  Using digitized images of the three-dimensional, branching structures for
root systems of bean seedlings, together with analytical and numerical methods
that map a common 'SIR' epidemiological model onto the bond percolation
problem, we show how the spatially-correlated branching structures of plant
roots affect transmission efficiencies, and hence the invasion criterion, for a
soil-borne pathogen as it spreads through ensembles of morphologically complex
hosts. We conclude that the inherent heterogeneities in transmissibilities
arising from correlations in the degrees of overlap between neighbouring
plants, render a population of root systems less susceptible to epidemic
invasion than a corresponding homogeneous system. Several components of
morphological complexity are analysed that contribute to disorder and
heterogeneities in transmissibility of infection. Anisotropy in root shape is
shown to increase resilience to epidemic invasion, while increasing the degree
of branching enhances the spread of epidemics in the population of roots. Some
extension of the methods for other epidemiological systems are discussed.
