Abstract
We propose a mathematical model based on a set of delay differential equations that describe intracellular HIV infection. The model includes three different subpopulations of cells and the HIV virus. The mathematical model is formulated in such a way that takes into account the time between viral entry into a target cell and the production of new virions. We study the local stability of the infection-free and endemic equilibrium states. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. In addition, we designed a non-standard difference scheme that preserves some relevant properties of the continuous mathematical model.
Highlights
History has recorded that infectious diseases have caused devastation in the human population
We design a non-standard finite difference ( non-standard finite difference schemes (NSFD) ) scheme that allows us to obtain numerical solutions of a set of delayed and ordinary differential equations, which describes the dynamics of Human Immunodeficiency Virus (HIV) infection within-host
Based on the previous assumptions, we propose a model that describes the intracellular dynamics of HIV and is given by the following system of ordinary differential equations, dIE (t) dt dI (t) dt dV (t) dt dT (t)
Summary
History has recorded that infectious diseases have caused devastation in the human population. This article presents a new mathematical model, by means of a set of differential equations with delay, to determine the effect of how to produce viruses by target cells inside the dynamics of viruses In this case, two types of virus-infected cells are analyzed: the cells in the eclipse phase that are not producing the virus IE , and the cells that are actively producing the virus I. We design a non-standard finite difference ( NSFD ) scheme that allows us to obtain numerical solutions of a set of delayed and ordinary differential equations, which describes the dynamics of HIV infection within-host.
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