Global Stability of a Secondary Dengue Viral Infection Model

Authors

A. A. Raezah, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia\\ Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 25145, Abha 61466, Saudi ArabiaFollow
A. M. Elaiw, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaFollow
A. S. Alofi, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaFollow

Author Country (or Countries)

Saudi Arabia

Abstract

This paper proposes and analyzes a secondary dengue viral infection model with two antibodies, namely heterologous antibody and homologous antibody. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We have shown that the model has four steady states, namely: infection-free steady state S0, infected steady state with inactive antibody immune response S1, infected steady state with only active heterologous antibody S2, and infected steady state with only active homologous antibody S3. We derive three bifurcation parameters: the basic infection reproduction number R0, the heterologous antibody immune response activation number R1, and the homologous antibody immune response activation number R2. These parameters define the existence and global stability of the steady states of the model. We prove the global asymptotic stability of all steady states utilizing Lyapunov function and LaSalle’s invariance principle. We illustrate the theoretical results via numerical simulations.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140412

Recommended Citation

A. Raezah, A.; M. Elaiw, A.; and S. Alofi, A. (2020) "Global Stability of a Secondary Dengue Viral Infection Model," Applied Mathematics & Information Sciences: Vol. 14: Iss. 4, Article 12.
DOI: http://dx.doi.org/10.18576/amis/140412
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss4/12