Stability analysis and comparative study on different eco‐epidemiological models: Stage structure for prey and predator concerning impulsive control

The asymptotic behavior of four integrated pest management models with stage structure is analyzed in this article. Stage structuring is suggested because almost all pests pass through two stages in their lives, namely immature larvae and mature adults. It is believed that immature susceptible pests and exposed pests are targeted by a natural enemy and infected pests that make them exposed are contacted by susceptible pests (immature and mature). After fixed times, infected pests, and natural enemies are infused impulsively. And we have also integrated the effects of nontarget pests here. The stability analysis of the periodic pest extinction solution is obtained by the floquet theory, the method of small amplitude perturbation, and the comparison theorem. The results obtained provide some valid theoretical results for successful management of pests and also established the threshold time limit for the impulsive release of various controls. A comparative analysis with computational simulation offers a good idea of each model and our primary outcomes.