Existence of a Conserved Quantity and Stability of In Vitro Virus Infection Dynamics Models with Absorption Effect

Autor: Cruz Vargas-De-León, M.A. Taneco-Hernández, Celia Martínez-Lázaro, Ramón Reyes-Carreto
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Lyapunov function
Article Subject
In Vitro Techniques
lcsh:Computer applications to medicine. Medical informatics
Models
Biological
01 natural sciences
Stability (probability)
General Biochemistry
Genetics and Molecular Biology
03 medical and health sciences
symbols.namesake
Humans
Computer Simulation
Least-Squares Analysis
0101 mathematics
Epidemics
030304 developmental biology
Mathematics
Equilibrium point
Infectious Disease Medicine
0303 health sciences
Conservation law
General Immunology and Microbiology
Systems Biology
Applied Mathematics
Dynamics (mechanics)
Ode
General Medicine
Models
Theoretical
Viral Load
Conserved quantity
010101 applied mathematics
Virus Diseases
Modeling and Simulation
Ordinary differential equation
Viruses
symbols
lcsh:R858-859.7
Biological system
Algorithms
Medical Informatics
Research Article
Zdroj: Computational and Mathematical Methods in Medicine
Computational and Mathematical Methods in Medicine, Vol 2019 (2019)
ISSN: 1748-6718
1748-670X
Popis: 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.
Databáze: OpenAIRE
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