Andrew F. Brouwer

Dose-response relationships for environmentally mediated infectious disease transmission models

Environmentally mediated infectious disease transmission models provide a mechanistic approach to examining environmental interventions for outbreaks, such as water treatment or surface decontamination. The shift from the classical SIR framework to one incorporating the environment requires codifying the relationship between exposure to environmental pathogens and infection, i.e. the dose–response relationship. Much of the work characterizing the functional forms of dose–response relationships has used statistical fit to experimental data. However, there has been little research examining the consequences of the choice of functional form in the context of transmission dynamics. To this end, we identify four properties of dose–response functions that should be considered when selecting a functional form: low-dose linearity, scalability, concavity, and whether it is a single-hit model. We find that i) middle- and high-dose data do not constrain the low-dose response, and different dose–response forms that are equally plausible given the data can lead to significant differences in simulated outbreak dynamics; ii) the choice of how to aggregate continuous exposure into discrete doses can impact the modeled force of infection; iii) low-dose linear, concave functions allow the basic reproduction number to control global dynamics; and iv) identifiability analysis offers a way to manage multiple sources of uncertainty and leverage environmental monitoring to make inference about infectivity. By applying an environmentally mediated infectious disease model to the 1993 Milwaukee Cryptosporidium outbreak, we demonstrate that environmental monitoring allows for inference regarding the infectivity of the pathogen and thus improves our ability to identify outbreak characteristics such as pathogen strain.

Age Effects and Temporal Trends in HPV-Related and HPV-Unrelated Oral Cancer in the United States: A Multistage Carcinogenesis Modeling Analysis.

Differences in prognosis in HPV-positive and HPV-negative oral (oropharyngeal and oral cavity) squamous cell carcinomas (OSCCs) and increasing incidence of HPV-related cancers have spurred interest in demographic and temporal trends in OSCC incidence. We leverage multistage clonal expansion (MSCE) models coupled with age—period—cohort (APC) epidemiological models to analyze OSCC data in the SEER cancer registry (1973–2012). MSCE models are based on the initiation—promotion—malignant conversion paradigm in carcinogenesis and allow for interpretation of trends in terms of biological mechanisms. APC models seek to differentiate between the temporal effects of age, period, and birth cohort on cancer risk. Previous studies have looked at the effect of period and cohort on tumor initiation, and we extend this to compare model fits of period and cohort effects on each of tumor initiation, promotion, and malignant conversion rates. HPV-related, HPV-unrelated except oral tongue, and HPV-unrelated oral tongue sites are best described by placing period and cohort effects on the initiation rate. HPV-related and non-oral-tongue HPV-unrelated cancers have similar promotion rates, suggesting similar tumorigenesis dynamics once initiated. Estimates of promotion rates at oral tongue sites are lower, corresponding to a longer sojourn time; this finding is consistent with the hypothesis of an etiology distinct from HPV or alcohol and tobacco use. Finally, for the three subsite groups, men have higher initiation rates than women of the same race, and black people have higher promotion than white people of the same sex. These differences explain part of the racial and sex differences in OSCC incidence.

Trends in HPV cervical and seroprevalence and associations between oral and genital infection and serum antibodies in NHANES 2003–2012

BackgroundHPV infects multiple sites in the epithelium, including the genitals and oral cavity. The relation between genital and oral infections and serum antibodies can help explain the natural history and epidemiology of HPV.MethodsWe analyzed HPV data from NHANES derived from self-collected vaginal swabs (women ages 14–59, 2003–12), oral rinses (men and women 14–69, 2009–12), and serum (men and women 14-59, 2003–10).ResultsType-concordance of cervicogenital and oral infections in women was found to vary widely by age. Prevalence of oral infections with type-concordant antibodies was low but varied by sex: 0.2 % (95 % CI 0.0–0.8) for women vs 0.8 % (95 % CI 0.4–1.3) for men. Vaccination was associated with a reduced risk of cervicogenital infection for vaccine genotypes among ages 14–17 (0.2 (95 % CI 0.1–0.8)) and 18–24 (0.2 (95 % CI 0.1–0.3). Seroprevalence trends in women showed a dramatic increase for recent birth cohorts, likely due to vaccination. By contrast, trends for men remained relatively constant. Age-specific cervicogenital prevalence showed a consistent peak in the late teens and twenties. Relative cervicogenital prevalence has largely been decreasing since the 1940–50 birth cohort.ConclusionsThere are complex patterns in HPV prevalence trends and type-concordance across infection sites and serum antibodies. A multisite sampling scheme is needed to better understand the epidemiology and natural history of HPV.

