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Combining biological and chemical control has been an efficient strategy to combat the evolution of pesticide resistance. Continuous releases of natural enemies could reduce the impact of a pesticide on them and the number to be released should be adapted to the development of pesticide resistance. To provide some insights towards this adaptation strategy, we developed a novel pest–natural enemy model considering both resistance development and inoculative releases of natural enemies. Three releasing functions which ensure the extinction of the pest population are proposed and their corresponding threshold conditions obtained. Aiming to eradicate the pest population, an analytic formula for the number of natural enemies to be released was obtained for each of the three different releasing functions, with emphasis on their biological implications. The results can assist in the design of appropriate control strategies and decision-making in pest management. [ABSTRACT FROM AUTHOR]

Sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay-logistic equation with impulsive effect N˙(t)=r(t)N(t)K−Np(t−τ)/K+c(t)Np(t−τ),N(τk+)=N(τk)expIklnN(τk)/Kp,N(τk+)=N(τk)expIklnN(τk)/Kp, where r(t), c(t) are continuous functions, p, K, τ are positive constants, and {τk}k=1∞ denotes the sequence of impulsive time which assumed to be strictly increasing. Some special cases are also considered. [Copyright &y& Elsevier]

A ratio-dependent predator–prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system and, therefore, does not imply global asymptotic stability. It is found that an orbitally asymptotically stable periodic orbit exists in that model. Some sufficient conditions which guarantee the global stability of positive equilibrium are given. [Copyright &y& Elsevier]