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Computational and Applied Mathematics : Volume 36

Computational and Applied Mathematics : Volume 35

Computational and Applied Mathematics : Volume 34

Computational and Applied Mathematics : Volume 34, Issue 3, October 2015

Global dynamics of a delay reaction–diffusion model for viral infection with specific functional response

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An approximate method for numerically solving multi-dimensional delay fractional optimal control problems by Bernstein polynomials

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Computational and Applied Mathematics : Volume 34, Issue 2, July 2015

Computational and Applied Mathematics : Volume 34, Issue 1, April 2015

Computational and Applied Mathematics : Volume 33

Computational and Applied Mathematics : Volume 32

Global dynamics of a delay reaction–diffusion model for viral infection with specific functional response

Content Provider	Springer Nature Link
Author	Hattaf, Khalid Yousfi, Noura
Copyright Year	2014
Abstract	In this paper, we propose a delay reaction–diffusion model that describes the dynamics of viral infections in vivo such as the human immunodeficiency virus, the hepatitis B virus, and the hepatitis C virus. The model has a nonlinear specific function which denotes the incidence rate of the virus infection in vivo, and it consists of a system of three coupled nonlinear differential equations in a smooth and bounded open set $$\Omega $$ . More precisely, the first equation is an ordinary differential equation, the second equation is a delay differential equation and the third equation is a partial differential equation of parabolic type with a delay and homogeneous Neumann boundary conditions. The dynamical behavior of the model is completely determined by a threshold parameter called the basic reproduction number $$R_{0}$$ . By using the direct Lyapunov method, we show that the disease-free steady state is globally asymptotically stable if $$R_{0}\le 1$$ , which means that the virus is cleared and the disease dies out. When $$R_{0}>1$$ , then disease-free steady state becomes unstable and a unique infected steady state exists and is globally asymptotically stable, it means that the virus persists in the host and the infection becomes chronic.
Starting Page	807
Ending Page	818
Page Count	12
File Format	PDF
ISSN	01018205
Journal	Computational and Applied Mathematics
Volume Number	34
Issue Number	3
e-ISSN	18070302
Language	English
Publisher	Springer Basel
Publisher Date	2014-04-29
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	PDEs in connection with biology and other natural sciences Computational Mathematics and Numerical Analysis General biology and biomathematics Mathematical Applications in Computer Science Applications of Mathematics Mathematical Applications in the Physical Sciences Viral infection Reaction–diffusion Delay stability Asymptotic behavior of solutions
Content Type	Text
Resource Type	Article

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