Modeling Biphasic Environmental Decay of Pathogens and Implications for Risk Analysis

As the appreciation for the importance of the environment in infectious disease transmission has grown, so too has interest in pathogen fate and transport. Fate has been traditionally described by simple exponential decay, but there is increasing recognition that some pathogens demonstrate a biphasic pattern of decay—fast followed by slow. While many have attributed this behavior to population heterogeneity, we demonstrate that biphasic dynamics can arise through a number of plausible mechanisms. We examine the identifiability of a general model encompassing three such mechanisms: population heterogeneity, hardening off, and the existence of viable-but-not-culturable states. Although the models are not fully identifiable from longitudinal sampling studies of pathogen concentrations, we use a differential algebra approach to determine identifiable parameter combinations. Through case studies using Cryptosporidium and Escherichia coli, we show that failure to consider biphasic pathogen dynamics can lead to substantial under- or overestimation of disease risks and pathogen concentrations, depending on the context. More reliable models for environmental hazards and human health risks are possible with an improved understanding of the conditions in which biphasic die-off is expected. Understanding the mechanisms of pathogen decay will ultimately enhance our control efforts to mitigate exposure to environmental contamination.

Transmission heterogeneity and autoinoculation in a multisite infection model of HPV

The human papillomavirus (HPV) is sexually transmitted and can infect oral, genital, and anal sites in the human epithelium. Here, we develop a multisite transmission model that includes autoinoculation to study HPV and other multisite diseases. Under a homogeneous-contacts assumption, we analyze the basic reproduction number R0, as well as type and target reproduction numbers, for a two-site model. In particular, we find that R0 occupies a space between taking the maximum of next generation matrix terms for same site transmission and taking the geometric average of cross-site transmission terms in such a way that heterogeneity in the same-site transmission rates increases R0 while heterogeneity in the cross-site transmission decreases it. Additionally, autoinoculation adds considerable complexity to the form of R0. We extend this analysis to a heterosexual population, which additionally yields dynamics analogous to those of vector-host models. We also examine how these issues of heterogeneity may affect disease control, using type and target reproduction numbers.

Parameter estimation for multistage clonal expansion models from cancer incidence data: A practical identifiability analysis

Many cancers are understood to be the product of multiple somatic mutations or other rate-limiting events. Multistage clonal expansion (MSCE) models are a class of continuous-time Markov chain models that capture the multi-hit initiation–promotion–malignant-conversion hypothesis of carcinogenesis. These models have been used broadly to investigate the epidemiology of many cancers, assess the impact of carcinogen exposures on cancer risk, and evaluate the potential impact of cancer prevention and control strategies on cancer rates. Structural identifiability (the analysis of the maximum parametric information available for a model given perfectly measured data) of certain MSCE models has been previously investigated. However, structural identifiability is a theoretical property and does not address the limitations of real data. In this study, we use pancreatic cancer as a case study to examine the practical identifiability of the two-, three-, and four-stage clonal expansion models given age-specific cancer incidence data using a numerical profile-likelihood approach. We demonstrate that, in the case of the three- and four-stage models, several parameters that are theoretically structurally identifiable, are, in practice, unidentifiable. This result means that key parameters such as the intermediate cell mutation rates are not individually identifiable from the data and that estimation of those parameters, even if structurally identifiable, will not be stable. We also show that products of these practically unidentifiable parameters are practically identifiable, and, based on this, we propose new reparameterizations of the model hazards that resolve the parameter estimation problems. Our results highlight the importance of identifiability to the interpretation of model parameter estimates.

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes.

Dynamics and Determinants of HPV Infection: The Michigan HPV and Oropharyngeal Cancer (M-HOC) Study

