Constructing a Basefile for Simulating Kunming’s Medical Insurance Scheme of Urban Employees

Focusing on China’s medical insurance scheme which covers all employers and employees in urban areas, this research aims to assess the distributional impacts of medical insurance policies and to predict medical expenses by using microsimulation techniques. As an important part of the project, this article provides a brief overview of China’s medical insurance reform of urban employees and detail the techniques and processes to construct a basefile in 2005 for projecting the medical expenditures for urban employees over the period of 2006-2010. The main data used are administrative medical records of medical insurance participants provided by the Bureau of Labour and Social Security of Kunming, Yunnan Province. Along with the initial analysis for the raw datasets and age processing and adjustment for the individual records, monthly income information was imputed and personal savings accounts were established for each individual record. Important modelling parameters such as death rates and income adjustment factors were constructed. Furthermore, this article identifies medical insurance for government officials by using the combination of logarithm curve fitting and binary discriminant analysis. Based on this basefile, a static microsimulation model can be built to assess the implementation effects of the medical insurance policy and analyse the impact of the medical insurance scheme on urban employees.Urban medical insurance, China, microsimulation, basefile, Policy Research

Evolving eco-system: a network of networks

Ecology and evolution are inseparable. Motivated by some recent experiments, we have developed models of evolutionary ecology from the perspective of dynamic networks. In these models, in addition to the intra-node dynamics, which corresponds to an individual-based population dynamics of species, the entire network itself changes slowly with time to capture evolutionary processes. After a brief summary of our recent published works on these network models of eco-systems, we extend the most recent version of the model incorporating predators that wander into neighbouring spatial patches for food.Comment: 7 pages including 2 figure

Ancestral processes with selection: Branching and Moran models

We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyze the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced back into the past. The second approach is the Moran model with selection. Here, the population has constant size N. Individuals reproduce (at rates depending on their types), the offspring inherits the parent's type, and replaces a randomly chosen individual (to keep population size constant). Independently of the reproduction process, individuals can change type. As in the branching model, we consider the ancestral lines of single individuals chosen from the equilibrium population. We use analytical results of Fearnhead (2002) to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution in forward time.Comment: minor changes, updated references; Banach Center Publications, in pres

The Age-Specific Force of Natural Selection and Walls of Death

W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full non-linear demographic model for mutation accumulation of Evans et al. (2007), we find surprising differences. Non-linear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine predictions in other cases, and allow Walls of Death at ages before the end of reproduction. Haldane's Principle for genetic load has an exact but unfamiliar generalization.Comment: 27 page

Evolutionary ecology in-silico: Does mathematical modelling help in understanding the "generic" trends?

Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time scales, several ``unified'' mathematical models of evolutionary ecology have been developed over the last few years with the aim of describing the statistical properties of data related to the evolution of ecosystems. Moreover, because of the availability of sufficiently fast computers, it has become possible to carry out detailed computer simulations of these models. For the sake of completeness and to put these recent developments in the proper perspective, we begin with a brief summary of some older models of ecological phenomena and evolutionary processes. However, the main aim of this article is to review critically these ``unified'' models, particularly those published in the physics literature, in simple language that makes the new theories accessible to wider audience.Comment: 28 pages, LATEX, 4 eps figure

Limit theorems for Markov processes indexed by continuous time Galton--Watson trees

We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time t. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. The latter has the same generator as the Markov process along the branches plus additional jumps, associated with branching events of accelerated rate and biased distribution. This comes from the fact that choosing an individual uniformly at time t favors lineages with more branching events and larger offspring number. The central limit theorem is considered on a special case. Several examples are developed, including applications to splitting diffusions, cellular aging, branching L\'{e}vy processes.Comment: Published in at http://dx.doi.org/10.1214/10-AAP757 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org