Two Generalized Predator-Prey Models for Integrated Pest Management with Stage Structure and Disease in the Prey Population

Abstract

Stage-structured predator-prey models with disease in the prey are constructed. For the purpose of integrated pest management, two types of impulsive control strategies (impulsive release of infective prey and impulsive release of predator) are used. For Case 1, infective prey applications are more frequent than releases of predator (natural enemies). For Case 2, predator (natural enemies) releases are more frequent than infective prey applications. In both cases, we get the sufficient conditions for the global attractivity of the susceptible prey-eradication periodic solution. In addition, the persistence of the systems is also discussed. At last, the results are discussed and some possible future work is put forward.

On impulsive integrated pest management models with stochastic effects

“…Typically, IPM models only considering biological means of control may incorporate both a natural predator as well as a disease. Such models have been considered by Shi et al ( 2009 ), Georgescu and Zhang ( 2010 ), Shi et al (Shi and Chen, 2010 ), and Shi et al ( 2013 ). In Shi et al ( 2009 ), the incidence rate is linear in each variable (bilinear) and the predation follows a Holling type II functional response, which is a rational function that increases and eventually levels off as the prey population density increases.…”

“…Shi et al ( 2013 ) consider a model in which the prey species is separated into immature, mature susceptible, and mature infective classes. The disease incidence rate is bilinear, and the predation rate follows a Holling type II functional response.…”

“…They consider two cases for the timing of the impulsive events for the introduction of infected pests and predators into the system: either the infected pests or the predators are introduced more frequently. Under both of these two timing conditions, Shi et al ( 2013 ) determine conditions for global attractivity of the susceptible pest eradication solution and for the permanence of the system.…”

Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate

“…In recent years, some authors ( [1]- [18]) studied the stage-structured predator-prey systems. The authors of [2]- [11] have studied the stability or Hopf bifurcation of these type systems. Since environmental and biological parameters (such as the seasonal effects of weather, food supplies, mating habits, hunting or harvesting season, etc.)…”