Abstract
Integrated Pest Management technique is used to formulate a mathematical model by using biological and chemical control impulsively. The uniform boundedness and the existence of pest extinction and nontrivial equilibrium points is discussed. Further, local stability of pest extinction equilibrium point is studied and it has been derived that if T≤T_max, the pest extinction equilibrium point is locally stable and for T>T_max, the system is permanent. It has also been obtained that how delay helps in eradicating pest population more quickly. Finally, analytic results have been validated numerically.
Highlights
Mathematical Model We have proposed our mathematical model by the following set of differential equations: ddpt = p(r − p) − a1pq ddqt = a1b1pq − a2q(t − τ)r2(t − τ)e−d1τ − Dq ddrt1 = a2b2q(t − τ)r2(t − τ)e−d1τ − (D3 + μ0)r1 ddrt2 = μ0r1 − D3r2 t ≠ nT
In this paper, we have examine the effects of hybrid approach to control the pests by release of natural enemies and pesticides impulsively
It is evident that pest population can become extinct when large amount of the natural enemies are released impulsively
Summary
Plants as we all know conflict between and pests has been a root cause of concern in our ecology from almost two decades. They studied various prospect of IPM method and its application. The organisation of the paper is as follows: In Section 2, 3 model formulation and preliminary lemmas are discussed. Λ1 = exp(rT) > 1, according to the Floquet theory (Bainov and Sineonov, 1993) the pest eradication periodic solution is unstable as |λ1| > 1. Pest eradication periodic solution of (1 − 2) is locally asymptotically stable as per Floquet theory (Bainov and Sineonov, 1993) if and only if |λ2| ≤ 1 which implies T ≤ Tmax.
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