Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation

Version 1 : Received: 27 April 2020 / Approved: 28 April 2020 / Online: 28 April 2020 (08:43:56 CEST)

A peer-reviewed article of this Preprint also exists.

Toro-Zapata, H.D.; Trujillo-Salazar, C.A.; Carranza-Mayorga, E.M. Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation. Processes 2020, 8, 782. Toro-Zapata, H.D.; Trujillo-Salazar, C.A.; Carranza-Mayorga, E.M. Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation. Processes 2020, 8, 782.

Journal reference: Processes 2020, 8, 782
DOI: 10.3390/pr8070782

Abstract

A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.

Subject Areas

mathematical model; delay differential equations; HIV; immune system

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