Prevention of crops from pest has always been a serious cause of concern throughout the world, especially in agricultural countries as it contributes majorly to the economy of these countries. Keeping in mind this issue, we have formulated a mathematical model of Eggplant fruit and shoot borer which has been controlled through biological control. The dynamical analysis of the system has been discussed which includes the boundedness and positivity of the system. Local stability analysis of the system is discussed followed by local bifurcation analysis of each steady state solutions.The global stability analysis of non-trivial is done by graph theoretic approach by constructing a Lyapunov function. The optimization of the biological control strategy has also been discussed using linear feedback control. Further, we have also proposed a Spatio-temporal model and investigated it to observe the evolution of diffusive pattern in a biological pest control model. The reason of discussing the Spatio-temporal model is to focus on how diffusion can also be a method to control the pest population. The numerical simulation has been discussed to validate our analytical results obtained. Finally, we have also obtained the global sensitivity analysis using LHS method for $U,x_2$ and $x_3$.

防止农作物受到有害生物侵害一直是全世界关注的一个严重问题，特别是在农业国家，因为它对这些国家的经济做出了重大贡献。考虑到这个问题，我们建立了茄子果实和嫩芽bore的数学模型，该模型已通过生物控制得到了控制。讨论了系统的动力学分析，其中包括系统的有界性和正性。讨论了系统的局部稳定性分析，然后讨论了每个稳态解的局部分歧。通过构造Lyapunov函数的图论方法对非平凡的全局稳定性进行了分析。还已经使用线性反馈控制讨论了生物控制策略的优化。更多，我们还提出了一个时空模型，并对其进行了研究，以观察生物虫害控制模型中扩散模式的演变。讨论时空模型的原因是要关注扩散如何也可以成为控制有害生物种群的一种方法。已经讨论了数值模拟，以验证我们获得的分析结果。最后，我们还使用LHS方法获得了用于$ü，X_{\mathrm{2个}}$ 和 $X_3$。