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

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

Intra-metropolitan Office Price and Trading Volume Dynamics: Evidence from Hong Kong

Previous studies of the office market have tended to focus on either the rental market or the aggregate sales market. This paper focuses on the intra-metropolitan sales market and on office price and trading volume dynamics in Hong Kong. According to our findings, buildings trading at higher prices are not necessarily traded more often than those trading at lower prices. In addition, the price of offices in different categories does not necessarily move in tandem. The trading volumes of higher priced buildings tend to Granger cause the lower priced buildings, and this conclusion is robust to alternative classifications. The paper contrasts several existing theories. Suggestions for future research are also discussed.Commercial property; Correlation

On the Stability of the Implicit Prices of Housing Attributes: A Dynamic Theory and Some Evidence

Given the dramatic fluctuations in aggregate housing prices, this paper attempts to examine whether the implicit prices of different housing attributes are “stable.” Theoretically, this paper provides perhaps the first dynamic, general equilibrium model in which housing attributes’ implicit prices fluctuate. Empirically, this paper models the time paths of different implicit prices as auto-regressive processes by employing a hedonic pricing model on a large set of housing transaction data over a relatively long period of time. An endogenous structural break test is then performed. Except for a few attributes, structural breaks are not detected. Directions for future research are discussed.hedonic pricing; structural break; evolution of valuation; housing attributes

TOM: Why Isn’t Price Enough?

In an efficient market, differences in quality should be fully reflected in differences in price. This paper examines a highly active residential property market and verifies whether housing attributes can explain time on the market (TOM) in addition to prices. In contrast to the previous literature, only the price ratio and inflation factor are found to be critical in affecting TOM. An interpretation of the results is suggested, along with some directions for future research.TOM, price ratio, inflation factor, physical attribute, time aggregation

A stochastic SIR network epidemic model with preventive dropping of edges

A Markovian SIR (Susceptible – Infectious - Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size N - ¥, assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy–Reed (in which the degrees of individuals are deterministic) and Newman–Strogatz–Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman–Strogatz–Watts version. The basic reproduction number R0 and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when R0 > 1, the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N

Gender asymmetry in concurrent partnerships and HIV prevalence

The structure of the sexual network of a population plays an essential role in the transmission of HIV. Concurrent partnerships, i.e. partnerships that overlap in time, are important in determining this network structure. Men and women may differ in their concurrent behavior, e.g. in the case of polygyny where women are monogamous while men may have concurrent partnerships. Polygyny has been shown empirically to be negatively associated with HIV prevalence, but the epidemiological impacts of other forms of gender-asymmetric concurrency have not been formally explored. Here we investigate how gender asymmetry in concurrency, including polygyny, can affect the disease dynamics. We use a model for a dynamic network where individuals may have concurrent partners. The maximum possible number of simultaneous partnerships can differ for men and women, e.g. in the case of polygyny. We control for mean partnership duration, mean lifetime number of partners, mean degree, and sexually active lifespan. We assess the effects of gender asymmetry in concurrency on two epidemic phase quantities (R0 and the contribution of the acute HIV stage to R0) and on the endemic HIV prevalence. We find that gender asymmetry in concurrent partnerships is associated with lower levels of all three epidemiological quantities, especially in the polygynous case. This effect on disease transmission can be attributed to changes in network structure, where increasing asymmetry leads to decreasing network connectivity