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Updated: Jan 26, 2026

Influenza A Virus Studies in a Mouse Model of Infection
Published on: September 7, 2017
Existence of a Conserved Quantity and Stability of In Vitro Virus Infection Dynamics Models with Absorption Effect
Celia Martínez-Lázaro1, Marco Antonio Taneco-Hernández1, Ramón Reyes-Carreto1
1Facultad de Matemáticas, Universidad Autónoma de Guerrero Chilpancingo, Av. Lázaro Cárdenas S/N, Cd. Universitaria, 39087 Chilpancingo, Guerrero, Mexico.
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.
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