Stability of general virus dynamics models with both cellular and viral infections
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Authors
A. M. Elaiw
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Al-Azhar University (Assiut Branch), Assiut, Egypt.
A. A. Raezah
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
- Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia.
A. M. Shehata
- Department of Mathematics, Faculty of Science, Al-Azhar University (Assiut Branch), Assiut, Egypt.
Abstract
We consider two general models for the virus dynamics with virus-to-target and infected-to-target infections. We assume
that the virus-target and infected-target incidences, the production and clearance rates of all compartments are modeled by
general nonlinear functions which satisfy a set of reasonable conditions. We incorporate the latently infected cells in the second
model. For each model we prove the existence of the equilibria and calculate the basic reproduction number \(R_0\). We use suitable
Lyapunov functions and apply LaSalle’s invariance principle to prove the global asymptotic stability of the all equilibria of the
models. We confirm the theoretical results by numerical simulations.
Share and Cite
ISRP Style
A. M. Elaiw, A. A. Raezah, A. M. Shehata, Stability of general virus dynamics models with both cellular and viral infections, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1538--1560
AMA Style
Elaiw A. M., Raezah A. A., Shehata A. M., Stability of general virus dynamics models with both cellular and viral infections. J. Nonlinear Sci. Appl. (2017); 10(4):1538--1560
Chicago/Turabian Style
Elaiw, A. M., Raezah, A. A., Shehata, A. M.. "Stability of general virus dynamics models with both cellular and viral infections." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1538--1560
Keywords
- Global stability
- viral infection
- cell-to-cell transfer
- Lyapunov function.
MSC
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