Dynamic analysis of pest control model with population dispersal in two patches and impulsive effect |
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Affiliation: | 1. Department of Mathematics, Amity Institute of Applied Science, Amity University, Sector-125, Noida 201313, India;2. PRECISIONheor, Los Angeles, CA, United States;3. Department of Mathematics, Illinois State University, Normal, IL, United States;4. College of Health Solutions, Arizona State University, Tempe, AZ, United States;5. Department of Mathematics, Graphic Era Hill University, Dehradun 248002, India |
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Abstract: | In this paper, we investigate the pest control model with population dispersal in two patches and impulsive effect. By exploiting the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we can obtain that the susceptible pest eradication periodic solution is globally asymptotically stable if the impulsive periodic τ is less than the critical value τ0 . Further, we also prove that the system is permanent when the impulsive periodic τ is larger than the critical value τ0. Hence, in order to drive the susceptible pest to extinction, we can take impulsive control strategy such that τ < τ0 according to the effect of the viruses on the environment and the cost of the releasing pest infected in a laboratory. Finally, numerical simulations validate the obtained theoretical results for the pest control model with population dispersal in two patches and impulsive effect. |
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Keywords: | Impulsive differential equations Global stability Floquet theorem Pest control |
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