Pest regulation by means of impulsive controls

Abstract

In this paper, we consider an integrated pest management model which is impulsively controlled by means of biological and chemical controls. These controls are assumed to act in a periodic fashion, a nonlinear incidence rate being used to account for the dynamics of the disease caused by the application of the biological control. The Floquet theory for impulsive ordinary differential equations is employed to obtain a condition in terms of an inequality involving the total action of the nonlinear force of infection in a period, under which the susceptible pest-eradication solution is globally asymptotically stable. If the opposite inequality is satisfied, then it is shown that the system under consideration becomes uniformly persistent. A biological interpretation of the persistence condition is also provided.

Analysis of pest-epidemic model by releasing diseased pest with impulsive transmission

“…(A2) The infected pests neither recover nor reproduce; the infected pests neither damage crops nor contribute to the total size of the environment-supported population (this assumption is in line with the findings of Paul et al [6] and Jiao et al [9] who have shown that when insect S 1 is laboratory-infected with disease I 1 , it ceases to reproduce, and when these diseased insects are released into the insect population, crops damage is dramatically reduced). (A3) The incidence rate of the infection is nonlinear in I and given by βS(t)I q (t), q > 0.…”

Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield

“…[7]. The proofs of the above-mentioned results are obvious [14] . Consequently, from the above mathematical results, the pathogenic microorganism-free state will be stabilized by using the appropriate dose of antibiotic injection and the suitable time interval for injection.…”

Solvability of a Kind of Sturm–Liouville Boundary Value Problems with Impulses via Variational Methods

“…Impulsive differential equations have become more important in recent years in mathematical models of real processes and phenomena studied in control theory [7,8], population dynamics and biotechnology [9,10], physics and mechanics problems [11]. There has been a significant development in the area of impulsive differential equations with fixed moments.…”