6533b85bfe1ef96bd12bbf79
RESEARCH PRODUCT
Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters
V. BeviaClara BurgosA. Navarro-quilesJuan Carlos CortésRafael-jacinto Villanuevasubject
Continuity partial differential equationStationary distributionDynamical systems theoryStochastic processGeneral MathematicsApplied MathematicsGompertz functionProbabilistic logicGeneral Physics and AstronomyStatistical and Nonlinear PhysicsProbability density function01 natural sciences010305 fluids & plasmasComplex systems with uncertainties0103 physical sciencesLiouville-Gibbs theoremApplied mathematicsInitial value problemUncertainty quantificationRandom nonlinear differential equationMATEMATICA APLICADA010301 acousticsMathematicsRandomized Gompertz modeldescription
[EN] In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biological quantities (usually, rates and number of individual/particles, respectively) whose nature is random rather than deterministic. In this paper, we present a complete uncertainty quantification analysis of the randomized Gomperz model via the computation of an explicit expression to the first probability density function of its solution stochastic process taking advantage of the Liouville-Gibbs theorem for dynamical systems. The stochastic analysis is completed by computing other important probabilistic information of the model like the distribution of the time until the solution reaches an arbitrary value of specific interest and the stationary distribution of the solution. Finally, we apply all our theoretical findings to two examples, the first of numerical nature and the second to model the dynamics of weight of a species using real data.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-09-01 |