Spatial analysis of vector-borne disease: A four-species model

Abstract

Disease can influence a host population's dynamics directly or indirectly through effects on the host's interactions with competitors and exploiters. We present a stochastic, spatially explicit model for the epidemiological landscape of a vector-borne disease. Two host species, of unequal competitive strength, are attacked by a selective parasite; the parasite serves as a vector for a pathogen. We emphasize the importance of the ecological stencil, the local area where ecological interactions govern a site's species composition. We point out how parallel computing can efficiently employ the geometry of the stencil's local transitions to predict large-scale spatio-temporal patterns of the model community. IntroductionSpatial heterogeneity in abiotic factors and biotic processes often generates patterns in population dynamics and the resulting attributes of ecological communities. Despite a long-standing recognition of the significance of spatial variation, analytical and computational models of spatially explicit, multispecies interactions have only recently influenced community theory (e.g. Hastings, 1990;Kareiva, 1990). We develop a spatially explicit model for the epidemiological landscape of a vector-borne disease. We focus on the "ecological stencil", the local area where ecological interactions govern the species composition at any specific location. Simulation of the local transition probabilities defining the stencil will predict large-scale spatio-temporal patterns of the model community.We first mention a few examples of vector-borne disease. Then we present a model for the dispersal-mortality dynamics of two competing host species, a pathogen that infects the hosts, and a parasite (on the hosts) that serves as a vector for the pathogen. Using a simplified version of the model, we show how variation in the size of the ecological stencil can influence "quasi-stationary" abundances of species competing in a probabilistic density-dependent manner. We briefly comment on the computational requirements for implementing the model efficiently (e.g. Sinharoy and Szymanski, 1993). We outline a series of applications of the model; these include spatially explicit analyses of ecological dispersal, the spread of an epidemic, and cultural diffusion of information. Finally, we consider how our model might provide spatial representations of evolutionary processes. Vector-borne diseasePathogens can influence a host's birth and death rates directly (e.g. Anderson, 1991), or indirectly through effects on the host's interactions with competitors and exploiters (e.g. Hochberg et al., 1990; Schall, in press). Ecological models of epidemics generally assume that a pathogen is directly transmitted when an infective host contacts a susceptible host individual. Recently, however, more attention has been directed to vector-borne diseases where individual parasites exploit many host individuals and consequently can transport a pathogen

Spatial Approaches to Modeling Dispersion of Communicable Diseases – A Review

“…A population may be divided into a greater number of smaller sub-populations using different criteria. Those models that divide a population based on spatial considerations are called spatially structured models (Szymanski and Caraco 1994, Lloyd 1995, Ferguson et al 1997, Grenfell and Harwood 1997, Rhodes and Anderson 1997, Torres-Sorando and Rodriguez 1997, Keeling 2000.…”

Compiler Technology for Parallel Scientific Computation

“…The above computation is an example of a reduction evaluated simultaneously over many overlapping continuous sections of an array. Other examples of usage of such operations are likely to be found in cluster recognition, fractal dimension computation in biological modeling [34], or in modeling physical phenomena (e.g., solvers of partial differential equations characterizing fluid flow). Simultaneous reduction is evaluated over a one-dimensional consecutive section of an arrav.…”

High-performance computing tools for modeling evolution in epidemics

“…A model that we proposed here is an extension of the spatially explicit individual based cellular automata model that we developed for vector born diseases [18]. The model enables the user to dene an interaction neighborhoods for each site.…”

“…Given the individual rate of propagule/ospring creation at each site, the formulas given in [18] can be modied to take into account the reproduction (now heterogeneous). To account for the interactions between the competing species, we consider also the post dispersal competition [18].…”

“…To account for the interactions between the competing species, we consider also the post dispersal competition [18].…”