Predatory dynamics in susceptible and resistant $\textit{Eriopis connexa}$ populations

The ladybird $\textit{Eriopis connexa}$ (Germar, 1824), a voracious aphid predator, faces challenges from insecticide applications, compromising biological control. As a result, there has been an increase in the number of studies analysing the resistance and susceptibility of ladybirds. Some studies have found that resistant populations exhibit distinct predation and foraging behaviour compared to susceptible ones. This study models the population dynamics of resistant and susceptible $\textit{E. connexa}$ preying on $\textit{Aphis gossypii}$ Glover, 1877 and $\textit{Myzus persicae}$ (Sulzer, 1776). We constructed a logistic model with density dependence and type-II functional response to analyse predation dynamics, incorporating bifurcation analysis on predation parameters (attack rate and handling time) and the mortality rate of susceptible ladybirds. We simulated scenarios with/without insecticide application and with/without aphid resistance. To simulate the effects of insecticide applications, the parameters related to aphids' intrinsic growth rate ($r_1$ and $r_2$) change to reflect the responses of susceptible and resistant populations. The same approach is used concerning the mortality rate of ladybirds ($d_2$ and $d_3$). Our results demonstrate that mortality, attack rate, and handling time are critical in shaping predator-prey interactions. Temporal simulations revealed fluctuating abundances, highlighting the fragility of these interactions under insecticide stress. Therefore, this study contributes to understanding the ecological implications of insecticides, which disrupt natural predation dynamics, and shows how variations in behavioural rates can impact prey control. This research demonstrated the importance of integrated strategies that balance insecticide applications with preserving natural enemies and promoting sustainable agricultural practices.