Dynamic analysis and control of a rice-pest system under transcritical bifurcations

Cultural methods were widely applied at an early stage of agricultural pest management but then replaced over time through pesticides with adverse effects on crop quality and the environment due to extensive and long-term use. In this study, we have reformulated a rice-pest-control model by first modelling a rice-pest system rigorously to then extend it to become an optimal control problem. We consider both, cultural methods and pesticides, and minimize thereby the density of agricultural pests, to increase the production of rice and to reduce gross annual losses. Pesticides have been applied only in an emergency scenario, which reduces environmental pollution and damage to nearby ecosystems. For the emergency case, we have developed a decision model to mitigate potential risks. The formulated models are verified by stability analysis at equilibrium points and investigated through transcritical bifurcations. Moreover, we have extensively confirmed our main results by numerical investigations and discussed the biological implications in more detail.