Mathematical analysis of a non‐convex optimal control problem for age‐structured mosquito populations

We present a rigorous mathematical analysis of a non‐convex optimal control problem for mosquito populations. The nonlinear model for the dynamics of the mosquito population takes in consideration the iterations among the immature (aquatic) subpopulation, the adult winged subpopulation, and the envi...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-08, Vol.48 (2), p.1381-1410
Main Authors: Filho, Cícero Alfredo da Silva, Boldrini, José Luiz
Format: Article
Language:English
Subjects:
age‐structured population
Aquatic environment
Dynamic structural analysis
Mathematical analysis
mosquito population
Mosquitoes
Nonlinear control
Nonlinear dynamics
non‐convex functional
Optimal control
Populations
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Summary:We present a rigorous mathematical analysis of a non‐convex optimal control problem for mosquito populations. The nonlinear model for the dynamics of the mosquito population takes in consideration the iterations among the immature (aquatic) subpopulation, the adult winged subpopulation, and the environment resources; the immature subpopulation is assumed to be age‐structured. Moreover, the action of certain control mechanisms on these subpopulations is also taken in account. The cost functional to be minimized is non‐convex. The proof of the existence of an optimal control is done by using fixed point arguments and a special minimizing sequence obtained with the help of Ekeland's variational principle.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10389