The effects of disease dispersal and host clustering on the epidemic threshold in plants

Abstract

For an epidemic to occur in a closed population, the transmission rate must be above a threshold level. In plant populations, the threshold depends not only on host density, but on the distribution of hosts in space. This paper presents an alternative analysis of a previously presented stochastic model for an epidemic in continuous space (Bolker, 1999, Bull. Math. Biol. 61, 849-874). A variety of moment closures are investigated to determine the dependence of the epidemic threshold on host spatial distribution and pathogen dispersal. Local correlations that arise during the early phase of the outbreak determine whether a true global epidemic will occur.

Moment Equations and Dynamics of a Household SIS Epidemiological Model

“…(6) if the infectious individuals are highly clustered. Another moment closure, the symmetric power-2 closure discussed by Murrell et al (2004) and also explored by Brown and Bolker (2004), is…”

“…Recently, there has been a surge of interest in epidemiological models or mathematically equivalent population models incorporating various spatial features such as spatially localized interactions (Levin and Durrett, 1996;Ellner et al, 1998;Gibson, 1998, 2001;Hiebeler, 2000;de Aguiar et al, 2003;Petermann and De Los Rios, 2004a,b;Hiebeler, 2005b), or infections over various spatial scales (Brown and Bolker, 2004;Watts et al, 2005) such as a combination of short and long distances (Harada and Iwasa, 1994;Boots and Sasaki, 1999;Harada, 1999;Hiebeler, 2004). Models of infections spreading through other systems such as scale-free networks and small-world networks have also been studied (Pastor-Satorras and Vespignani, 2001;Newman, 2002;Newman et al, 2002;Read and Keeling, 2003;Barthélemy et al, 2005;Hwang et al, 2005;Keeling, 2005;Saramäki and Kaski, 2005).…”

Spatial Point Processes and Moment Dynamics in the Life Sciences: A Parsimonious Derivation and Some Extensions

“…Some models include special cases of agents switching types, for example infection of a susceptible agent in an epidemic model (Bolker 1999;Brown and Bolker 2004). However, other types of switching and mutation are possible (e.g.…”

Spatial Genetic Structure of a Vector-Borne Generalist Pathogen

“…Generalist pathogens could have access to a larger number of competent reservoirs and, through the activity of polyphagous vectors, be disseminated more evenly and widely in the landscape. In addition, complex plant communities may support larger populations of polyphagous vectors than simpler communities (4). This is of relevance to agricultural systems, where pathogen spillover from vegetation adjacent to fields into crops is a hallmark of many vector-borne diseases (33).…”