Existence of a Conserved Quantity and Stability of In Vitro Virus Infection Dynamics Models with Absorption Effect. (3rd March 2019)

• Record Type: Journal Article
• Authors: Martínez-Lázaro, Celia; Taneco-Hernández, Marco Antonio; Reyes-Carreto, Ramón; Vargas-De-León, Cruz
• Other Names: Blyuss Konstantin Academic Editor.
• Is Part Of: Computational and mathematical methods in medicine. Volume 2019(2019)
• Publication Date: 2019-03-03
• Subjects: Medicine -- Computer simulation -- Periodicals; Medicine -- Mathematical models -- Periodicals; 610.11
• DOI: 10.1155/2019/2954041
• Languages: English
• ISSNs: 1748-670X

Abstract

Abstract : The estimation of parameters in biomathematical models is useful to characterize quantitatively the dynamics of biological processes. In this paper, we consider some systems of ordinary differential equations (ODEs) modelling the viral dynamics in a cell culture. These models incorporate the loss of viral particles due to the absorption into target cells. We estimated the parameters of models by least-squares minimization between numerical solution of the system and experimental data of cell cultures. We derived a first integral or conserved quantity, and we proved the use of experimental data in order to test the conservation law. The systems have nonhyperbolic equilibrium points, and the conditions for their stability are obtained by using a Lyapunov function. We complemented these theoretical results with some numerical simulations.