On impulsive integrated pest management models with stochastic effects

Abstract

We extend existing impulsive differential equation models for integrated pest management (IPM) by including stage structure for both predator and prey as well as by adding stochastic elements in the birth rate of the prey. Based on our model, we propose an approach that incorporates various competing stochastic components. This approach enables us to select a model with optimally determined weights for maximum accuracy and precision in parameter estimation. This is significant in the case of IPM because the proposed model accommodates varying unknown environmental and climatic conditions, which affect the resources needed for pest eradication.

Optimal Pest Control Strategies with Cost-effectiveness Analysis

“…In [ 24 ], the framework of deterministic and stochastic modelling revealed that the parameters on disease transmission are crucial to the dynamical process, as a small perturbation in these parameters contributes detrimental effects in the infective populations. Another pest control model considering the stochastic effect was carried out by [ 30 ].…”

A stochastic predator–prey model for integrated pest management

“…When considering the interference of external factors, model (2.1) is not applicable. In order to describe these phenomena more accurately, some authors considered the stability of Stochastic Differential Equations (SDE) [13][14][15][16][17][18][19][20][21][22][23][24]. When a pesticide kills a pest instantly, impulsive differential equations (hybrid dynamical systems) can provide a natural description of pulse-like actions.…”

Controlling Pest by Integrated Pest Management: A Dynamical Approach

“…Authors studied a model in which they formulated a mathematical model and obtained a threshold value below which pests gets eradicated. Later, many more IPM approach inclined models were proposed where impulsive control strategies for pest eradication were introduced and to name a few are (Tang et al, 2005;Akman et al, 2015;El-Shafie, 2018;Paez Chavez et al, 2018). They studied various prospect of IPM method and its application.…”