Allee threshold and stochasticity in biological invasions: colonization time at low propagule pressure.

We consider the problem of estimating the time needed for species colonization. The analysis is based upon the known population dynamic models by Dennis with minor modification to the Allee effect description, which allows us to obtain an analytical expression for the colonization time. For the stochastic counterpart of the models in diffusion approximation, we (1) propose the description of immigration stochasticity, (2) provide the estimates of time required for the population to overcome strong demographic Allee effect, and (3) consider the numerical results for mean colonization time and its uncertainty. Strong Allee effect strictly disallows populations at small immigration rates to colonize new habitats, unless the stochasticity in immigration, environment, or demography is present, or incorporated into the model. Immigration stochasticity, complementing with environmental and demographic stochasticity, enables the populations to overcome the Allee threshold even at low values of propagule pressure.

Wildlife disease elimination and density dependence.

Disease control by managers is a crucial response to emerging wildlife epidemics, yet the means of control may be limited by the method of disease transmission. In particular, it is widely held that population reduction, while effective for controlling diseases that are subject to density-dependent (DD) transmission, is ineffective for controlling diseases that are subject to frequency-dependent (FD) transmission. We investigate control for horizontally transmitted diseases with FD transmission where the control is via culling or harvest that is non-selective with respect to infection and the population can compensate through DD recruitment or survival. Using a mathematical model, we show that culling or harvesting can eradicate the disease, even when transmission dynamics are FD. Eradication can be achieved under FD transmission when DD birth or recruitment induces compensatory growth of new, healthy individuals, which has the net effect of reducing disease prevalence by dilution. We also show that if harvest is used simultaneously with vaccination, and there is high enough transmission coefficient, application of both controls may be less efficient than vaccination alone. We illustrate the effects of these control approaches on disease prevalence for chronic wasting disease in deer where the disease is transmitted directly among deer and through the environment.

Chronic Wasting Disease: Transmission Mechanisms and the Possibility of Harvest Management.

We develop a model of CWD management by nonselective deer harvest, currently the most feasible approach available for managing CWD in wild populations. We use the model to explore the effects of 6 common harvest strategies on disease prevalence and to identify potential optimal harvest policies for reducing disease prevalence without population collapse. The model includes 4 deer categories (juveniles, adult females, younger adult males, older adult males) that may be harvested at different rates, a food-based carrying capacity, which influences juvenile survival but not adult reproduction or survival, and seasonal force of infection terms for each deer category under differing frequency-dependent transmission dynamics resulting from environmental and direct contact mechanisms. Numerical experiments show that the interval of transmission coefficients ß where the disease can be controlled is generally narrow and efficiency of a harvest policy to reduce disease prevalence depends crucially on the details of the disease transmission mechanism, in particular on the intensity of disease transmission to juveniles and the potential differences in the behavior of older and younger males that influence contact rates. Optimal harvest policy to minimize disease prevalence for each of the assumed transmission mechanisms is shown to depend on harvest intensity. Across mechanisms, a harvest that focuses on antlered deer, without distinguishing between age classes reduces disease prevalence most consistently, whereas distinguishing between young and older antlered deer produces higher uncertainty in the harvest effects on disease prevalence. Our results show that, despite uncertainties, a modelling approach can determine classes of harvest strategy that are most likely to be effective in combatting CWD.

Empirical Estimation of R0 for Unknown Transmission Functions: The Case of Chronic Wasting Disease in Alberta.

We consider the problem of estimating the basic reproduction number R0 from data on prevalence dynamics at the beginning of a disease outbreak. We derive discrete and continuous time models, some coefficients of which are to be fitted from data. We show that prevalence of the disease is sufficient to determine R0. We apply this method to chronic wasting disease spread in Alberta determining a range of possible R0 and their sensitivity to the probability of deer annual survival.

Quality Indicators of End-of-Life Care in Patients With Cancer: What Rate Is Right?

PURPOSE: To develop data-driven and achievable benchmark rates for end-of-life quality indicators using administrative data from four provinces in Canada. METHODS: Indicators of end-of-life care were defined and measured using linked administrative data for 33 health regions across British Columbia, Alberta, Ontario, and Nova Scotia. These were emergency department use, intensive care unit admission, physician house calls and home care visits before death, and death in hospital. An empiric benchmark was defined using indicator rates from the top-ranked regions to include the top decile of patients overall. Funnel plots were used to graph each region's age- and sex-adjusted indicator rates along with the overall rate and 95% confidence limits. RESULTS: Rates varied approximately two- to four-fold across the regions, with physician house calls showing the greatest variation. Benchmark rates based on the top decile performers were emergency department use, 34%; intensive care unit admission, 2%; physician house calls, 34%; home care visits, 63%; and death in hospital, 38%. With the exception of intensive care unit admission, funnel plots demonstrated that overall indicator rates and their confidence limits were uniformly worse than benchmarks even after adjusting for age and sex. Few regions met the benchmark rates. CONCLUSION: There is significant variation in end-of-life quality indicators across regions in four provinces in Canada. Using this study's methods-deriving empiric benchmarks and funnel plots-regions can determine their relative performance with greater context that facilitates priority setting and resource deployment. Applying this study's methods can support quality improvement by decreasing variation and striving for a target.

Conformational modes in biomolecules: dynamics and approximate invariance.

Understanding the physical mechanisms behind the folding and conformational dynamics of biomolecules is one of the major unsolved challenges of soft matter theory. In this contribution, a theoretical framework for biomolecular dynamics is introduced, employing selected aspects of statistical mechanics, dimensionality reduction, the perturbation theory, and the theory of matrices. Biomolecular dynamics is represented by time-dependent orthogonal conformational modes, the dynamics of the modes is investigated, and invariant properties that persist are identified. As an example, the dynamics of a human prion protein is considered. The theory provides a rigorous background for assessing the stable dynamical properties of biomolecules, such as their coarse-grained structure, through a multiscale approach using short subnanosecond segments of molecular dynamics trajectories. Furthermore, the paper offers a theoretical platform for models of conformational changes in macromolecules, which may allow complementing molecular dynamics simulations.