The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission

Background : Mathematical models of tuberculosis (TB) transmission have been used to characterize disease dynamics, investigate the potential effects of public health interventions, and prioritize control measures. While previous work has addressed the mathematical description of TB natural history, the impact of demography on the behaviour of TB models has not been assessed. Methods : A simple model of TB transmission, with alternative assumptions about survivorship, is used to explore the effect of age structure on the prevalence of infection, disease, basic reproductive ratio and the projected impact of control interventions. We focus our analytic arguments on the differences between constant and exponentially distributed lifespans and use an individual-based model to investigate the range of behaviour arising from realistic distributions of survivorship. Results : The choice of age structure and natural (non-disease related) mortality strongly affects steady-state dynamics, parameter estimation and predictions about the effectiveness of control interventions. Since most individuals infected with TB develop an asymptomatic latent infection and never progress to active disease, we find that assuming a constant mortality rate results in a larger reproductive ratio and an overestimation of the effort required for disease control in comparison to using more realistic age-specific mortality rates. Conclusions : Demographic modelling assumptions should be considered in the interpretation of models of chronic infectious diseases such as TB. For simple models, we find that assuming constant lifetimes, rather than exponential lifetimes, produces dynamics more representative of models with realistic age structure

High speed video capture for mobile phone cameras

We consider an electromechanical model for the operation of a voice coil motor in a mobile phone camera, with the aim of optimizing how a lens can be moved to a desired focusing motion. Although a methodology is developed for optimizing lens shift, there is some concern about the experimentally-determined model parameters that are at our disposal. Central to the model is the value of the estimated magnetic force constant, Kf: its value determines how far it is actually possible to move lens, but it appears that, from the value given, it would not be possible to shift the lens through the displacements desired. Furthermore, earlier experiments have also estimated the value of the back EMF constant, Kg , to be roughly five times greater than Kf, even though we present two theoretical arguments that show that Kf = Kg: a conclusion supported by readily-available manufacturers’ data

Tuberculosis incidence correlates with sunshine : an ecological 28-year time series study

Birmingham is the largest UK city after London, and central Birmingham has an annual tuberculosis incidence of 80 per 100,000. We examined seasonality and sunlight as drivers of tuberculosis incidence. Hours of sunshine are seasonal, sunshine exposure is necessary for the production of vitamin D by the body and vitamin D plays a role in the host response to tuberculosis. Methods: We performed an ecological study that examined tuberculosis incidence in Birmingham from Dec 1981 to Nov 2009, using publicly-available data from statutory tuberculosis notifications, and related this to the seasons and hours of sunshine (UK Meteorological Office data) using unmeasured component models. Results: There were 9,739 tuberculosis cases over the study period. There was strong evidence for seasonality, with notifications being 24.1% higher in summer than winter (p<0.001). Winter dips in sunshine correlated with peaks in tuberculosis incidence six months later (4.7% increase in incidence for each 100 hours decrease in sunshine, p<0.001). Discussion and Conclusion: A potential mechanism for these associations includes decreased vitamin D levels with consequent impaired host defence arising from reduced sunshine exposure in winter. This is the longest time series of any published study and our use of statutory notifications means this data is essentially complete. We cannot, however, exclude the possibility that another factor closely correlated with the seasons, other than sunshine, is responsible. Furthermore, exposure to sunlight depends not only on total hours of sunshine but also on multiple individual factors. Our results should therefore be considered hypothesis-generating. Confirmation of a potential causal relationship between winter vitamin D deficiency and summer peaks in tuberculosis incidence would require a randomized-controlled trial of the effect of vitamin D supplementation on future tuberculosis incidence

Observational study to estimate the changes in the effectiveness of bacillus Calmette-Guérin (BCG) vaccination with time since vaccination for preventing tuberculosis in the UK.

