Intrinsic growth rate and evolution of the Premnotrypes Vorax population using fuzzy information

The white potato worm (Premnotrypes Vorax (Hustache)) is one of the pests that causes the greatest damage to the potato crop and the greatest economic losses to the grower; therefore, knowing its life cycle and estimating its intrinsic growth rate is crucial for selecting an appropriate chemical control method, in order to reduce the environmental impact and ensure a profitable production suitable for consumption. In this article, we present a fuzzy Malthusian model describing the evolution of the white potato worm in the crop, considering that the intrinsic growth rate and the reported initial data on the problem are of fuzzy nature. The main contributions and novelty of this paper are summarized in the following two aspects: first, the estimation of the intrinsic growth rate of the white potato worm, in function of the temperature, by using a Takagi–Sugeno–Kang type fuzzy rule-based model; and second, since in practice the initial white potato worm population in a crop is subjective, imprecise and vague, knowing the intrinsic growth rate, we propose and solve a fuzzy initial value problem to determine the evolution in time of the white potato worm population. In conclusion, given a weekly average temperature, it is possible to know the white potato worm population per unit area oscillating in an interval whose length depends on the degree of inaccuracy of the initial population and the intrinsic growth rate. This study can be relevant for grower decision making in terms of the type and frequency of pest control on his crop.