TY - JOUR
T1 - Existence of a Conserved Quantity and Stability of In Vitro Virus Infection Dynamics Models with Absorption Effect
AU - Martínez-Lázaro, Celia
AU - Taneco-Hernández, Marco Antonio
AU - Reyes-Carreto, Ramón
AU - Vargas-De-León, Cruz
N1 - Publisher Copyright:
© 2019 Celia Martínez-Lázaro et al.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85063228771&partnerID=8YFLogxK
U2 - 10.1155/2019/2954041
DO - 10.1155/2019/2954041
M3 - Artículo
C2 - 30944575
SN - 1748-670X
VL - 2019
JO - Computational and Mathematical Methods in Medicine
JF - Computational and Mathematical Methods in Medicine
M1 - 2954041
ER -