The study of epidemiological systems has generated deep interest in exploring the dynamical complexity of common infectious diseases driven by seasonally varying contact rates. Mathematical modeling and field observations have shown that, under seasonal variation, the incidence rates of some endemic infectious diseases fluctuate dramatically and the dynamics is often characterized by chaotic oscillations in the absence of specific vaccination programs. In fact, the existence of chaotic behavior has been precisely stated in the literature as a noticeable feature in the dynamics of the classical Susceptible-Infected-Recovered (SIR) seasonally forced epidemic model. However, in the context of epidemiology, chaos is often regarded as an undesirable phenomenon associated with the unpredictability of infectious diseases. As a consequence, the problem of converting chaotic motions into regular motions becomes particularly relevant. In this article, we consider the phase control technique applied to the seasonally forced SIR epidemic model to suppress chaos. Interestingly, this method of controlling chaos takes on a clear meaning as a weak perturbation on a seasonal vaccination strategy. Numerical simulations show that the phase difference between the two periodic forces - contact rate and vaccination - plays a very important role in controlling chaos.
Modeling the effects of information-dependent vaccination behavior on meningitis transmission
我们提出了一个数学模型来研究信息依赖的接种行为对脑膜炎传播的影响。信息通过信息索引来表示，如在（d 'Onofrio et al.，Theor.流行生物学，2007年）。我们进行定性分析的基础上的稳定性理论，专注于全局稳定性的无病平衡（DFE）和相关的跨临界分岔发生在阈值的DFE。最后，我们通过数值模拟评估了流行病学和信息参数在模型动力学中的作用。我们的模拟表明，人类行为的影响严重依赖于平均信息延迟。例如，它可以诱发复发性流行病，只要从携带者到传染状态的转移率超过阈值。否则，地方病平衡点（至少）局部稳定。
