Focus expansion and stability of the spread parameter estimate of the power law model for dispersal gradients

Abstract

Empirical and mechanistic modeling indicate that pathogens transmitted via aerially dispersed inoculum follow a power law, resulting in dispersive epidemic waves. The spread parameter (b) of the power law model, which is an indicator of the distance of the epidemic wave front from an initial focus per unit time, has been found to be approximately 2 for several animal and plant diseases over a wide range of spatial scales under conditions favorable for disease spread. Although disease spread and epidemic expansion can be influenced by several factors, the stability of the parameter b over multiple epidemic years has not been determined. Additionally, the size of the initial epidemic area is expected to be strongly related to the final epidemic extent for epidemics, but the stability of this relationship is also not well established. Here, empirical data of cucurbit downy mildew epidemics collected from 2008 to 2014 were analyzed using a spatio-temporal model of disease spread that incorporates logistic growth in time with a power law function for dispersal. Final epidemic extent ranged from 4.16 ×108 km2 in 2012 to 6.44 ×108 km2 in 2009. Current epidemic extent became significantly associated (P < 0.0332; 0.56 < R2 < 0.99) with final epidemic area beginning near the end of April, with the association increasing monotonically to 1.0 by the end of the epidemic season in July. The position of the epidemic wave-front became exponentially more distant with time, and epidemic velocity increased linearly with distance. Slopes from the temporal and spatial regression models varied with about a 2.5-fold range across epidemic years. Estimates of b varied substantially ranging from 1.51 to 4.16 across epidemic years. We observed a significant b ×time (or distance) interaction (P < 0.05) for epidemic years where data were well described by the power law model. These results suggest that the spread parameter b may not be stable over multiple epidemic years. However, b ≈ 2 may be considered the lower limit of the distance traveled by epidemic wave-fronts for aerially transmitted pathogens that follow a power law dispersal function.

Global Cropland Connectivity: A Risk Factor for Invasion and Saturation by Emerging Pathogens and Pests

“…Parameter estimates for six casesincluding plant and human pathogens and distances ranging from experimental field plots (32 m) to continental-scale (9329 km) -ranged from 1.75 to 2.36 (Mundt et al 2009a). For cucurbit downy mildew, the observed maximum annual disease spread distance ranged from 1,914 km to 2,221 km across seven years, with inverse power law parameter estimates approximately 2 or more (Ojiambo et al 2017). Gravity models are frequently used to describe the risk of movement between two locations, in applications including zoology, ecology, and epidemiology (Jongejans et al 2014).…”

A General Framework for Spatio-Temporal Modeling of Epidemics With Multiple Epicenters: Application to an Aerially Dispersed Plant Pathogen

“…Epidemics caused by invasive pathogens can be managed through several approaches that include quarantine, containment, eradication programs, and chemical control measures. Understanding the risk of disease invasion is vital in facilitating the planning of disease control, prediction, prevention of epidemics, and development of mitigation policies [1]. These needs are particularly acute for fecund organisms capable of long-distance dispersal that are not spatially restricted.…”

“…For aerially dispersed pathogens, wind is the main dispersal mechanism of inoculum. Epidemics driven by aerial dispersal exhibit wave-like behavior in which spatial dispersal at any given time can be accurately approximated by a power-law [1]. The power-law model is of the form dy dr…”

“…negative). Ojiambo et al [1] used this model to estimate the spread parameter b of epidemic waves resulting from the spread of cucurbit downy mildew in the eastern U.S. The authors of [1] assumed that all epidemics are first observed at the same initial distance r 0 given that P. cubensis overwinters in south Florida and the inoculum is aerially dispersed northward when the environment is conducive [1,13,17].…”

Global Cropland Connectivity: A Risk Factor for Invasion and Saturation by Emerging Pathogens and Pests

“…Parameter estimates for six case studies—including plant and human pathogens and distances ranging from experimental field plots (32 meters) to continental scale (9329 km)—ranged from 1.75 to 2.36 (Mundt et al 2009a ). For cucurbit downy mildew, the observed maximum annual disease spread distance ranged from 1914 to 2221 km across 7 years, with inverse power law parameter estimates of approximately 2 or more (Ojiambo et al 2017 ). Gravity models are frequently used to describe the risk of movement between two locations, in applications including zoology, ecology, and epidemiology (Jongejans et al 2014 ).…”