Population dynamics of botanical epidemics involving primary and secondary infection

In this paper we study the dynamical properties of models for botanical epidemics, especially for soil-borne fungal infection. The models develop several new concepts, involving dual sources of infection, host and inoculum dynamics. Epidemics are modelled with respect to the infection status of whole plants and plant organs (the G model) or to lesion density and size (the SW model). The infection can originate in two sources, either from the initial inoculum (primary infection) or by a direct transmission between plant tissue (secondary infection). The first term corresponds to the transmission through the free-living stages of macroparasites or an external source of infection in certain medical models, whereas the second term is equivalent to direct transmission between the hosts in microparasitic infections. The models allow for dynamics of host growth and inoculum decay. We show that the two models for root and lesion dynamics can be derived as special cases of a single generic model. Analytical and numerical methods are used to analyse the behaviour of the models for static, unlimited (exponential) and asymptotically limited host growth with and without secondary infection, and with and without decay of initial inoculum. The models are shown to exhibit a range of epidemic behaviour within single seasons that extends from simple monotonic increase with saturation of the host population, through temporary plateaux as the system switches from primary to secondary infection, to effective elimination of the pathogen by the host outgrowing the fungal infection. For certain conditions, the equilibrium values are shown to depend on initial conditions. These results have important consequences for the control of plant disease. They can be applied beyond soil-borne plant pathogens to mycorrhizal fungi and aerial pathogens while the principles of primary and secondary infection with host and inoculum dynamics may be used to link classical models for both microparasitic and macroparasitic infections.