Until recently, evidence that protection from the bacillus Calmette-Guérin (BCG) vaccination lasted beyond 10 years was limited. In the past few years, studies in Brazil and the USA (in Native Americans) have suggested that protection from BCG vaccination against tuberculosis (TB) in childhood can last for several decades. The UK's universal school-age BCG vaccination programme was stopped in 2005 and the programme of selective vaccination of high-risk (usually ethnic minority) infants was enhanced. To assess the duration of protection of infant and school-age BCG vaccination against TB in the UK. Two case-control studies of the duration of protection of BCG vaccination were conducted, the first on minority ethnic groups who were eligible for infant BCG vaccination 0-19 years earlier and the second on white subjects eligible for school-age BCG vaccination 10-29 years earlier. TB cases were selected from notifications to the UK national Enhanced Tuberculosis Surveillance system from 2003 to 2012. Population-based control subjects, frequency matched for age, were recruited. BCG vaccination status was established from BCG records, scar reading and BCG history. Information on potential confounders was collected using computer-assisted interviews. Vaccine effectiveness was estimated as a function of time since vaccination, using a case-cohort analysis based on Cox regression. In the infant BCG study, vaccination status was determined using vaccination records as recall was poor and concordance between records and scar reading was limited. A protective effect was seen up to 10 years following infant vaccination [&lt; 5 years since vaccination: vaccine effectiveness (VE) 66%, 95% confidence interval (CI) 17% to 86%; 5-10 years since vaccination: VE 75%, 95% CI 43% to 89%], but there was weak evidence of an effect 10-15 years after vaccination (VE 36%, 95% CI negative to 77%; p = 0.396). The analyses of the protective effect of infant BCG vaccination were adjusted for confounders, including birth cohort and ethnicity. For school-aged BCG vaccination, VE was 51% (95% CI 21% to 69%) 10-15 years after vaccination and 57% (95% CI 33% to 72%) 15-20 years after vaccination, beyond which time protection appeared to wane. Ascertainment of vaccination status was based on self-reported history and scar reading. The difficulty in examining vaccination sites in older women in the high-risk minority ethnic study population and the sparsity of vaccine record data in the later time periods precluded robust assessment of protection from infant BCG vaccination &gt; 10 years after vaccination. Infant BCG vaccination in a population at high risk for TB was shown to provide protection for at least 10 years, whereas in the white population school-age vaccination was shown to provide protection for at least 20 years. This evidence may inform TB vaccination programmes (e.g. the timing of administration of improved TB vaccines, if they become available) and cost-effectiveness studies. Methods to deal with missing record data in the infant study could be explored, including the use of scar reading. The National Institute for Health Research Health Technology Assessment programme. During the conduct of the study, Jonathan Sterne, Ibrahim Abubakar and Laura C Rodrigues received other funding from NIHR; Ibrahim Abubakar and Laura C Rodrigues have also received funding from the Medical Research Council. Punam Mangtani received funding from the Biotechnology and Biological Sciences Research Council

Using Seroprevalence and Immunisation Coverage Data to Estimate the Global Burden of Congenital Rubella Syndrome, 1996-2010: A Systematic Review.

BACKGROUND: The burden of Congenital Rubella Syndrome (CRS) is typically underestimated in routine surveillance. Updated estimates are needed following the recent WHO position paper on rubella and recent GAVI initiatives, funding rubella vaccination in eligible countries. Previous estimates considered the year 1996 and only 78 (developing) countries. METHODS: We reviewed the literature to identify rubella seroprevalence studies conducted before countries introduced rubella-containing vaccination (RCV). These data and the estimated vaccination coverage in the routine schedule and mass campaigns were incorporated in mathematical models to estimate the CRS incidence in 1996 and 2000-2010 for each country, region and globally. RESULTS: The estimated CRS decreased in the three regions (Americas, Europe and Eastern Mediterranean) which had introduced widespread RCV by 2010, reaching <2 per 100,000 live births (the Americas and Europe) and 25 (95% CI 4-61) per 100,000 live births (the Eastern Mediterranean). The estimated incidence in 2010 ranged from 90 (95% CI: 46-195) in the Western Pacific, excluding China, to 116 (95% CI: 56-235) and 121 (95% CI: 31-238) per 100,000 live births in Africa and SE Asia respectively. Highest numbers of cases were predicted in Africa (39,000, 95% CI: 18,000-80,000) and SE Asia (49,000, 95% CI: 11,000-97,000). In 2010, 105,000 (95% CI: 54,000-158,000) CRS cases were estimated globally, compared to 119,000 (95% CI: 72,000-169,000) in 1996. CONCLUSIONS: Whilst falling dramatically in the Americas, Europe and the Eastern Mediterranean after vaccination, the estimated CRS incidence remains high elsewhere. Well-conducted seroprevalence studies can help to improve the reliability of these estimates and monitor the impact of rubella vaccination

Periodic Active Case Finding for TB: When to Look?

