Stability of pathogen dynamics models with viral and cellular infections and immune impairment

Volume 11, Issue 4, pp 456--468 Publication Date: March 10, 2018       Article History
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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
A. A. Raezah - Department of Mathematics, Faculty of Science, King Khalid University, P. O. Box 25145, Abha 61466, Saudi Arabia
B. S. Alofi - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Abstract

We study the global stability analysis of pathogen infection models with immune impairment. Both pathogen-to-susceptible and infected-to-susceptible transmissions have been considered. We drive the basic reproduction parameter $\mathcal{R}_{0}$, which determines the global dynamics of models. Using the method of Lyapunov function, we established the global stability of the steady states of the models. Numerical simulations are used to confirm the theoretical results.

Keywords

• Global stability
• pathogen infection
• immune impairment transfer
• Lyapunov function
• cell-to-cell transmission

•  34D23
•  92D30
•  37B25

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