Methods and measures for the description of epidemiologic contact networks.

This article describes new methods to characterize epidemiologic contact networks that involve links that are being dynamically formed and dissolved. The new social network measures are designed with an epidemiologic interpretation in mind. These methods are intended to capture dynamic aspects of networks related to their potential to spread infection. This differs from many social network measures that are based on static networks. The networks are formulated as transmission graphs (TGs), in which nodes represent relationships between two individuals and directed edges (links) represent the potential of an individual in one relationship to carry infection to an individual in another relationship. Network measures derived from transmission graphs include "source counts," which are defined as the number of prior relationships that could potentially transmit infection to a particular node or individual.

Infection transmission system models for microbial risk assessment.

Chemical risk assessments often focus on measuring exposure as if individuals were subject only to exogenous environmental sources of risk. For infectious diseases, exposure might not only depend on exogenous sources of microbes, but also on the infection status of other individuals in the population. For example, waterborne infections from agents such as Cryptosporidium parvum and Escherichia coli: O157:H7 might be transmitted from contaminated water to humans through drinking water; from interpersonal contact; or from infected individuals to the environment, and back to other susceptible individuals. These multiple pathways and the dependency of exposure on the prevalence of infection in a population suggest that epidemiological models are required to complement standard risk assessments in order to quantify the risk of infection. This paper presents new models of infection transmission systems that are being developed for the US Environmental Protection Agency as part of a project to quantify the risk of microbial infection. The models are designed to help inform water treatment system design decisions.

Bias reduction for risk ratio and vaccine effect estimators.

We examine the structural bias for established estimators of vaccine effects on susceptibility and for newer estimates of vaccine effects on infectiousness. We then propose and analyse new bias corrections for vaccine effect estimators of both susceptibility and infectiousness, as well as their combined effect on infection transmission. Each estimator is evaluated empirically with computer simulations. Of the estimators examined in this paper, those with the least bias and root mean squared error are computed by adding one to the positive count in the placebo population. We also identify a source of bias for a standard Bayesian estimator of risk ratios.

New data and tools for integrating discrete and continuous population modeling strategies.

Realistic population models have interactions between individuals. Such interactions cause populations to behave as systems with nonlinear dynamics. Much population data analysis is done using linear models assuming no interactions between individuals. Such analyses miss strong influences on population behavior and can lead to serious errors--especially for infectious diseases. To promote more effective population system analyses, we present a flexible and intuitive modeling framework for infection transmission systems. This framework will help population scientists gain insight into population dynamics, develop theory about population processes, better analyze and interpret population data, design more powerful and informative studies, and better inform policy decisions. Our framework uses a hierarchy of infection transmission system models. Four levels are presented here: deterministic compartmental models using ordinary differential equations (DE); stochastic compartmental (SC) models that relax assumptions about population size and include stochastic effects; individual event history models (IEH) that relax the SC compartmental structure assumptions by allowing each individual to be unique. IEH models also track each individual's history, and thus, allow the simulation of field studies. Finally, dynamic network (DNW) models relax the assumption of the previous models that contacts between individuals are instantaneous events that do not affect subsequent contacts. Eventually it should be possible to transit between these model forms at the click of a mouse. An example is presented dealing with Cryptosporidium. It illustrates how transiting model forms helps assess water contamination effects, evaluate control options, and design studies of infection transmission systems using nucleotide sequences of infectious agents.

Modeling contact networks and infection transmission in geographic and social space using GERMS.

BACKGROUND: Stochastic models of discrete individuals and deterministic models of continuous populations may give different answers to questions about infectious diseases. GOAL: Discrete individual model formulations are sought that extend deterministic models of infection transmission systems so that both model forms contribute cooperatively to model-based decision making. STUDY DESIGN: GERMS models are defined as stochastic processes in continuous time with parameters analogous to those in deterministic models. A GERMS model simulator was developed that insured that the rate of events depended only on the current state of model. RESULTS: The confidence intervals of long-term averages of infection level in simulated GERMS models were shown to contain the deterministic model means. CONCLUSION: GERMS models provide a convenient framework for testing the sensitivity of model-based decisions to a variety of unrealistic assumptions that are characteristic of differential equation models. GERMS especially facilitates making more realistic assumptions about contact patterns in geographic and social space.

Analysis and simulation of a stochastic, discrete-individual model of STD transmission with partnership concurrency.

Deterministic differential equation models indicate that partnership concurrency and non-homogeneous mixing patterns play an important role in the spread of sexually transmitted infections. Stochastic discrete-individual simulation studies arrive at similar conclusions, but from a very different modeling perspective. This paper presents a stochastic discrete-individual infection model that helps to unify these two approaches to infection modeling. The model allows for both partnership concurrency, as well as the infection, recovery, and reinfection of an individual from repeated contact with a partner, as occurs with many mucosal infections. The simplest form of the model is a network-valued Markov chain, where the network's nodes are individuals and arcs represent partnerships. Connections between the differential equation and discrete-individual approaches are constructed with large-population limits that approximate endemic levels and equilibrium probability distributions that describe partnership concurrency. A more general form of the discrete-individual model that allows for semi-Markovian dynamics and heterogeneous contact patterns is implemented in simulation software. Analytical and simulation results indicate that the basic reproduction number R(0) increases when reinfection is possible, and the epidemic rate of rise and endemic levels are not related by 1-1/R(0), when partnerships are not point-time processes.