Host Spatial Heterogeneity and Extinction of an SIS Epidemic

Caraco, Thomas; Duryea, Maria; Gardner, Geoffrey; Maniatty, William; Szymanski, Boleslaw K.

doi:10.1006/jtbi.1998.0663

Cited by 15 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Models for spatial population processes may be deterministic or stochastic, but the associated invasion criteria typically are deduced from linear, deterministic approximations to a rare type's dynamics. However, most introductions in nature presumably begin with a small number of colonists, implying that a more realistic approach to invasion analysis would model discrete individuals and include a random component in the dynamics of rarity (Caraco et al, 1998;Durrett and Levin, 1994a). Nucleation theory characterizes stochastic properties of introduction and invasion that must often result from spatially structured interactions and locally clustered growth.…”

Section: Discussionmentioning

confidence: 99%

Spatial dynamics of invasion: the geometry of introduced species

Korniss

Caraco

2005

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyze this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single-cluster and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almostdeterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.

show abstract

Section: Discussionmentioning

confidence: 99%

Spatial dynamics of invasion: the geometry of introduced species

Korniss

Caraco

2005

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the epidemic model, generally, it is assumed that the population is a continuous entity and as a result, it is often neglected that the population are composed of single interacting individuals. In fact, the spread of disease must be governed by the localized process [1]. The cellular automata (CA) or lattice gas cellular automata (LGCA) is a discrete approach to the time, spatial and state.…”

Section: Introductionmentioning

confidence: 99%

A cellular automata model with probability infection and spatial dispersion

Jin

Liu

Haque³

2007

Chinese Phys.

View full text Add to dashboard Cite

In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic and satisfactory from the practical point of view. A discrete and spatiotemporal approach are shown by using cellular automata theory. It is interesting to note that both size of the endemic equilibrium and density of the individual increase with the increasing of the neighborhood size and infection rate, but the infections decrease with the increasing of the recovery rate. The stability of the system around the positive interior equilibrium have been shown by using suitable Lyapunov function. Finally experimental data simulation for SARS disease in China and a brief discussion conclude the paper.

show abstract

“…Localized contacts between susceptible and infectious individuals, or between susceptibles and disease vectors, commonly drive the advance of disease (Dwyer, 1992). Heterogeneity in host density can induce variation in the number of susceptibles contacted, and so influence the chance that a disease advances when rare (Keeling and Grenfell, 1997;Caraco et al, 1998) and the frequency of infection when an epidemic occurs (Duryea et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

“…We previously analyzed effects of host spatial heterogeneity on lattice-based epidemics with direct infection transmission (Caraco et al, 1998;Duryea et al, 1999). We considered a spatial epidemic with recovery (Bramson et al, 1989).…”

Section: Introductionmentioning

confidence: 99%

“…Once infected, a host could recover without immunity. Caraco et al (1998) studied the pathogen's probability of rapid extinction and found that increasing host spatial aggregation decreases the probability that the disease advances when rare. For a given global host density, greater spatial heterogeneity increases the number and size of``gaps'' in the host population (see Neuhauser, 1998).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation