Work

(CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications

Year: 2019

Type: article

Abstract: The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.5440

Authors: Juan Carlos Cortés, Ana Navarro‐Quiles, José‐Vicente Romero, María‐Dolores Roselló

Institutions: Universitat Politècnica de València, Universidad de Deusto

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: green

Funder: Ministerio de Economía y Competitividad

Award: G363611379