期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Stability Analysis of a Two-dose Measles Model
摘要/Abstract
建立了一类具有2次接种和潜伏期的SV1V2EIR麻疹模型.首先，得到了平衡点和基本再生数，通过比较原理等方法确定了模型解的非负性和有界性，用线性化、Hurwitz判据、构造Lyapunov函数等方法证明了当R0<1时，无病平衡点全局渐近稳定；当R0>1时，无病平衡点不稳定且正平衡点全局渐近稳定.最后，对模型进行数值模拟，用敏感性分析、偏置相关系数（PRCC）等方法研究了影响麻疹传播的关键因素.结合中国大陆2007-2017年真实患者数据对模型进行了数值模拟，结果显示了麻疹疫情的流行趋势.
In this paper,we establish an SV1V2EIR measles model with two vaccinations and the incubation period.First,we obtain the equilibrium point and the basic reproduction number of the model,and non-negativity and boundedness of the model solutions are determined by using comparison principle.Using the linearization,Hurwitz criterion and Lyapunov functions,we obtain the globally asymptotically stabling of the infection-free equilibrium when R0<1.When R0>1 the infection-free equilibrium is unstable,and there exists a unique globally asymptotically stable positive equilibrium.Finally,we simulate the model and study the key factors affecting measles transmission by sensitivity analysis and partial rank correlation coefficients (PRCC).Combining with the real patient data from 2007 to 2017 in China,the model was simulated.The results of numerical simulation show the epidemic measles spread trends of measles in China.
关键词
参考文献 15
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