Stability analysis of general viral infection models with humoral immunity

Volume 9, Issue 2, pp 684--704 http://dx.doi.org/10.22436/jnsa.009.02.31

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Authors

A. M. Elaiw - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. N. H. AlShamrani - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

We present two nonlinear viral infection models with humoral immune response and investigate their global stability. The first model describes the interaction of the virus, uninfected cells, infected cells and B cells. This model is an improvement of some existing models by incorporating more general nonlinear functions for: (i) the intrinsic growth rate of uninfected cells; (ii) the incidence rate of infection; (iii) the removal rate of infected cells; (iv) the production, death and neutralize rates of viruses; (v) the activation and removal rate of B cells. In the second model, we introduce an additional population representing the latently infected cells. The latent-to-active conversion rate is also given by a more general nonlinear function. For each model, we derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functions and LaSalle's invariance principle, we prove the global asymptotic stability of all equilibria of the models.

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Keywords

• Viral infection
• global stability
• humoral immune response
• Lyapunov function.

MSC

•  92D30

References

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