• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.393-407
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• 2022

In this paper, a diffusive predator-prey system with Beddington DeAngelis functional response and the modified Leslie-Gower type predator dynamics when a prey population is infected is considered. The predator is assumed to predate both the susceptible prey and infected prey following the Beddington-DeAngelis functional response and Holling type II functional response, respectively. The predator follows the modified Leslie-Gower predator dynamics. Both the prey, susceptible and infected, and predator are assumed to be distributed in-homogeneous in space. A reaction-diffusion equation with Neumann boundary conditions is considered to capture the dynamics of the prey and predator population. The global attractor and persistence properties of the system are studied. The priori estimates of the non-constant positive steady state of the system are obtained. The existence of non-constant positive steady state of the system is investigated by the use of Leray-Schauder Theorem. The existence of non-constant positive steady state of the system, with large diffusivity, guarantees for the occurrence of interesting Turing patterns.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.835-850
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infected prey and predator system in which both the susceptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to investigate the golbal properties of the system.

• Korean journal of applied entomology
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• v.48 no.2
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• pp.123-158
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• 2009

An attempt was made to stimulate future research by providing exemplary information, which would integrate published knowledge to solve specific pest problem caused by resistance. This review was directed to find a way for delaying resistance development with consideration of chemical(s) nature, of mixture, rotation, or mosaics, and of insecticide(s) compatible with the biological agents in integrated pest management (IPM). The application frequency, related to the resistance development, was influenced by insecticide activity from potentiation, residual period, and the vulnerability to resistance development of chemical, with secondary pest. Chemical affected feeding, locomotion, flight, mating, and predator avoidance. Insecticides with negative cross-resistance by the difference of target sites and mode of action would be adapted to mixture, rotation and mosaic. Mixtures for delaying resistance depend on each component killing very high percentage of the insects, considering allele dominance, cross-resistance, and immigration and fitness disadvantage. Potential disadvantages associated with mixtures include disruption of biological control, resistance in secondary pests, selecting very resistant population, and extending cross-resistance range. The rotation would use insecticides in high and low doses, or with different metabolic mechanisms. Mosaic apply insecticides to the different sectors of a grid for highly mobile insects, spray unrelated insecticides to sedentary aphids in different areas, or mix plots of insecticide-treated and untreated rows. On the evolution of pest resistance, selectivity and resistance of parasitoids and predator decreased the number of generations in which pesticide treatment is required and they could be complementary to refuges from pesticides To enhance the viability of parasitoids, the terms on the insecticides selectivity and factors affecting to the selectivity in field were examined. For establishment of resistant parasitoid, migration, survivorship, refuge, alternative pesticides were considered. To use parasitoids under the pressure of pesticides, resistant or tolerant parasitoids were tested, collected, and/or selected. A parasitoid parasitized more successfully in the susceptible host than the resistant. Factors affecting to selective toxicity of predator are mixing mineral oil, application method, insecticide contaminated prey, trait of individual insecticide, sub-lethal doses, and the developmental stage of predators. To improve the predator/prey ratio in field, application time, method, and formulation of pesticide, reducing dose rate, using mulches and weeds, multicropping and managing of surroundings are suggested. Plant resistance, predator activity, selective insect growth regulator, and alternative prey positively contributed to the increase of the ratio. Using selective insecticides or insecticide resistant predator controlled its phytophagous prey mites, kept them below an economic level, increased yield, and reduced the spray number and fruits damaged.

• Korean journal of applied entomology
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• v.34 no.4
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• pp.360-367
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• 1995

The relative toxicity of abamectin was assessed to the predatory mite Amblyseius womersleyi Schicha and to dicofol-resistant and -susceptible twospotted spider mite (TSM) Tetranychus urticae Koch in the laboratory. Abamectin was much les toxic to the predator than to the spider mite. At 0.12 and 0.6 ppm, all TSM adult females of the tow strains were killed within 48 h after dipping n the solutions. The lower concentrations (0.06 and 0.012 ppm) killed more than 77% of TSM female adults of the two strains at 120 h after treatment. However, abmectin did not significantly affect the survival and mobility of A. womersleyi female adults at a concentration of 0.12 ppm but the mortality was slightly increased up to 20~23% at 0.6 and 6 ppm. Abamectin did not significantly affect hatchability of one-day old TSM eggs at 0.06~0.6 ppm. The Four-day old eggs were much more susceptible to abamectin than one-day old eggs were. Within 0.006-6 ppm, abamectin did not affect the hatchability of A. womersleyi eggs and the development of resulting immature predators. When the predator female adults were dipped in 0.6 and 0.12 ppm solution, their reproduction was not affected, but at 6 ppm it was decreased by 35%. However, the reproduction of TSM reduced significantly at concentrations between 0.006 and 0.6 ppm. The differential toxicity of abamectin between TSM and the predator could be of practical importance in managing spider mite populations in the field. Abamectin at selective sublethal concentrations (i.e., 0.012~0.06 ppm) could be of value in adjusting predator/prey ratios in integrated management of spider mites.