Host Diversification May Split Epidemic Spread into Two Successive Fronts Advancing at Different Speeds.

Host diversification methods such as within-field mixtures (or field mosaics, depending on the spatial scale considered) are promising methods for agroecological plant disease control. We explore disease spread in host mixtures (or field mosaics) composed of two host genotypes (susceptible and resistant). The pathogen population is composed of two genotypes (wild-type and resistance-breaking). We show that for intermediate fractions of resistant hosts, the spatial spread of the disease may be split into two successive fronts. The first front is led by the wild-type pathogen and the disease spreads faster, but at a lower prevalence, than in a resistant pure stand (or landscape). The second front is led by the resistance-breaking type, which spreads slower than in a pure resistant stand (or landscape). The wild-type and the resistance-breaking genotypes coexist behind the invasion fronts, resulting in the same prevalence as in a resistant pure stand. This study shows that host diversification methods may have a twofold effect on pathogen spread compared to a resistant pure stand (or landscape): on the one hand, they accelerate disease spread, and on the other hand they slow down the spread of the resistance-breaking genotype. This work contributes to a better understanding of the multiple effects underlying the performance of host diversification methods in agroecology.

Optimal Control of Plant Disease Epidemics with Clean Seed Usage.

The distribution and use of pathogen-free planting material ("clean seeds") is a promising method to control plant diseases in developing countries. We address the question of minimizing disease prevalence in plants through the optimal usage of clean seeds. We consider the simplest possible S-I model together with a simple economic criterion to be maximized. The static optimization problem shows a diversity of possible outcomes depending on economical and epidemiological parameters. We derive a simple condition showing to what extent subsidizing clean seeds relative to the epidemiological features of the disease may help eradicate or control the disease. Then we consider dynamic optimal control and Pontryagin's maximum principle to study the optimal usage of clean seeds to control the disease. The dynamical results are comparable to the static ones and are even simpler in some sense. In particular, the condition on the critical subsidy rate that makes clean seed usage economically viable is unchanged from the static optimization case. We discuss how these results may apply to the control of maize lethal necrosis in East-Africa.

Separate seasons of infection and reproduction can lead to multi-year population cycles.

Many host-pathogen systems are characterized by a temporal order of disease transmission and host reproduction. For example, this can be due to pathogens infecting certain life cycle stages of insect hosts; transmission occurring during the aggregation of migratory birds; or plant diseases spreading between planting seasons. We develop a simple discrete-time epidemic model with density-dependent transmission and disease affecting host fecundity and survival. The model shows sustained multi-annual cycles in host population abundance and disease prevalence, both in the presence and absence of density dependence in host reproduction, for large horizontal transmissibility, imperfect vertical transmission, high virulence, and high reproductive capability. The multi-annual cycles emerge as invariant curves in a Neimark-Sacker bifurcation. They are caused by a carry-over effect, because the reproductive fitness of an individual can be reduced by virulent effects due to infection in an earlier season. As the infection process is density-dependent but shows an effect only in a later season, this produces delayed density dependence typical for second-order oscillations. The temporal separation between the infection and reproduction season is crucial in driving the cycles; if these processes occur simultaneously as in differential equation models, there are no sustained oscillations. Our model highlights the destabilizing effects of inter-seasonal feedbacks and is one of the simplest epidemic models that can generate population cycles.