Age Structured Control Measure Interaction of Delay Impulse and Nonlinearity

Culling has been a common method for pest control and ecosystem management. Despite different formats such as shooting, trapping and crop spraying, culling often takes place at certain particular times only. These culling times are regulated by many factors including the maturation status of individuals of the species involved. For example, crop spraying may be exercised at certain times coinciding with critical stages in the insects' development.

Culling has also been a widely adopted tool to control vector-borne diseases in the hope that culling the vector at carefully chosen times may intervene the transmission cycle and reduce the infection. A specific example is larvicides the number of uninfected birds the number of uninfected birds

(a) Uninfected birds

the number of infected birds the number of infected birds

time t

(b) Infected birds time t

(b) Infected birds the number of mosquitoes the number of mosquitoes

time t

(c) Infected mosquitoes

Fig. 4.1. The DFE is stable time t

(c) Infected mosquitoes

Fig. 4.1. The DFE is stable the number of uninfected birds the number of uninfected birds

(a) Uninfected birds

the number of infected birds the number of infected birds

(b) Infected birds

the number of mosquitoes the number of mosquitoes

(c) Infected mosquitoes

Fig. 4.2. The DFE is unstable and the solution evolves to an endemic equilibrium

(c) Infected mosquitoes

Fig. 4.2. The DFE is unstable and the solution evolves to an endemic equilibrium the number of uninfected birds

- the number of uninfected junvenile birds

- the number of uninfected adult birds

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