Ahmed M. Elaiw This email address is being protected from spambots. You need JavaScript enabled to view it.1,2 and Matuka A. Alshaikh1,3

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
3Department of Mathematics, Faculty of Science, Taif University, Saudi Arabia


 

Received: October 28, 2019
Accepted: November 7, 2019
Download Citation: ||https://doi.org/10.6180/jase.202003_23(1).0011  

ABSTRACT


This paper studies the global stability of a pathogen dynamics model with pathogen-to-cell and cell-to-cell transmissions. Both latently and actively infected cells are incorporated into the models. Three time delays are considered. The production and clearance rates of the cells and pathogens are given by general functions. The model is given by systems of nonlinear delay differential equations which are discretized by using nonstandard finite difference approach.We first establish the existence and positivity of the solutions and then we study the global stability of the model’s equilibria. Lyapunov functions are constructed and LaSalle’s invariance principal is applied to proven the global stability.We confirm the theoretical results by numerical simulations.


Keywords: Pathogen Infection, Latency, Cellular Infection, Global Stability, Nonstandard Finite Difference, Lyapunov Function



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