论文标题
SIRWS模型的动力学，免疫力减弱和免疫增强时期
Dynamics of an SIRWS model with waning of immunity and varying immune boosting period
论文作者
论文摘要
SIRS模型捕获免疫力不是终生的传染病的传播动力学。可以通过W隔室扩展这些模型，以使免疫力减弱的个体重复接触时免疫系统的增强。先前的分析假设从r到w以及从W到S的相同衰减率相同。该隐含的假设在完全免疫和降低的免疫力期间的长度相等。我们放宽了这一限制，并允许对总免疫周期进行不对称分配。通过分析和数值工具的组合研究了地方性平衡的稳定性转换。然后，将延续方法应用于沿平衡分支的分叉。我们发现了丰富的动态：Hopf分叉，地方性双重气泡和双重区域。我们的结果表明，可以提高免疫力的时期长度是一个关键参数，从而显着影响长期流行病学动力学。
SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure may be incorporated. Previous analyses assumed identical waning rates from R to W and from W to S. This implicitly assumes equal length for the period of full immunity and of waned immunity. We relax this restriction, and allow an asymmetric partitioning of the total immune period. Stability switches of the endemic equilibrium are investigated with a combination of analytic and numerical tools. Then, continuation methods are applied to track bifurcations along the equilibrium branch. We find rich dynamics: Hopf bifurcations, endemic double bubbles, and regions of bistability. Our results highlight that the length of the period in which waning immunity can be boosted is a crucial parameter significantly influencing long term epidemiological dynamics.
