Dénes Attila, Székely László
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged H-6720, Hungary.
Institute for Environmental Systems, Szent István University, Páter Károly utca 1., Gödöllő H-2103, Hungary.
Math Biosci. 2017 Nov;293:64-74. doi: 10.1016/j.mbs.2017.08.010. Epub 2017 Aug 30.
Motivated by studies warning about a possible re-emergence of poliomyelitis in Europe, we analyse a compartmental model for the transmission of polio describing the possible effect of unvaccinated people arriving to a region with low vaccination coverage. We calculate the basic reproduction number, and determine the global dynamics of the system: we show that, depending on the parameters, one of the two equilibria is globally asymptotically stable. The main tools applied are Lyapunov functions and persistence theory. We illustrate the analytic results by numerical examples, which also suggest that in order to avoid the risk of polio re-emergence, vaccinating the immigrant population might result insufficient, and also the vaccination coverage of countries with low rates should be increased.
受有关欧洲可能再次出现脊髓灰质炎的研究启发，我们分析了一个描述脊髓灰质炎传播的分区模型，该模型描述了未接种疫苗的人群进入疫苗接种覆盖率低的地区可能产生的影响。我们计算了基本再生数，并确定了该系统的全局动态：我们表明，根据参数的不同，两个平衡点之一是全局渐近稳定的。所应用的主要工具是李雅普诺夫函数和持续性理论。我们通过数值例子来说明分析结果，这些例子还表明，为了避免脊髓灰质炎再次出现的风险，仅对移民人群进行疫苗接种可能是不够的，而且疫苗接种率低的国家的疫苗接种覆盖率也应提高。
