A Generalized Model of a Host-Pathogen System

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Abstract
A host-pathogen system satisfying the following conditions was considered. The pathogen reproduces on the host. The host may be differentiated into varieties on the basis of its resistance to the races of the pathogen. The pathogen may be differentiated into races on the basis of its ability to grow on a set of host varieties. Host resistance to a particular race of the pathogen is genetically controlled. The damage to the host caused by the pathogen in a given time interval is directly related to the increase in number in the pathogen population during the given time interval. A mathematical model of a host-pathogen system satisfying the above conditions was constructed. These host-pathogen systems were classified according to the criterium of constant or non-constant population number in both the host and pathogen populations. This classification gave four classes. Sufficient conditions for the stability of the relative frequencies of the races of the pathogen and varieties of the host were given in each of the four classes.

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