ASYMPTOTIC ANALYSIS OF AN EPIDEMIC MODEL WITH PRIMARY AND SECONDARY INFECTION

Far many biological systems, the behavior of interest is contained in the evolution of transients rather than in the stability of equilibria . These include systems in which perturbations and interruptions occur on a time scale much shorter than the equilibration time, and those i n which any final equilibrium is sensitive to initial conditions. In t his article, we examine a model of fungal root disease in a crop invol ving primary and secondary infection mechanisms. This system is subjec t to regular interruptions in the form of harvesting and sowing. Using an asymptotic approach in which certain parameter values are assumed to be small, the model can be broken down into a set of simpler subsys tems respresenting recognizable biological mechanisms. These linear mo dels can be solved to give closed-form analytical solutions for transi ent evolution. From this information, it is possible to construct an a nnual map of disease severity in the crop, and determine the parameter values under which the infection will bulk up or fade out. (C) 1997 S ociety for Mathematical Biology.