Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

Changes in Cognition and Mortality in Relation to Exercise in Late Life: A Population Based Study

BACKGROUND: On average, cognition declines with age but this average hides considerable variability, including the chance of improvement. Here, we investigate how exercise is associated with cognitive change and mortality in older people and, particularly, whether exercise might paradoxically increase the risk of dementia by allowing people to live longer. METHODS AND PRINCIPAL FINDINGS: In the Canadian Study of Health and Aging (CSHA), of 8403 people who had baseline cognition measured and exercise reported at CSHA-1, 2219 had died and 5376 were re-examined at CSHA-2. We used a parametric Markov chain model to estimate the probabilities of cognitive improvement, decline, and death, adjusted for age and education, from any cognitive state as measured by the Modified Mini-Mental State Examination. High exercisers (at least three times per week, at least as intense as walking, n = 3264) had more frequent stable or improved cognition (42.3%, 95% confidence interval: 40.6-44.0) over 5 years than did low/no exercisers (all other exercisers and non exercisers, n = 4331) (27.8% (95% CI 26.4-29.2)). The difference widened as baseline cognition worsened. The proportion whose cognition declined was higher amongst the high exercisers but was more similar between exercise groups (39.4% (95% CI 37.7-41.1) for high exercisers versus 34.8% (95% CI 33.4-36.2) otherwise). People who did not exercise were also more likely to die (37.5% (95% CI 36.0-39.0) versus 18.3% (95% CI 16.9-19.7)). Even so, exercise conferred its greatest mortality benefit to people with the highest baseline cognition. CONCLUSIONS: Exercise is strongly associated with improving cognition. As the majority of mortality benefit of exercise is at the highest level of cognition, and declines as cognition declines, the net effect of exercise should be to improve cognition at the population level, even with more people living longer

Environmental risk factors for dementia: a systematic review

Background - Dementia risk reduction is a major and growing public health priority. While certain modifiable risk factors for dementia have been identified, there remains a substantial proportion of unexplained risk. There is evidence that environmental risk factors may explain some of this risk. Thus, we present the first comprehensive systematic review of environmental risk factors for dementia. Methods - We searched the PubMed and Web of Science databases from their inception to January 2016, bibliographies of review articles, and articles related to publically available environmental data. Articles were included if they examined the association between an environmental risk factor and dementia. Studies with another outcome (for example, cognition), a physiological measure of the exposure, case studies, animal studies, and studies of nutrition were excluded. Data were extracted from individual studies which were, in turn, appraised for methodological quality. The strength and consistency of the overall evidence for each risk factor identified was assessed. Results - We screened 4784 studies and included 60 in the review. Risk factors were considered in six categories: air quality, toxic heavy metals, other metals, other trace elements, occupational-related exposures, and miscellaneous environmental factors. Few studies took a life course approach. There is at least moderate evidence implicating the following risk factors: air pollution; aluminium; silicon; selenium; pesticides; vitamin D deficiency; and electric and magnetic fields. Conclusions - Studies varied widely in size and quality and therefore we must be circumspect in our conclusions. Nevertheless, this extensive review suggests that future research could focus on a short list of environmental risk factors for dementia. Furthermore, further robust, longitudinal studies with repeated measures of environmental exposures are required to confirm these associations