<![CDATA[Significant agricultural losses worldwide can be caused by pests, such as aphids, especially in tropical regions like Indonesia. It is interesting to analyze aphid population growth to determine the proper steps in controlling plant pests to minimize these losses. Pesticides are a common way to reduce aphid populations. In this study, a mathematical model is used to predict aphid growth when pesticides and the presence of ladybugs, their natural predator, are considered. This model consists of three nonlinear differential equations with four equilibrium points, one of which is the interior equilibrium point. The stability characteristics of the interior equilibrium point are evaluated using Monte Carlo simulations, as the system's complexity renders analytical methods impractical in this context. Additionally, the robustness of the stability is examined by analyzing its sensitivity to parameter variations, providing insights into the system's stability under different conditions. The model was then solved numerically using Micken's Non-Standard Finite Difference (NSFD) scheme. NSFD is a more robust and reliable option than standard finite-difference methods, especially for modeling complex dynamics. In this numerical scheme, the time step size is adjusted based on the eigenvalues of the Jacobian matrix for a nonlinear system model. As a result, the numerical scheme shows higher accuracy than the 4th-order Runge-Kutta scheme. Several simulations were carried out here and validated analytically using the equilibrium points. Furthermore, this paper analyzes the model's sensitivity to examine the behaviour of aphids and ladybugs under parameter changes, thereby minimizing the trial-and-error process of controlling plant pests that may not be effective.]]>
