A Multistage Age-structured Insect Population Model And Optimal Control

Physiologically based demographic models are helpful in the development of sustainable pest control.We study a multistage age-structured model which lies in the biological context of European grapevine moth.Firstly,we prove the well-posedness of solutions by contraction map and fixed point.Secondly,we construct approximate solutions and prove the stability and convergence.Then we use MATLAB to make some numerical simulations.Finally,we consider two optimal control problems,to achieve the best insecticidal efficiency and the lowest financial loss.We also prove the existence of an optimal control and optimality conditions.