Fengchen Liu

Assessing Measles Transmission in the United States Following a Large Outbreak in California.

The recent increase in measles cases in California may raise questions regarding the continuing success of measles control. To determine whether the dynamics of measles is qualitatively different in comparison to previous years, we assess whether the 2014-2015 measles outbreak associated with an Anaheim theme park is consistent with subcriticality by calculating maximum-likelihood estimates for the effective reproduction numbe given this year’s outbreak, using the Galton-Watson branching process model. We find that the dynamics after the initial transmission event are consistent with prior transmission, but does not exclude the possibilty that the effective reproduction number has increased.

The efficacy of oral azithromycin in clearing ocular chlamydia: Mathematical modeling from a community-randomized trachoma trial☆

Mass oral azithromycin distributions have dramatically reduced the prevalence of the ocular strains of chlamydia that cause trachoma. Assessing efficacy of the antibiotic in an individual is important in planning trachoma elimination. However, the efficacy is difficult to estimate, because post-treatment laboratory testing may be complicated by nonviable organisms or reinfection. Here, we monitored ocular chlamydial infection twice a year in pre-school children in 32 communities as part of a cluster-randomized clinical trial in Tanzania (prevalence in children was lowered from 22.0% to 4.7% after 3-year of annual treatment). We used a mathematical transmission model to estimate the prevalence of infection immediately after treatment, and found the effective field efficacy of antibiotic in an individual to be 67.6% (95% CI: 56.5–75.1%) in this setting. Sensitivity analyses suggested that these results were not dependent on specific assumptions about the duration of infection. We found no evidence of decreased efficacy during the course of the trial. We estimated an 89% chance of elimination after 10 years of annual treatment with 95% coverage.

Short-term Forecasting of the Prevalence of Trachoma: Expert Opinion, Statistical Regression, versus Transmission Models.

Background Trachoma programs rely on guidelines made in large part using expert opinion of what will happen with and without intervention. Large community-randomized trials offer an opportunity to actually compare forecasting methods in a masked fashion. Methods The Program for the Rapid Elimination of Trachoma trials estimated longitudinal prevalence of ocular chlamydial infection from 24 communities treated annually with mass azithromycin. Given antibiotic coverage and biannual assessments from baseline through 30 months, forecasts of the prevalence of infection in each of the 24 communities at 36 months were made by three methods: the sum of 15 experts’ opinion, statistical regression of the square-root-transformed prevalence, and a stochastic hidden Markov model of infection transmission (Susceptible-Infectious-Susceptible, or SIS model). All forecasters were masked to the 36-month results and to the other forecasts. Forecasts of the 24 communities were scored by the likelihood of the observed results and compared using Wilcoxon’s signed-rank statistic. Findings Regression and SIS hidden Markov models had significantly better likelihood than community expert opinion (p = 0.004 and p = 0.01, respectively). All forecasts scored better when perturbed to decrease Fisher’s information. Each individual expert’s forecast was poorer than the sum of experts. Interpretation Regression and SIS models performed significantly better than expert opinion, although all forecasts were overly confident. Further model refinements may score better, although would need to be tested and compared in new masked studies. Construction of guidelines that rely on forecasting future prevalence could consider use of mathematical and statistical models.

Assessment of Transmission in Trachoma Programs over Time Suggests No Short-Term Loss of Immunity

Trachoma programs have dramatically reduced the prevalence of the ocular chlamydia that cause the disease. Some have hypothesized that immunity to the infection may be reduced because of program success in reducing the incidence of infection, and transmission may then increase. Longitudinal studies of multiple communities would be necessary to test this hypothesis. Here, we quantify transmission using an estimated basic reproduction number based on 32 communities during the first, second, and third years of an antibiotic treatment program. We found that there is little to no increase in the basic reproduction number over time. The estimated linear trend in the basic reproduction number, , was found to be −0.025 per year, 95% CI −0.167 to 0.117 per year. We are unable to find evidence supporting any loss of immunity over the course of a 3-year program. This is encouraging, as it allows the possibility that repeated mass antibiotic distributions may eliminate infection from even the most severely affected areas.

A multilevel model of postmenopausal breast cancer incidence

Background: Breast cancer has a complex etiology that includes genetic, biologic, behavioral, environmental, and social factors. Etiologic factors are frequently studied in isolation with adjustment for confounding, mediating, and moderating effects of other factors. A complex systems model approach may present a more comprehensive picture of the multifactorial etiology of breast cancer. Methods: We took a transdisciplinary approach with experts from relevant fields to develop a conceptual model of the etiology of postmenopausal breast cancer. The model incorporated evidence of both the strength of association and the quality of the evidence. We operationalized this conceptual model through a mathematical simulation model with a subset of variables, namely, age, race/ethnicity, age at menarche, age at first birth, age at menopause, obesity, alcohol consumption, income, tobacco use, use of hormone therapy (HT), and BRCA1/2 genotype. Results: In simulating incidence for California in 2000, the separate impact of individual variables was modest, but reduction in HT, increase in the age at menarche, and to a lesser extent reduction in excess BMI >30 kg/m2 were more substantial. Conclusions: Complex systems models can yield new insights on the etiologic factors involved in postmenopausal breast cancer. Modification of factors at a population level may only modestly affect risk estimates, while still having an important impact on the absolute number of women affected. Impact: This novel effort highlighted the complexity of breast cancer etiology, revealed areas of challenge in the methodology of developing complex systems models, and suggested additional areas for further study. Cancer Epidemiol Biomarkers Prev; 23(10); 2078–92. ©2014 AACR.

