A MATHEMATICAL MODEL FOR FUNGAL POPULATION GROWTH AND THE FUNGICIDE RESISTANCE PROBLEM

A deterministic mathematical model which includes impulses occurring at fixed time periods is proposed in the study of the effects of different dosages on the population dynamics of resistant fungi. The model includes the following parameters which characterize the phenomenon: rS and rR (the apparent infection rates in the sense of Vanderplank for susceptible and resistant fungi), α (change rate from susceptible to resistant populations) and F (the rate by which the population is reduced by fungicide application). As a preliminary step, the model is solved in the absence of fungicide, in order to establish the resistance frequency in the initial population. Numerical simulations have been carried out considering low dosages and high dosages and varying the parameters α, rS, rR. According to the simulations, smaller dosages result in a lower reduced efficacy and delay the instant for total population resistance.