Dangerous connections: on binding site models of infectious disease dynamics

We formulate models for the spread of infection on networks that are amenable to analysis in the large population limit. We distinguish three different levels: (1) binding sites, (2) individuals, and (3) the population. In the tradition of Physiologically Structured Population Models, the formulation starts on the individual level. Influences from the `outside world' on an individual are captured by environmental variables. These environmental variables are population level quantities. A key characteristic of the network models is that individuals can be decomposed into a number of conditionally independent components: each individual has a fixed number of `binding sites' for partners. The Markov chain dynamics of binding sites are described by only a few equations. In particular, individual-level probabilities are obtained from binding-site-level probabilities by combinatorics while population-level quantities are obtained by averaging over individuals in the population. Thus we are able to characterize population-level epidemiological quantities, such as $R_0$, $r$, the final size, and the endemic equilibrium, in terms of the corresponding variables

Sensitivity analysis applied to computer-aided circuit design

Imperial Users onl

Mean field at distance one

To be able to understand how infectious diseases spread on networks, it is important to understand the network structure itself in the absence of infection. In this text we consider dynamic network models that are inspired by the (static) configuration network. The networks are described by population-level averages such as the fraction of the population with $k$ partners, $k=0,1,2,\ldots$ This means that the bookkeeping contains information about individuals and their partners, but no information about partners of partners. Can we average over the population to obtain information about partners of partners? The answer is `it depends', and this is where the mean field at distance one assumption comes into play. In this text we explain that, yes, we may average over the population (in the right way) in the static network. Moreover, we provide evidence in support of a positive answer for the network model that is dynamic due to partnership changes. If, however, we additionally allow for demographic changes, dependencies between partners arise. In earlier work we used the slogan `mean field at distance one' as a justification of simply ignoring the dependencies. Here we discuss the subtleties that come with the mean field at distance one assumption, especially when demography is involved. Particular attention is given to the accuracy of the approximation in the setting with demography. Next, the mean field at distance one assumption is discussed in the context of an infection superimposed on the network. We end with the conjecture that an extension of the bookkeeping leads to an exact description of the network structure.Comment: revised versio

“Fire Sales” in housing market: is the house-searching process similar to a theme park visit?

Three striking empirical regularities have been repeatedly reported: the positive correlation between housing prices and trading volume, between housing price and the time-on-the-market (TOM), and the existence of price dispersion. This short paper provides perhaps the first unifying framework which mimics these phenomena in a simple competitive search framework. In the equilibrium, sellers with heterogeneous waiting cost and buyers are endogenously segregated into different submarkets, each with distinct market tightness and prices. With endogenous search effort, our model also reproduces the well-documented price-volume correlation. Directions for future research are also discussed.housing market, competitive search, price dispersion, trading volume, time on the market

The stress experience among Chinese young people in Australia

Australia is a multicultural country. It has one of the world's diversed terms of ethnic and culture population. In response to the absorption of migrants from non English-speaking background in Australia, the population of ethnic young people has increased significantly in recent decades. Many disturbing trends in Australia is of 1990s, affect all the population particular young people with ethnic background. Ethnic youth are usually being confronted with additional burden of stress and conflicts, which arise out of the migration and resettlement process, coping with two cultures and value systems, and being a minority group in the society. Chinese, like other minority youth groups in Australia, are confronted with variety of stressful life events. Little attention has been paid to the psychological stresses experienced by these minority youth. This study is to explore the experience of stress among the Chinese young people in Australia. By reviewing relevant literature, this study will examine the Chinese culture and values, which can influence the experience of stress among the Chinese youth. Other stress factors such as being a minority group in a Western country will also be explored