Mathematical models have been used to investigate the dynamics of infectious disease transmission since Bernoulli's smallpox modelling in 1760. Their use has become widespread for exploring how epidemics can be prevented or contained. Here we discuss the importance of modelling the dynamics of sexually transmitted infections, the technology-driven dichotomy in methodology, and the need to 'keep it simple' to explore sensitivity, to link the models to reality and to provide understandable mechanistic explanations for real-world policy-makers. The aim of models, after all, is to influence or change public health policy by providing rational forecasting based on sound scientific principles.
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"The risk of influenza-related morbidity and mortality is typically the highest among the elderly, particularly among residents of long-term care facilities (LTCFs) . Vaccination against influenza in LTCFs is a priority and the Centers for Disease Control and Prevention (CDC) recommend that health care workers (HCWs) in these facilities get vaccinated against influenza annually . "
[Show abstract][Hide abstract] ABSTRACT: Introduction:
Vaccinating healthcare workers (HCWs) in long-term care facilities (LTCFs) may effectively induce herd immunity and protect residents against influenza-related morbidity and mortality. We used influenza surveillance data from all LTCFs in New Mexico to validate a transmission dynamics model developed to investigate herd immunity induction.
Material and methods:
We adjusted a previously published transmission dynamics model and used surveillance data from an active system among 76 LTCFs in New Mexico during 2006-2007 for model validation. We used a deterministic compartmental model with a stochastic component for transmission between residents and HCWs in each facility in order to simulate the random variation expected in such populations.
When outbreaks were defined as a dichotomous variable, our model predicted that herd immunity could be induced. When defined as an attack rate, the model demonstrated a curvilinear trend, but insufficiently strong to induce herd immunity. The model was sensitive to changes in the contact parameter β but was robust to changes in the visitor contact probability.
These results further elucidate previous studies' findings that herd immunity may not be induced by vaccinating HCWs in LTCFs; however, increased influenza vaccination coverage among HCWs reduces the probability of influenza infection among residents.
Full-text · Article · Jun 2015 · Computational and Mathematical Methods in Medicine
"The latter approach is particularly useful for low prevalence infections where there is a possibility of extinction and/or where it is necessary to capture events that occur at the level of the individual (e.g., tracing and treating sexual partners of infected individuals). However, for their computational efficiency, analytical tractability and ability to provide mechanistic insights to epidemic dynamics, deterministic ordinary differential equation (ODE) models are often preferred, particularly for endemic infections such as HPV . We have previously developed a deterministic single-type transmission model for HPV-16  and more recently multi-type models for HPV types 6, 11, 16 and 18 in order to evaluate the potential impact of vaccination. "
[Show abstract][Hide abstract] ABSTRACT: A Bayesian statistical model and estimation methodology based on forward projection adaptive Markov chain Monte Carlo is developed in order to perform the calibration of a high-dimensional nonlinear system of ordinary differential equations representing an epidemic model for human papillomavirus types 6 and 11 (HPV-6, HPV-11). The model is compartmental and involves stratification by age, gender and sexual-activity group. Developing this model and a means to calibrate it efficiently is relevant because HPV is a very multi-typed and common sexually transmitted infection with more than 100 types currently known. The two types studied in this paper, types 6 and 11, are causing about 90% of anogenital warts.
We extend the development of a sexual mixing matrix on the basis of a formulation first suggested by Garnett and Anderson, frequently used to model sexually transmitted infections. In particular, we consider a stochastic mixing matrix framework that allows us to jointly estimate unknown attributes and parameters of the mixing matrix along with the parameters involved in the calibration of the HPV epidemic model. This matrix describes the sexual interactions between members of the population under study and relies on several quantities that are a priori unknown. The Bayesian model developed allows one to estimate jointly the HPV-6 and HPV-11 epidemic model parameters as well as unknown sexual mixing matrix parameters related to assortativity.
Finally, we explore the ability of an extension to the class of adaptive Markov chain Monte Carlo algorithms to incorporate a forward projection strategy for the ordinary differential equation state trajectories. Efficient exploration of the Bayesian posterior distribution developed for the ordinary differential equation parameters provides a challenge for any Markov chain sampling methodology, hence the interest in adaptive Markov chain methods. We conclude with simulation studies on synthetic and recent actual data. Copyright
Full-text · Article · May 2013 · Statistics in Medicine
[Show abstract][Hide abstract] ABSTRACT: To assess the impact of screening programmes in reducing the prevalence of Chlamydia trachomatis, mathematical and computational models are used as a guideline for decision support. Unfortunately, large uncertainties exist about the parameters that determine the transmission dynamics of C. trachomatis. Here, we use a SEIRS (susceptible-exposed-infected-recovered-susceptible) model to critically analyze the turnover of C. trachomatis in a population and the impact of a screening programme. We perform a sensitivity analysis on the most important steps during an infection with C. trachomatis. Varying the fraction of the infections becoming symptomatic as well as the duration of the symptomatic period within the range of previously used parameter estimates has little effect on the transmission dynamics. However, uncertainties in the duration of temporary immunity and the asymptomatic period can result in large differences in the predicted impact of a screening programme. We therefore analyze previously published data on the persistence of asymptomatic C. trachomatis infection in women and estimate the mean duration of the asymptomatic period to be longer than anticipated so far, namely 433 days (95% CI: 420-447 days). Our study shows that a longer duration of the asymptomatic period results in a more pronounced impact of a screening programme. However, due to the slower turnover of the infection, a substantial reduction in prevalence can only be achieved after screening for several years or decades.