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

Abstract

World-wide rice consummation constantly grows constantly with non-proportional yield as large amounts of rice are lost due to pest infestations. Cultural methods were widely applied at an early stage of agricultural pest management but then replaced over time through insecticides. To describe a rice-pest system and to control the corresponding pests applying cultural methods and/or insecticides, statistical analyses have been used, and also other mathematical models using an Integrated Pest Management (IPM) strategy considering long time period and more parametric values. Considering the limitations of IPM, we have developed a mathematical model for a rice-pest system found in agricultural management. The mathematical model consists of two non-linear differential equations (NDEs) to illustrate the interrelation of rice and its corresponding agricultural pests. This model is extended to become an optimal control problem (minimization problem), considering both, cultural methods and pesticides, to minimize the density of agricultural pests and to increase the production of rice, reducing gross annual losses. Pesticides have been applied only in emergencies to reduce environmental pollution and damage to nearby ecosystems such as aquatic ecosystems, and a decision model has also been developed to mitigate potential risks. To compare the effectiveness of the considered controls, the ratio of annual production of rice is studied for both controls and without control. This study contributes to building a relationship between NDEs and agricultural management as well as connecting mathematically rice-pest relationships to global food security.