Stochastic models to estimate population dynamics

  • Saba Infante School of Mathematical Sciences and Information Technology, Yachay Tech University, Ecuador Department of Mathematics, Faculty of Science and Technology, University of Carabobo, Venezuela
  • Luis Sanchez Instituto de Matem´atica y C´alculo Aplicado, Facultad de Ingenier´ıa, Universidad de Carabobo, Venezuela
  • Aracelis Hernandez School of Mathematical Sciences and Information Technology, Yachay Tech University, Ecuador
Keywords: Markov Chain Monte Carlo,, Secuential Monte Carlo, Particle Markov Chain Monte Carlo, Stochastic Differential Equations

Abstract

The growth dynamics that a population follows is mainly due to births, deaths or migrations, each of thesephenomena is affected by other factors such as public health, birth control, work sources, economy, safety and conditions of quality of life in neighboring countries, among many others. In this paper is proposed two statistical models based on a system of stochastic differential equations (SDE) that model the dynamics of population growth, and three computational algorithms that allow the generation of probability distribution samples in high dimensions, in models that have non-linear structures and that are useful for making inferences. The algorithms allow to estimate simultaneously states solutions and parameters in SDE models. The interpretation of the parameters is important because they are related to the variables of growth, mortality, migration, physical-chemical conditions of the environment, among other factors. The algorithms are illustrated using real data from a sector of the population of the Republic of Ecuador, and are compared with the results obtained with the models used by theWorld Bank for the same data, which shows that stochastic models Proposals based on an SDE more adequately and reliably adjust the dynamics of demographic randomness, sampling errors and environmental randomness in comparison with the deterministic models used by the World Bank. It is observed that the population grows year by year and seems to have a definite tendency; that is, a clearly growing behavior is seen. To measure the relative success of the algorithms, the relative error was estimated, obtaining small percentage errors.

Author Biographies

Saba Infante, School of Mathematical Sciences and Information Technology, Yachay Tech University, Ecuador Department of Mathematics, Faculty of Science and Technology, University of Carabobo, Venezuela
School of Mathematical Sciences and Information Technology, Yachay Tech University, EcuadorDepartment of Mathematics, Faculty of Science and Technology, University of Carabobo, Venezuela
Luis Sanchez, Instituto de Matem´atica y C´alculo Aplicado, Facultad de Ingenier´ıa, Universidad de Carabobo, Venezuela
Departamento de Matem´atica y Estad´ıstica, Instituto de Ciencias B´asicas, Universidad T´ecnica de Manab´ı, Ecuador  
Aracelis Hernandez, School of Mathematical Sciences and Information Technology, Yachay Tech University, Ecuador
School of Mathematical Sciences and Information Technology, Yachay Tech University, Ecuador Department of Mathematics, Faculty of Science and Technology, University of Carabobo, Venezuela

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Published
2020-02-17
How to Cite
Infante, S., Sanchez, L., & Hernandez, A. (2020). Stochastic models to estimate population dynamics. Statistics, Optimization & Information Computing, 8(1), 136-152. https://doi.org/10.19139/soic-2310-5070-488
Section
Research Articles