An adaptative model for a multistage structured population under fluctuating environment

Aïnseba, Bedr’Eddine; Bouguima, Sidi Mohammed

doi:10.3934/dcdsb.2020037

Cited by 1 publication

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“…Thus, some research have been conducted to study the behavior and the life cycle of the insect Lobesia-Botrana (see [2][3][4][5][6][7][8][9]), and the references therein. The acquisition of this knowledge gradually allowed the construction of mathematical models able to describe with varying precision degrees the evolution in time and space of the insect densities, see also [2,3,6], and the references therein. The integrated pest management programs usually includes chemical, and biological controls that acts at different stages of the pest.…”

Section: Introductionmentioning

confidence: 99%

Modeling the adaptive behavior of an agricultural pest population

Aïnseba¹,

Bouguima²,

Kada³

2023

Math. Model. Comput.

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In this work, we formulate a model describing the growth of a pest population with seasonal diapause at the larval stage. The model includes the insect resistance to chemical treatments and their adaptation against a hostile environment. It consists on the description of three classes: the immature stage that includes eggs, larvae and pupae, and two mature stages corresponding to the vulnerable adult stage and the insecticide resistant adult stage. The main result consists in an analytical approach for the existence of a nonnegative periodic solution. The proof uses comparison results and Kamke's Theorem for cooperative systems. As an important illustration, a threshold type result on the global dynamics of the pest population is given in terms of an index R. When R≤1, the trivial solution is globally asymptotically stable. When R>1, the positive periodic solution is globally asymptotically stable. Numerical simulations confirm the analytical results.

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