Stability analysis of humoral immunity HIV infection models with RTI and discrete delays
| Autor: | E. Kh. Elnahary, M. Abul-Ez, Ahmed M. Elaiw, A. M. Shehata |
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| Rok vydání: | 2016 |
| Předmět: |
Lyapunov function
Control and Optimization Mechanical Engineering 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Stability (probability) Quantitative Biology::Cell Behavior symbols.namesake Nonlinear system Immune system Exponential stability Control and Systems Engineering Modeling and Simulation Humoral immunity symbols Applied mathematics 0101 mathematics Electrical and Electronic Engineering Basic reproduction number Bifurcation Civil and Structural Engineering Mathematics |
| Zdroj: | International Journal of Dynamics and Control. 5:811-831 |
| ISSN: | 2195-2698 2195-268X |
| DOI: | 10.1007/s40435-016-0235-0 |
| Popis: | A class of HIV infection models are proposed and analyzed. The models incorporate three types of immune cells, CD4 $$^{+}$$ T cells, macrophages and B cells. We consider also two types of intracellular discrete delays to describe the latent period from the virus contacts an uninfected target cell and the production of new HIV particles. The infection rate is represented by bilinear incidence and saturation incidence in the first two models. In the third model, both the infection rate and neutralization rate of viruses are given by nonlinear general functions. Two bifurcation parameters, the basic reproduction number and the humoral immunity activation number are derived. We established a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. We utilize Lyapunov method to investigate the global asymptotic stability of all steady states of the models. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior. |
| Databáze: | OpenAIRE |
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