Direct and inverse analysis of diffusive logistic population evolution with time delay and impulsive culling via integral transforms and hybrid optimization

Motivated by the fact that several species act as a vector in the spread of human or livestock diseases, many works propose mathematical formulations for the modeling of these populations, most of them considering Fickian dispersion and logistic like growth rates. For the best use of these models in a real application of optimal population control, the model parameters should be identified as accurately as possible for a given species population. In this work, this parameter identification problem is formulated as an inverse problem, which is tackled with a combination of the Generalized Integral Transform Technique (GITT), for the direct problem solution, and a hybrid stochastic–deterministic procedure for the minimization of the defined objective function in the inverse analysis, employing the Differential Evolution and the Levenberg–Marquardt methods. The direct problem solution with GITT and the inverse analysis are critically investigated. In order to improve the computational performance of the inverse problem solution, a second order semi-analytical integration and a solution refinement scheme are proposed.