Some dynamic models for development of insecticide resistance in insect population

In present study, we proposed a fundamental model for development of insecticide resistance in insect population, which comprises two differential equations and an algebraic equation: dx/dt = r1(c, t) x - f1(c, t) x + g1(c, t) y - a(c, t) x y; dy/dt = r2(c, t) y - g2(c, t) y + f2(c, t) x - b(c, t) x y; c = u(t). where t: time (insect generation, year, etc.); x(c, t): resistant subpopulation at t; y(c, t): susceptible subpopulation at t; c: dosage / concentration of the insecticide. Two special models for election theory and induce variation theory were derived from the fundamental model. We provided the solution of the model and analyzed some of the model behavior. Resistant strength was proposed based on the model, which is positively related to the common used resistance indices, e.g., LC50. Finally, an alternative model, revised from Lotka-Volterra competition model was given. The mechanism of formation and development of insecticide resistance may change with various factors including insect species and environmental conditions. The present models are expected to provide a fundamental for further research