Stability analysis of mathematical model for spread of pest in tea plant by RKM-4 and ABM-2

Abstract

Tea is an aromatic beverage, obtained from the leaves of the tree Camellia sinensis. It is one of the popular beverages. Presently it is the matter of great concern to control pest by using reduced amount of chemical fertilizer. Beneficial insects that eat dangerous insects and mites are known as predators. But both pest and predators cause huge loss in Tea production. So, in this article we have studied the tritrophic model which consists of tea plant, pest and predator. We have studied stability of positive fixed points and boundary (boundedness). For positive equilibrium point, the global stability properties are also examined. The dynamical behaviour of the system has been shown analytically as well as numerically by computer simulation. Two step Adams–Bashforth and Runge–Kutta method of fourth order has been employed in the solution and simulation of the system of non-linear ordinary differential equation of tritrophic model. The imperative feature of our proposed model is that it suggests some measures theoretically which is useful in implementing biological control strategy.