| The rational use of multicomponent treatments such as multidrug therapies, combination vaccines/chemicals, and plants carrying multigenic resistance requires an understanding of pathogen adaptive dynamics. Here, we studied the rate of pathogen adaptation to a host population which was subjected to a multicom- ponent treatment. To describe the adaptive dynamics of a pathogen population spreading through a host population diversi ed by the treatment, we formulated and analyzed a stochastic model of pathogen dynamics based on a birth and death processes with mutations and migrations of individual pathogens. Our main nding is that stochastic migration process plays a key role in the estimation of the pathogen adaptation rate. In particular, taking the stochastic migration process into consideration in modelling pathogen adaptive dynamics alters the criteria for the critical proportion of the host treated in order to impede pathogen adaptation. Moreover, our results show that we should avoid identifying treatment durability with mutation cost, since its impact on the adaptation rate depends on the structure of the treatment-diversi ed host population and the pathogen migration rate. We also found that a multicom- ponent treatment can be durable, if it is not combined with intermediate treatments including only some of the components. Our model helps to elucidate the interplay between the treatment strategy used and the processes underlying pathogen adaptive dynamics. The model can be used for designing durable multicomponent treatment strategies that impede the evolution of harmful populations. |
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