Stability of latent pathogen infection model with adaptive immunity and delays

Article type: Research Article

Authors: Elaiw, A.M.^{; *} | AlShamrani, N.H.

Affiliations: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. E-mails: a_m_elaiw@yahoo.com, nalshmrane@kau.edu.sa

Correspondence: [*] Corresponding author. E-mail: a_m_elaiw@yahoo.com.

Abstract: In this paper we propose and analyze a pathogen dynamics model with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We incorporate latently infected cells and three distributed time delays into the model. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters which fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.

Keywords: Pathogen infection, distributed time delay, global stability, adaptive immune response, Lyapunov function

DOI: 10.3233/JIN-180087

Journal: Journal of Integrative Neuroscience, vol. 17, no. 3-4, pp. 547-576, 2018