The Modeling Dynamics of HIV and CD4 $$^{+}$$ + T-cells During Primary Infection in Fractional Order: Numerical Simulation

The Modeling Dynamics of HIV and CD4 $$^{+}$$ + T-cells During Primary Infection in... This article is devoted to introduce a numerical treatment using Adams–Bashforth–Moulton method of the fractional model of HIV-1 infection of CD4 $$^{+}$$ + T-cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. The fractional derivative is described in Caputo sense. Special attention is given to present the local stability of the proposed model using fractional Routh–Hurwitz stability criterion. Qualitative results show that the model has two equilibria: the disease-free equilibrium and the endemic equilibrium points. We compare our numerical solutions with those numerical solutions using fourth-order Runge–Kutta method (RK4). The obtained numerical results of the proposed model show the simplicity and the efficiency of the proposed method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

The Modeling Dynamics of HIV and CD4 $$^{+}$$ + T-cells During Primary Infection in Fractional Order: Numerical Simulation

Loading next page...
 
/lp/springer_journal/the-modeling-dynamics-of-hiv-and-cd4-t-cells-during-primary-infection-CCgVeZA7lA
Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-018-1178-9
Publisher site
See Article on Publisher Site

Abstract

This article is devoted to introduce a numerical treatment using Adams–Bashforth–Moulton method of the fractional model of HIV-1 infection of CD4 $$^{+}$$ + T-cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. The fractional derivative is described in Caputo sense. Special attention is given to present the local stability of the proposed model using fractional Routh–Hurwitz stability criterion. Qualitative results show that the model has two equilibria: the disease-free equilibrium and the endemic equilibrium points. We compare our numerical solutions with those numerical solutions using fourth-order Runge–Kutta method (RK4). The obtained numerical results of the proposed model show the simplicity and the efficiency of the proposed method.

Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jun 1, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off