Stability of discrete-time latent pathogen dynamics model with delay and cellular infection

Issue title: Mathematical Modelling in Computational and Life Sciences

Guest editors: Ahmed Farouk

Article type: Research Article

Authors: Elaiw, Ahmed M.^{a; *} | Alshaikh, Matuka A.^{a; b}

Affiliations: [a] Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia | [b] Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia

Correspondence: [*] Corresponding author. Ahmed M. Elaiw, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia. E-mail: a_m_elaiw@yahoo.com.

Abstract:  This paper studies the global stability of pathogen dynamics model with pathogen-to-cell and cell-to-cell transmissions. We consider three types of time delays and two types of infected cells, latent and active. The model is given by a system of nonlinear delay differential equations which is discretized by utilizing nonstandard finite difference scheme. Positivity and boundedness properties of the solutions are proven. Global stability of the equilibria is established by constructing Lyapunov functions and applying LaSalle’s invariance principle.

Keywords: Pathogen infection, cellular infection, global stability, nonstandard finite difference, Lyapunov function

DOI: 10.3233/JIFS-179564

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 3, pp. 2789-2799, 2020