Fractional Dynamics of an Infection Model With Time-Varying Drug Exposure-Reference-Cited by-同舟云学术

Fractional Dynamics of an Infection Model With Time-Varying Drug Exposure

Published:2018-07-26 Issue:9 Volume:13 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Pinto Carla M. A.¹,Carvalho Ana R. M.²

Affiliation:

1. School of Engineering, Polytechnic of Porto, Rua Dr António Bernardino de Almeida, 431, Porto 4249-015, Portugal e-mail:

2. Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, Porto 4440-452, Portugal e-mail:

Abstract

We introduce a fractional order model for the human immunodeficiency virus (HIV) dynamics, where time-varying drug exposure and drug resistance are assumed. We derive conditions for the local and global asymptotic stability of the disease-free equilibrium. We find periodic stable endemic states for certain parameter values, for sinusoidal drug efficacies, and when considering a density-dependent decay rate for the T cells. Other classes of periodic drug efficacies are considered and the effect of the phases of these functions on the dynamics of the model is also studied. The order of the fractional derivative plays an important role in the severity of the epidemics.

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4038643/6008965/cnd_013_09_090904.pdf

Reference36 articles.

1. HIV Dynamics: Analysis and Robust Multirate Mpc-Based Treatment Schedules;J. Math. Anal. Appl.,2009

2. Emergence of Drug-Resistance in Hiv Dynamics Under Distinct Haart Regimes;Commun. Nonlinear Sci. Numer. Simul.,2016

3. Within-Host and Synaptic Transmissions: Contributions to the Spread of HIV Infection;Math. Methods Appl. Sci.,2017

4. Opportunistic Infection as a Cause of Transient Viremia in Chronically Infected HIV Patients Under Treatment With Haart;Bull. Math. Biol.,2005

5. Backward Bifurcation in a Mathematical Model for HIV Infection In Vivo With Anti-Retroviral Treatment;Nonlinear Anal.: Real World Appl.,2014

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