Effect of the One-Child Policy on Influenza Transmission in China: A Stochastic Transmission Model

Background Chinas one-child-per-couple policy, introduced in 1979, led to profound demographic changes for nearly a quarter of the worlds population. Several decades later, the consequences include decreased fertility rates, population aging, decreased household sizes, changes in family structure, and imbalanced sex ratios. The epidemiology of communicable diseases may have been affected by these changes since the transmission dynamics of infectious diseases depend on demographic characteristics of the population. Of particular interest is influenza because China and Southeast Asia lie at the center of a global transmission network of influenza. Moreover, changes in household structure may affect influenza transmission. Is it possible that the pronounced demographic changes that have occurred in China have affected influenza transmission? Methods and Findings To address this question, we developed a continuous-time, stochastic, individual-based simulation model for influenza transmission. With this model, we simulated 30 years of influenza transmission and compared influenza transmission rates in populations with and without the one-child policy control. We found that the average annual attack rate is reduced by 6.08% (SD 2.21%) in the presence of the one-child policy compared to a population in which no demographic changes occurred. There was no discernible difference in the secondary attack rate, −0.15% (SD 1.85%), between the populations with and without a one-child policy. We also forecasted influenza transmission over a ten-year time period in a population with a two-child policy under a hypothesis that a two-child-per-couple policy will be carried out in 2015, and found a negligible difference in the average annual attack rate compared to the population with the one-child policy. Conclusions This study found that the average annual attack rate is slightly lowered in a population with a one-child policy, which may have resulted from a decrease in household size and the proportion of children in the population.

Optimal Seasonal Timing of Oral Azithromycin for Malaria

Mass administration of azithromycin for trachoma has been shown to reduce malarial parasitemia. However, the optimal seasonal timing of such distributions for antimalarial benefit has not been established. We performed numerical analyses on a seasonally forced epidemic model (of Ross-Macdonald type) with periodic impulsive annual mass treatment to address this question. We conclude that when azithromycin-based trachoma elimination programs occur in regions of seasonal malaria transmission, such as Niger, the optimal seasonal timing of mass drug administration (MDA) may not occur during the season of maximum transmission.

Probabilistic forecasts of trachoma transmission at the district level: A statistical model comparison

The World Health Organization and its partners are aiming to eliminate trachoma as a public health problem by 2020. In this study, we compare forecasts of TF prevalence in 2011 for 7 different statistical and mechanistic models across 9 de-identified trachoma endemic districts, representing 4 unique trachoma endemic countries. We forecast TF prevalence between 1–6 years ahead in time and compare the 7 different models to the observed 2011 data using a log-likelihood score. An SIS model, including a district-specific random effect for the district-specific transmission coefficient, had the highest log-likelihood score across all 9 districts and was therefore the best performing model. While overall the deterministic transmission model was the least well performing model, although it did comparably well to the other models for 8 of 9 districts. We perform a statistically rigorous comparison of the forecasting ability of a range of mathematical and statistical models across multiple endemic districts between 1 and 6 years ahead of the last collected TF prevalence data point in 2011, assessing results against surveillance data. This study is a step towards making statements about likelihood and time to elimination with regard to the WHO GET2020 goals.

The Effect of Contact Investigations and Public Health Interventions in the Control and Prevention of Measles Transmission: A Simulation Study

Background Measles cases continue to occur despite its elimination status in the United States. To control transmission, public health officials confirm the measles diagnosis, identify close contacts of infectious cases, deliver public health interventions (i.e., post-exposure prophylaxis) among those who are eligible, and follow-up with the close contacts to determine overall health outcomes. A stochastic network simulation of measles contact tracing was conducted using existing agent-based modeling software and a synthetic population with high levels of immunity in order to estimate the impact of different interventions in controlling measles transmission. Methods and Findings The synthetic population was created to simulate California`s population in terms of population demographics, household, workplace, school, and neighborhood characteristics using California Department of Finance 2010 census data. Parameters for the model were obtained from a review of the literature, California measles case surveillance data, and expert opinion. Eight different scenarios defined by the use of three different public health interventions were evaluated: (a) post-exposure measles, mumps, and rubella (MMR) vaccine, (b) post-exposure immune globulin (IG), and (c) voluntary isolation and home quarantine in the presence or absence of public health response delays. Voluntary isolation and home quarantine coupled with one or two other interventions had the greatest reduction in the number of secondary cases infected by the index case and the probability of escape situations (i.e., the outbreak continues after 90 days). Conclusions Interrupting contact patterns via voluntary isolation and home quarantine are particularly important in reducing the number of secondary cases infected by the index case and the probability of uncontrolled outbreaks.

Evaluating Subcriticality during the Ebola Epidemic in West Africa

The 2014–2015 Ebola outbreak is the largest and most widespread to date. In order to estimate ongoing transmission in the affected countries, we estimated the weekly average number of secondary cases caused by one individual infected with Ebola throughout the infectious period for each affected West African country using a stochastic hidden Markov model fitted to case data from the World Health Organization. If the average number of infections caused by one Ebola infection is less than 1.0, the epidemic is subcritical and cannot sustain itself. The epidemics in Liberia and Sierra Leone have approached subcriticality at some point during the epidemic; the epidemic in Guinea is ongoing with no evidence that it is subcritical. Response efforts to control the epidemic should continue in order to eliminate Ebola cases in West Africa.