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

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...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2021, Vol.7 (5), Article 189
Main Authors: Friguis, Maiquison S., Knupp, Diego C., Abreu, Luiz A. S., Stutz, Leonardo T., Neto, Antônio J. Silva
Format: Article
Language:English
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
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Summary: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.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-021-01120-4