Introduction Human papillomavirus (HPV) is the primary cause of cervical and other anogenital cancers and is also associated with head and neck cancers. Incidence of HPV-related oropharyngeal squamous cell cancers (OPSCCs) is increasing, and HPV-related OPSCCs have surpassed cervical cancer as the most common HPV-related cancer in the USA. Given the multisite nature of HPV, there is strong interest in collecting data from both genital and oral sites, as well as associated data on social and sexual behaviours. The overarching goal of this study is to evaluate patterns of oral HPV infection incidence, clearance and persistence and their relationship to sexual behaviour history. Methods and analysis Participants are recruited from two populations: college students at a large public university and general population from the surrounding area. At the first study visit, participants complete a detailed sexual history, health and behaviour questionnaire. Follow-up visits occur every 3–4 months over 3 years, when participants complete an abbreviated questionnaire. All participants provide a saliva sample at each visit, and eligible participants may provide a cervicovaginal self-swab. Genetic material isolated from specimens is tested for 15 high-risk and 3 low-risk HPV types. Statistical analyses will examine outcome variables including HPV prevalence, incidence, persistence and clearance. Logistic regression models will be used to estimate odds ratios and 95% confidence intervals for associations between the outcomes of interest and demographic/behavioural variables collected in the questionnaires. The longitudinal HPV infection data and detailed sexual history data collected in the questionnaires will allow us to develop individual-based network models of HPV transmission and will be used to parameterise multiscale models of HPV-related OPSC carcinogenesis. Ethics and dissemination This study has been approved by the University of Michigan Institutional Review Board. All participants are consented in person by trained study staff. Study results will be disseminated through peer-reviewed publications.

Epidemiology of the silent polio outbreak in Rahat, Israel, based on modeling of environmental surveillance data

Significance The 2013–2014 silent polio epidemic in Israel was a setback to global eradication efforts because Israel had previously been certified as polio-free by the World Health Organization. Fortunately, Israel has a robust environmental surveillance program that detected the epidemic and allowed rapid mobilization of a vaccine campaign before any cases of acute flaccid paralysis. This kind of silent (caseless) epidemic will be increasingly common as we approach global eradication, demonstrating the need for both enhanced environmental surveillance and an accompanying inference framework to translate environmental data into public health metrics. We incorporate environmental data into a population-level disease transmission model, generating insights into the epidemiology of the outbreak. This framework can be used to guide future interventions. Israel experienced an outbreak of wild poliovirus type 1 (WPV1) in 2013–2014, detected through environmental surveillance of the sewage system. No cases of acute flaccid paralysis were reported, and the epidemic subsided after a bivalent oral polio vaccination (bOPV) campaign. As we approach global eradication, polio will increasingly be detected only through environmental surveillance. We developed a framework to convert quantitative polymerase chain reaction (qPCR) cycle threshold data into scaled WPV1 and OPV1 concentrations for inference within a deterministic, compartmental infectious disease transmission model. We used this approach to estimate the epidemic curve and transmission dynamics, as well as assess alternate vaccination scenarios. Our analysis estimates the outbreak peaked in late June, much earlier than previous estimates derived from analysis of stool samples, although the exact epidemic trajectory remains uncertain. We estimate the basic reproduction number was 1.62 (95% CI 1.04–2.02). Model estimates indicate that 59% (95% CI 9–77%) of susceptible individuals (primarily children under 10 years old) were infected with WPV1 over a little more than six months, mostly before the vaccination campaign onset, and that the vaccination campaign averted 10% (95% CI 1–24%) of WPV1 infections. As we approach global polio eradication, environmental monitoring with qPCR can be used as a highly sensitive method to enhance disease surveillance. Our analytic approach brings public health relevance to environmental data that, if systematically collected, can guide eradication efforts.

Determinants of short-term movement in a developing region and implications for disease transmission

Background: Human mobility is important for infectious disease spread. However, little is known about how travel varies by demographic groups and how this heterogeneity influences infectious disease risk. Methods: We analyzed 10 years of survey data from 15 communities in a remote but rapidly changing region in rural Ecuador where road development in the past 15–20 years has dramatically changed travel. We identify determinants of travel and incorporate them into an infection transmission model. Results: Individuals living in communities more remote at baseline had lower travel rates compared with less remote villages (adjusted odds ratio [OR] = 0.51; 95% confidence interval [CI] = 0.38, 0.67). Our model predicts that less remote villages are, therefore, at increased disease risk. Though road building and travel increased for all communities, this risk differential remained over 10 years of observation. Our transmission model also suggests that travelers and nontravelers have different roles in disease transmission. Adults travel more than children (adjusted OR = 1.73; 95% CI = 1.30, 2.31) and therefore disseminate infection from population centers to rural communities. Children are more likely than adults to be infected locally (attributable fraction = 0.24 and 0.09, respectively) and were indirectly affected by adult travel patterns. Conclusions: These results reinforce the importance of large population centers for regional transmission and show that children and adults may play different roles in disease spread. Changing transportation infrastructure and subsequent economic and social transitions are occurring worldwide, potentially causing increased regional risk of disease.