Showing papers by "Benjamin M. Bolker published in 1995"

Space, persistence and dynamics of measles epidemics

Abstract: This paper explores the relations between persistence and dynamics in measles epidemics. Most current models, including the stochastic seasonally forced and age-structured models examined here, fail to capture simultaneously the observed dynamics and persistence characteristics of epidemics in large urban populations before vaccination. Summary measures of persistence and trienniality allow us to compare epidemics in England, New York and Copenhagen with results of non-spatial and spatial stochastic models. Spatial (metapopulation) structure allow persistence and triennial dynamics to coexist i this class of models. The spatial dynamics of measles, for which detailed spatiotemporal data are available, may serve as a useful test of ideas applicable to other epidemiological and ecological systems with an important spatial component.

Seasonality and extinction in chaotic metapopulations

Abstract: A body of recent work has used coupled logistic maps to show that these model metapopulations show a decrease in global extinction rate in the chaotic region of model behaviour. In fact, many of the main ecological candidates for low-dimensional chaos are continuous-time host-parasite and predator-prey systems, driven by strong seasonal ‘forcing’ of one or more population parameters. This paper, therefore, explores the relation between seasonal forcing and metapopulation extinction for such systems. We base the analysis on extensive simulations of a stochastic metapopulation model for measles, based on a standard compartmental model, tracking the density of susceptible, exposed, infectious and recovered individuals (the SEIR model). The results show that, by contrast with coupled logistic maps, the increased seasonality which causes chaos maintains or increases levels of global extinction of infection, by increasing the synchrony of sub-population epidemics. The model also illustrates that the population interaction (here between susceptible and infective hosts) has a significant effect on patterns of synchrony and extinction.

Species diversity and ecosystem response to carbon dioxide fertilization: conclusions from a temperate forest model

Abstract: This paper explores how the response of a temperate forest ecosystem to climate change might depend on species diversity and community change. In particular, we look at the dynamics of a model of temperate forest growth under doubled CO2. We combine a detailed, field-calibrated model of forest dynamics (Pacala et al 1993) with greenhouse data on the range of seedling biomass growth response to doubled CO2 concentrations (Bazzaz et al. 1990; Bazzaz & Miao 1993). Because total ecosystem response to climate change depends delicately on many environmental variables other than CO2, we isolate the effects of community change by comparing runs of the regular model, allowing dynamic community change, with runs of a reduced model that holds species composition static by using a single tree species with average parameters. Simulations that allowed community change instead of holding species composition constant showed a roughly 30% additional increase in total basal area over time scales of 50-150 years. Although the model omits many possible feedbacks and mechanisms associated with climate change, it suggests the large potential effects that species differences and feedbacks can have in ecosystem models and reinforces the possible importance of diversity to ecosystem function (Naeem et ai 1994; Tilman & Downing 1994) over time scales within the planning horizon for global change policy.

Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases.

Abstract: There is currently considerable interest in the role of nonlinear phenomena in the population dynamics of infectious diseases. Childhood diseases such as measles are particularly well documented dynamically, and have recently been the subject of analyses (of both models and notification data) to establish whether the pattern of epidemics is chaotic. Though the spatial dynamics of measles have also been extensively studied, spatial and nonlinear dynamics have only recently been brought together. The present review concentrates mainly on describing this synthesis. We begin with a general review of the nonlinear dynamics of measles models, in a spatially homogeneous environment. Simple compartmental models (specifically the SEIR model) can behave chaotically, under the influence of strong seasonal 'forcing' of infection rate associated with patterns of schooling. However, adding observed heterogeneities such as age structure can simplify the deterministic dynamics back to limit cycles. By contrast all curren...