Department of Mathematics, University of Sussex, Falmer, Brighton, UK.
Bull Math Biol. 2012 Oct;74(10):2488-509. doi: 10.1007/s11538-012-9763-8. Epub 2012 Aug 15.
Effects of immune delay on symmetric dynamics are investigated within a model of antigenic variation in malaria. Using isotypic decomposition of the phase space, stability problem is reduced to the analysis of a cubic transcendental equation for the eigenvalues. This allows one to identify periodic solutions with different symmetries arising at a Hopf bifurcation. In the case of small immune delay, the boundary of the Hopf bifurcation is found in a closed form in terms of system parameters. For arbitrary values of the time delay, general expressions for the critical time delay are found, which indicate bifurcation to an odd or even periodic solution. Numerical simulations of the full system are performed to illustrate different types of dynamical behaviour. The results of this analysis are quite generic and can be used to study within-host dynamics of many infectious diseases.
在疟疾抗原变异模型中，研究了免疫延迟对对称动力学的影响。通过对相空间的同型分解，稳定性问题简化为对特征值的三次超越方程的分析。这使得人们能够在 Hopf 分岔处识别出具有不同对称性的周期解。在免疫延迟较小的情况下，Hopf 分岔的边界以系统参数的封闭形式找到。对于任意的时滞值，找到了临界时滞的一般表达式，表明分岔到奇数或偶数周期解。对完整系统进行数值模拟，以说明不同类型的动力学行为。该分析的结果具有很强的通用性，可以用于研究许多传染病的宿主内动力学。
