How does the resistance threshold in spatially explicit epidemic dynamics depend on the basic reproductive ratio and spatial correlation of crop genotypes?

Suzuki SU & Sasaki A (2011). How does the resistance threshold in spatially explicit epidemic dynamics depend on the basic reproductive ratio and spatial correlation of crop genotypes? Journal of Theoretical Biology 276 (1): 117-125. DOI:10.1016/j.jtbi.2011.02.002.

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We examined the fraction of resistant cultivars necessary to prevent a global pathogen outbreak (the resistance threshold) using a spatially explicit epidemiological model (SIR model) in a finite, two-dimensional, lattice-structured host population. Infectious diseases in our model could be transmitted to susceptible nearest-neighbour sites, and the infected site either recovered or died after an exponentially distributed infectious period. Threshold behaviour of this spatially explicit SIR model cannot be reduced to that of bond percolation, as was previously noted in the literature, unless extreme assumptions (synchronized infection events with a fixed lag) are imposed on infection process. The resistance threshold is significantly lower than that of conventional mean-field epidemic models, and is even lower if the spatial configuration of resistant and susceptible crops are negatively correlated. Finite size scaling applied to the resistance threshold for a finite basic reproductive ratio rho of pathogen reveals that its difference from static percolation threshold (0.41) is inversely proportional to rho. Our formula for the basic reproductive ratio dependency of the resistance threshold produced an estimate for the critical basic reproductive ratio (4.7) in a universally susceptible population, which is much larger than the corresponding critical value (1) in the mean-field model and nearly three times larger than the critical growth rate of a basic contact process (SIS model). Pair approximation reveals that the resistance threshold for preventing a global epidemic is factor 1/(1-eta) greater with spatially correlated planting than with random planting, where eta is initial correlation in host genotypes between nearest-neighbour sites. Thus the eradication is harder with a positive spatial correlation (eta>0) in mixed susceptible/resistant plantings, and is easier with a negative correlation (eta<0). The effect of finite field size (L), which corresponded to the mean distance between sources of infections, is given by the increased resistance threshold (by the amount L^-0.75) from its infinite size limit. Implications of these results on effective planting strategies in multi-line control plans are discussed.

Item Type: Article
Uncontrolled Keywords: Resistant cultivar; Spatially explicit epidemiology; Pair approximation; Finite size scaling; Multi-line control
Research Programs: Evolution and Ecology (EEP)
Bibliographic Reference: Journal of Theoretical Biology; 276(1):117-125 (7 May 2011) (Published online 5 February 2011)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:45
Last Modified: 24 Feb 2016 15:15

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