An impulsively controlled predator-pest model with disease in the pest. (English) Zbl 1192.34057
The authors consider an integrated pest management model with disease in the pest and a stage structure for its natural predator, which is the subject to impulsive and periodic controls. A nonlinear incidence rate expressed in an abstract form, is used to describe the propagation of the disease. Sufficient conditions for the local and global stability of the susceptible pest-eradication periodic solution are found by means of Floquet theory and comparison methods, the permanence of the system is also discussed. The stability conditions are shown to be biologically significant, they are reformulated as balance conditions for the susceptible pest class.
Reviewer: Xinyu Song (Xinyang)
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34A37 | Ordinary differential equations with impulses |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 92D30 | Epidemiology |
| 34C25 | Periodic solutions to ordinary differential equations |
Keywords:
predator-pest model; impulsive controls; nonlinear incidence; stage structure; global stability; permanenceReferences:
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