Inverse Population Dynamics Problem Employing a Low Cost Integral Transform Solution and Bayesian Inference with Approximation Error Model

• Published in: International journal of applied and computational mathematics Vol. 7; no. 5
• Main Authors: Friguis, Maiquison S., Knupp, Diego C., Abreu, Luiz A. S., Stutz, Leonardo T., Neto, Antônio J. Silva
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.10.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied mathematics; Approximation; Bayesian analysis; Computational mathematics; Computational Science and Engineering; Errors; Integral transforms; Inverse problems; Livestock; Low cost; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Partial differential equations; Population density; Statistical inference; Theoretical; Approximation error model; Integral transforms; Diffusive populations; Impulsive culling; Bayesian inference
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-021-01120-4

Population dynamics modeling is a subject of major relevance, especially when involving human or livestock disease vectors. Such importance is due to the fact that there are several diseases that are spread by some particular species, and the knowledge on the behavior of such populations is relevant when it is intended to create public policies to control their proliferation. This work describes a problem of population dynamics with diffusive behavior, with impulsive culling and delayed reproduction. The direct problem describes the space and time evolution of the population density when the model parameters are known, and the solution of the partial differential equation is obtained with the Generalized Integral Transform Technique (GITT), a hybrid numerical-analytical approach. For practical purposes it is crucial to fit the model to a population of interest, by estimating the equation coefficients through an inverse problem approach. In this work the inverse problem is illustrated within the Bayesian framework employing a low-cost direct problem solution, and the Approximation Error Model is used to take in account the error introduced by the low-cost solution.