Yousfi Noura, Hattaf Khalid, Tridane Abdessamad
Department of Mathematics and Computer Science, Hassan II University, Casablanca, Morocco.
J Math Biol. 2011 Nov;63(5):933-57. doi: 10.1007/s00285-010-0397-x. Epub 2011 Jan 14.
The aim of this work is to investigate a new mathematical model that describes the interactions between Hepatitis B virus (HBV), liver cells (hepatocytes), and the adaptive immune response. The qualitative analysis of this as cytotoxic T lymphocytes (CTL) cells and the antibodies. These outcomes are (1) a disease free steady state, which its local stability is characterized as usual by R (0) < 1, (2) and the existence of four endemic steady states when R (0) > 1. The local stability of these steady states depends on functions of R (0). Our study shows that although we give conditions of stability of these steady states, not all conditions are feasible. This rules out the local stability of two steady states. The conditions of stability of the two other steady states (which represent the complete failure of the adaptive immunity and the persistence of the disease) are formulated based on the domination of CTL cells response or the antibody response.
这项工作的目的是研究一种新的数学模型，该模型描述了乙型肝炎病毒（HBV）、肝细胞（肝实质细胞）和适应性免疫反应之间的相互作用。对该模型进行定性分析，涉及细胞毒性T淋巴细胞（CTL）细胞和抗体。这些结果包括：（1）一个无病稳态，其局部稳定性通常由R(0) < 1来表征；（2）当R(0) > 1时存在四个地方病稳态。这些稳态的局部稳定性取决于R(0)的函数。我们的研究表明，尽管我们给出了这些稳态稳定性的条件，但并非所有条件都是可行的。这排除了两个稳态的局部稳定性。另外两个稳态（代表适应性免疫完全失效和疾病持续存在）的稳定性条件是根据CTL细胞反应或抗体反应的主导作用来制定的。