OBJECTIVE: To investigate the factors influencing the performance and cost-efficacy of periodic rounds of active case finding (ACF) for TB. METHODS: A mathematical model of TB dynamics and periodic ACF (PACF) in the HIV era, simplified by assuming constant prevalence of latent TB infection, is analyzed for features that control intervention outcome, measured as cases averted and cases found. Explanatory variables include baseline TB incidence, interval between PACF rounds, and different routine and PACF case-detection rates among HIV-infected and uninfected TB cases. FINDINGS: PACF can be cost-saving over a 10 year time frame if the cost-per-round is lower than a threshold proportional to initial incidence and cost-per-case-treated. More cases are averted at higher baseline incidence rates, when more potent PACF strategies are used, intervals between PACF rounds are shorter, and when the ratio of HIV-negative to positive TB cases detected is higher. More costly approaches, e.g. radiographic screening, can be as cost-effective as less costly alternatives if PACF case-detection is higher and/or implementation less frequent. CONCLUSION: Periodic ACF can both improve control and save medium-term health care costs in high TB burden settings. Greater costs of highly effective PACF at frequent (e.g. yearly) intervals may be offset by higher numbers of cases averted in populations with high baseline TB incidence, higher prevalence of HIV-uninfected cases, higher costs per-case-treated, and more effective routine case-detection. Less intensive approaches may still be cost-neutral or cost-saving in populations lacking one or more of these key determinants

The social contact hypothesis under the assumption of endemic equilibrium: Elucidating the transmission potential of VZV in Europe.

The basic reproduction number R0 and the effective reproduction number R are pivotal parameters in infectious disease epidemiology, quantifying the transmission potential of an infection in a population. We estimate both parameters from 13 pre-vaccination serological data sets on varicella zoster virus (VZV) in 12 European countries and from population-based social contact surveys under the commonly made assumptions of endemic and demographic equilibrium. The fit to the serology is evaluated using the inferred effective reproduction number R as a model eligibility criterion combined with AIC as a model selection criterion. For only 2 out of 12 countries, the common choice of a constant proportionality factor is sufficient to provide a good fit to the seroprevalence data. For the other countries, an age-specific proportionality factor provides a better fit, assuming physical contacts lasting longer than 15 min are a good proxy for potential varicella transmission events. In all countries, primary infection with VZV most often occurs in early childhood, but there is substantial variation in transmission potential with R0 ranging from 2.8 in England and Wales to 7.6 in The Netherlands. Two non-parametric methods, the maximal information coefficient (MIC) and a random forest approach, are used to explain these differences in R0 in terms of relevant country-specific characteristics. Our results suggest an association with three general factors: inequality in wealth, infant vaccination coverage and child care attendance. This illustrates the need to consider fundamental differences between European countries when formulating and parameterizing infectious disease models

Simulations for designing and interpreting intervention trials in infectious diseases.

BACKGROUND: Interventions in infectious diseases can have both direct effects on individuals who receive the intervention as well as indirect effects in the population. In addition, intervention combinations can have complex interactions at the population level, which are often difficult to adequately assess with standard study designs and analytical methods. DISCUSSION: Herein, we urge the adoption of a new paradigm for the design and interpretation of intervention trials in infectious diseases, particularly with regard to emerging infectious diseases, one that more accurately reflects the dynamics of the transmission process. In an increasingly complex world, simulations can explicitly represent transmission dynamics, which are critical for proper trial design and interpretation. Certain ethical aspects of a trial can also be quantified using simulations. Further, after a trial has been conducted, simulations can be used to explore the possible explanations for the observed effects. CONCLUSION: Much is to be gained through a multidisciplinary approach that builds collaborations among experts in infectious disease dynamics, epidemiology, statistical science, economics, simulation methods, and the conduct of clinical trials

An evaluation of indices for quantifying tuberculosis transmission using genotypes of pathogen isolates

BACKGROUND: Infectious diseases are often studied by characterising the population structure of the pathogen using genetic markers. An unresolved problem is the effective quantification of the extent of transmission using genetic variation data from such pathogen isolates. METHODS: It is important that transmission indices reflect the growth of the infectious population as well as account for the mutation rate of the marker and the effects of sampling. That is, while responding to this growth rate, indices should be unresponsive to the sample size and the mutation rate. We use simulation methods taking into account both the mutation and sampling processes to evaluate indices designed to quantify transmission of tuberculosis. RESULTS: Previously proposed indices generally perform inadequately according to the above criteria, with the partial exception of the recently proposed Transmission-Mutation Index. CONCLUSION: Any transmission index needs to take into account mutation of the marker and the effects of sampling. Simple indices are unlikely to capture the full complexity of the underlying processes