Abstract
In this study, we depicted the spread of pests in tea plants and their control by biological enemies in the frame of a fractional-order model, and its dynamics are surveyed in terms of boundedness, uniqueness, and the existence of the solutions. To reduce the harm to the tea plant, a harvesting term is introduced into the equation that estimates the growth of tea leaves. We analyzed various points of equilibrium of the projected model and derived the conditions for the stability of these equilibrium points. The complex nature is examined by changing the values of various parameters and fractional derivatives. Numerical computations are conducted to strengthen the theoretical findings.
Highlights
IntroductionThe majority of tea-producing countries are located in Asia, with India, China, and Sri Lanka being the most prominent producers [2]
The aim of this research is to perform a qualitative survey of the performance of the three classes, namely tea plants, pests that damage tea leaves, and the biological enemies of pests in terms of a mathematical model involving the Caputo fractional derivative
Impacts of pests attack tea plant, pests natural death, tea plant harvesting, and natural enemies attack pests are analyzed in the presence of the fractional derivative
Summary
The majority of tea-producing countries are located in Asia, with India, China, and Sri Lanka being the most prominent producers [2]. Whether it be green, white, black or yellow, come from the same plant, Camellia sinensis. Around 52% of the total tea is produced in India, coming from the State of Assam. Tea is grown within the tropics and subtropics in various types of porous, well-drained, acidic soils (PH 3.3 to 6.0) in diverse agroecological conditions and undergoes a broad range of climatic conditions such as annual rainfall from 938 to 6000 mm, temperatures from 12 ◦ C to 40 ◦ C, and the relative humidity may vary from 30 percent to 90 percent [3]. Tea trees can grow up to 15 m in height in the wild [4,5]
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