|OJIAMBO, PETER - North Carolina State University|
|Gent, David - Dave|
|MEHRA, LUCKY - North Carolina State University|
|CHRISTIE, DAVID - North Carolina State University|
|MAGAREY, ROGER - North Carolina State University|
Submitted to: PeerJ
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/24/2017
Publication Date: 6/20/2017
Citation: Ojiambo, P.S., Gent, D.H., Mehra, L.K., Christie, D., Magarey, R. 2017. Focus expansion and stability of the spread parameter estimate of the power law model for dispersal gradients. PeerJ. doi: 10.7717/peerj.3465.
Interpretive Summary: Understanding factors that favor spread of endemic and foreign diseases, and the rate of disease spread, is of utmost importance for developing appropriate strategies for disease monitoring and mitigation. Both experimental data and theoretical modeling indicate that dispersal of organisms that spread over long distances can be explained by a mathematical representation of what is known as a power law. In this research we used long-term data sets for the disease cucurbit downy mildew to estimate how stable the spread parameter (b) of the power law model may be under natural conditions. We found that this parameter could vary about 2.5 fold across epidemics, which has important implications for predicting the speed of disease spread. We also discovered that b ˜ 2 may be considered the approximate lower limit of this parameter. Using the same data, we also discovered a relationship between the size of the initial area affected by disease and the final extent of disease spread. This finding suggests that the severity of entire disease outbreaks is closely associated with factors in the early stages of epidemics, which may have relevance for both prediction of disease spread and its control.
Technical Abstract: Empirical and mechanistic modeling indicate that aerially transmitted pathogens follow a power law, resulting in dispersive epidemic waves. The spread parameter (b) of the power law model, which defines the distance travelled by the epidemic wave front, 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.