A delayed epidemic model with stage-structure and pulses for pest management strategy
ABSTRACT From a biological pest management standpoint, epidemic diseases models have become important tools in control of pest populations. This paper deals with an impulsive delay epidemic disease model with stage-structure and a general form of the incidence rate concerning pest control strategy, in which the pest population is subdivided into three subgroups: pest eggs, susceptible pests, infectious pests that do not attack crops. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic susceptible pest-eradication solution of the system and observe that the susceptible pest-eradication periodic solution is globally attractive, provided that the amount of infective pests released periodically is larger than some critical value. When the amount of infective pests released is less than another critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its attractivity. Our results indicate that besides the release amount of infective pests, the incidence rate, time delay and impulsive period can have great effects on the dynamics of our system.
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ABSTRACT: A periodic boundary value problem for a special type of functional differential equations with impulses at fixed moments is studied. A comparison result is presented that allows to construct a sequence of approximate solutions and to give an existence result. Several particular cases are considered.Mathematische Nachrichten 09/2000; 218(1):49 - 60. · 0.58 Impact Factor
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ABSTRACT: A single-species growth model with stage structure consisting of immature and mature stages is developed using a discrete time delay. It is shown that under suitable hypotheses there exists a globally asymptotically stable positive equilibrium. Questions concerning oscillation and nonoscillation of solutions are addressed analytically and numerically. The effect of the delay on the populations at equilibrium is also considered.Mathematical Biosciences 11/1990; 101(2):139-53. · 1.45 Impact Factor
- Rocky Mountain Journal of Mathematics 01/1995; · 0.39 Impact Factor