A study on time-limited control of single-pest with stage-structure. (English) Zbl 1198.92039
Summary: Two kinds of time-limited pest control models of single-pest with stage-structure, which can be described by a boundary value problem of ordinary differential equations and impulsive differential equations, are presented according to the ways of artificial control (continuous control and impulsive control). The conditions under which the corresponding model has a solution are given. If the model has a solution, the corresponding aim of pest control can be achieved. The theoretical results show that both the mature and the immature pest should be controlled synchronously, otherwise the aims of pest control can not be achieved in a finite time. Finally, some discussions and numerical simulations show that the impulsive control is more practical than the continuous control.
MSC:
| 92D30 | Epidemiology |
| 92D40 | Ecology |
| 34H05 | Control problems involving ordinary differential equations |
| 34B37 | Boundary value problems with impulses for ordinary differential equations |
Keywords:
impulsive control; boundary value problem; impulsive differential equation; single species; stage-structureReferences:
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