Bayesian Inversion in Fractional Models for Cell Migration

Francisco J. Ariza-Hernandez (), Jorge Sanchez-Ortiz (), Erika González-Nava (), Juan Carlos Najera-Tinoco (), Martin P. Arciga-Alejandre () and Eduardo Castañeda-Saucedo
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Francisco J. Ariza-Hernandez: Universidad Autónoma de Guerrero, Facultad de Matemáticas
Jorge Sanchez-Ortiz: Universidad Autónoma de Guerrero, Facultad de Matemáticas
Erika González-Nava: Universidad Autónoma de Guerrero, Facultad de Matemáticas
Juan Carlos Najera-Tinoco: Universidad Autónoma de Guerrero, Facultad de Matemáticas
Martin P. Arciga-Alejandre: Universidad Autónoma de Guerrero, Facultad de Matemáticas
Eduardo Castañeda-Saucedo: Universidad Autónoma de Guerrero, Facultad de Ciencias Químicas

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 1825-1845 from Springer

Abstract: Abstract Mathematical models based on differential equations play a fundamental role in describing the behavior of biological phenomena. In particular, in the study of cell migration, a process by which cells move from one place to another, these models allow not only to characterize cell movement qualitatively, but also to provide quantitative tools to evaluate the efficacy of different treatments or experimental conditions. In this chapter, we study two time-fractional differential equations to model cell migration phenomena. These models allow capturing memory effects and nonlocal behaviors, important features in biological processes such as cell migration and wound closure. The first model refers to a fractional logistic equation, designed to describe the evolution of the wound area, and provides a quantitative measure of the overall progress in wound closure. The second model is based on the Fisher-type fractional diffusion equation, which combines diffusion with growth terms to describe cell propagation during healing. In order to achieve the objective, the direct and inverse problems are addressed. For the direct problems, solutions are obtained using the Fourier analysis for the fractional diffusion equation and the homotopic perturbation method for the logistic equation. On the other hand, the inverse problem is solved from a Bayesian statistics approach, using data obtained from wound closure assays of laboratory experiments. The uncertainty quantification of the parameter is obtained from the posterior distributions.

Keywords: Bayesian estimation; Uncertainty quantification; Wound closure; Caputo derivative; Homotopy method; Fourier series; MCMC; JAGS package (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_82

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