An impulsively controlled predator–pest model with disease in the pest

The periodic solutions for general periodic impulsive population systems of functional differential equations and its applications

“…For more details see Theorem 3.1 in [19]. At the same time, we also see that the dynamical properties for many special cases of systems (1) and (2) have been extensively studied, for example [1,5,20,21,2,3,22,6,7,[23][24][25][26][27][28][29][30][31][32][33]8,[34][35][36] and the references cited therein. The main study subjects are the permanence, persistence and extinction of species, the local and global asymptotic stability of systems, the existence and uniqueness of positive periodic solution and almost periodic solution, and the bifurcation and dynamical complexity, etc.…”

“…These ephemeral perturbation behaviors of species consist of physical and factitious perturbations, for example, the seasonal migration or the seasonal birth of some species, the releasing or harvesting in the fixed times for the species, the crop-dusting or releasing natural enemy in the fixed times to eliminate pests in agriculture production, etc. For example, see [5][6][7][8] and the references cited therein.…”

Dynamic Analysis of General Integrated Pest Management Model with Double Impulsive Control

“…They assumed that the disease incidence rate should be distinguished; as far as disease transmission is concerned, nonlinear, bilinear, and standard incidence rates have often been used in establishing ecoepidemic models, which depends on different infective disease and environment. Georgescu and Zhang (see [10]) investigated a predator-pest model with incidence rate given by ( ) , Pang and Chen (see [12]) discussed an model with bilinear incidence rate , Wang et al (see [13]) analyzed an model with incidence rate given by ( ) , and so forth. Main results of these theses have focused on conditions of pest eradication and permanence of the system.…”

“…People use natural enemy, as in some sense like a pesticide, to control pest via augmentation or releasing natural enemy once the quantity of pest has reached or exceeded the economic threshold (see [9,10,14,15]). Shi et al (see [14]) analyzed a predator-pest model with disease in the pest and functional response given by Holling-II type and the time-dependent impulsive strategy including release of infective pest individuals and those natural predators at different point in time; the threshold on pest eradication was obtained.…”

“…The approach to biological control which we adopted is to release both infective pest individuals and natural predators periodically with constant amount at different point in time; what is more, the functional response is also a more general form. Motivated by the valuable contributions of Georgescu and Zhang [10], Wang et al [13], and Shi et al [14], in this paper general IPM model will be considered as follows:…”