Analysis of a model for the dynamics of prions II
Analysis of a model for the dynamics of prions II
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DOI：
10.1016/j.jmaa.2005.11.021
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发表时间：
2006-12-01
影响因子：
1.3
通讯作者：
Webb, Glenn F.
中科院分区：
文献类型：
--
作者：
Engler, Hans;Pruess, Jan;Webb, Glenn F.
分析了朊病毒增殖动力学的一个新的数学模型，该模型涉及与偏积分微分方程耦合的常微分方程，继续了[J. Pruss，L. Pujo-Menjouet，G.F.韦布河Zacher，朊病毒动力学模型的分析，离散连续。Dyn. 6（2006）225-235]。我们证明了这个问题在其自然相空间Z（+）：= R+ xL-1（+）（（x（0），无穷大）; xdx）中的适定性，即，在Z+上存在与该问题相关联的唯一全局半流。对这类数学传染病模型，导出了一个阈值型定理。如果动力学参数的某个组合低于或等于阈值，则存在唯一的稳态，即无病平衡，它在Z+中全局渐近稳定;高于阈值则不稳定，并且存在另一个唯一的稳态，即疾病平衡，它继承了该属性。(c)2005年爱思唯尔公司All rights reserved.
A new mathematical model for the dynamics of prion proliferation involving an ordinary differential equation coupled with a partial integro-differential equation is analyzed, continuing the work in [J. Pruss, L. Pujo-Menjouet, G.F. Webb, R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. 6 (2006) 225-235]. We show the well-posedness of this problem in its natural phase space Z(+) := R+ x L-1(+) ((x(0), infinity); x dx), i.e., there is a unique global semiflow on Z+ associated to the problem. A theorem of threshold type is derived for this model which is typical for mathematical epidemics. If a certain combination of kinetic parameters is below or at the threshold, there is a unique steady state, the disease-free equilibrium, which is globally asymptotically stable in Z+; above the threshold it is unstable, and there is another unique steady state, the disease equilibrium, which inherits that property. (c) 2005 Elsevier Inc. All rights reserved.