.016), but rose again in 2001. Results from curve fitting analyses showed that the number of cases in 2001 (177) was higher than expected (0.0001<p<0.0044). This rate rebound and the absence of a sustained effect suggest that targeted mass treatment for syphilis, even though feasible, should not be done routinely.

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.

Heterogeneous bond percolation on multitype networks with an application to epidemic dynamics

Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes-in which the final state can be obtained by studying the underlying network percolation properties-have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology.