The influence of root growth and inoculum density on the dynamics of root disease epidemics: theoretical analysis

Including root growth and inoculum density as variables in a simple model of disease progress of a monocyclic root pathogen often leads to a sigmoid curve. If the product of root density and inoculum density is constant, then a monomolecular curve (without an inflexion point) results. When the product is a function of time, then either an asymptotic exponential or a sigmoid curve results, depending upon the parameter values. Where the product of root density and inoculum density increases exponentially, then a Gompertz function in the incidence of surviving plants results. Where root growth is fast relative to the reduction in inoculum through infection, then an asymptotic value of disease less than 1.0 is predicted. Detailed models of dynamics of root infection, incorporating root extension and loss of inoculum due to infection, and cases without and with lesion expansion, lead to the following conclusions: (1) increase in lesion numbers without lesion expansion, does not constrain or provide an upper limit to root growth; (2) where there is no root growth, then the proportion of root surface covered by lesions approaches an asymptote strictly less than 1.0 in the case without lesion expansion, but approaches 1.0 in the case with lesion expansion; (3) where the rate of infection is greater than the rate of root extension (without lesion expansion), then there is an upper limit to lesion surface area on roots; otherwise both root surface area and lesion numbers increase without limit; (4) where the rate of lesion expansion is greater than the rate of root extension, then the proportion of root surface area covered by lesions approaches 1.0 asymptotically. Explicit solutions giving the healthy root area as a function of time are obtained. Analysis of the dynamics of root infection indicates that root disease control strategies should aim to reduce pathogen density, maintain a low rate of root extension relative to root infection and restrict lesion expansion.