Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property is observed asymptotically as time tends to infinity , which is due to the fact that a mixture failure rate is ‘bent down’, as the weakest populations are dying out...

In the paper basic epidemiological indicators, produced by an aging population of vectors, are calculated. In the study we follow two lines: calculations for demographically structured population and individual life-history approach. We discuss the advantages and limitations of these approaches...

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In this paper, a recently developed mathematical model of age related changes in population of peripheral T cells (Romanyukha, Yashin, 2003) is used to describe ontogenetic changes of the immune system. The treatise is based on the assumption of linear dependence of antigen load from basal...

A bivariate competing risks problem is considered for a rather general class of survival models. The lifetime distribution of each component is indexed by a frailty parameter. Under the assumption of conditional independence of components the correlated frailty model is considered. The explicit...

A mixture model in multivariate survival analysis is presented, whereby heterogeneity among subjects creates divergent paths for the individual's risk of experiencing an event (i.e., disease), as well as for the associated length of survival. Dependence among competing risks is included and...

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Individuals at the same age in the same population differ along numerous risk factors that affect their chances of various causes of death. The frail and susceptible tend to die first. This differential selection may partially account for some of the puzzles in cancer epidemiology, including the...

Simple series systems of identical components with spare parts are considered. It is shown that the cumulative distribution function of a system failure time tends to a step function as the number of components increases and resources can be shared. An example of ‘continuous resources’ is...