Stability analysis of a general discrete-time pathogen infection model with humoral immunity

Abstract

This paper studies the global stability of a discrete-time pathogen infection model with humoral immunity. The incidence rate of infection as well as the production and clearance rates of the cells, pathogens and antibodies are modelled by general functions. We use nonstandard finite difference method to discretize the continuous-time model. Two threshold parameters are derived, the basic reproduction number ${\mathcal{R}}_0$ and the humoral immune response activation number ${\mathcal{R}}_1$. The basic and global properties of the model are established. A global stability analysis of the equilibria is performed using the Lyapunov method. Theoretical results are illustrated by numerical simulations.

Keywords:

• Pathogen infection
• humoral immune response
• global stability
• discrete-time models
• Lyapunov function

2010 Mathematics Subject Classifications:

• 34D23
• 93D20
• 37C75
• 93D05
• 93C55

Acknowledgment

This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (DF-090-130-1441). The authors, therefore, gratefully acknowledge DSR technical and financial support.

Disclosure statement

No potential conflict of interest was reported by the authors.