一类具有疫苗接种且潜伏期传染的SVEIAR腮腺炎传染病模型  

An SVEIAR mumps infection model with vaccination and latent infection

作　　者：蒋为平 张太雷[1] 刘宗萱 曹欢 JIANG Weiping;ZHANG Tailei;LIU Zongxuan;CAO Huan(School of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《中山大学学报(自然科学版)(中英文)》2025年第2期148-159,共12页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：陕西省自然科学基金(2022JM-023)。

摘　　要：根据已知的腮腺炎传播机制,本文运用常微分方程定性与稳定性理论,建立了一类具有疫苗接种且潜伏期传染的SVEIAR腮腺炎传染病模型,得出了模型的基本再生数.给出了平衡点的存在性并得到了当R_(0)≤1时,无病平衡点全局渐近稳定;当R_(0)>1时,无病平衡点不稳定且地方病平衡点全局渐近稳定.选取江苏省腮腺炎患者病例数据,应用模型模拟了腮腺炎未来几年的流行趋势.敏感性分析显示,疫苗接种是影响腮腺炎的非常重要的因素.提高公众对腮腺炎的防范意识、制定有效的疫苗接种策略、加强锻炼能够提升机体素质以及免疫功能,从而预防腮腺炎的发生,进而控制腮腺炎的持续蔓延.According to the known mechanism of mumps transmission,a SVEIAR mumps infectious disease model with vaccination and incubation period was established by using the qualitative and stability theory of ordinary differential equation,and the basic regeneration number of the model was obtained.The existence of the equilibrium points is given and it is found that the disease-free equilibrium point is globally asymptotically stable when R_(0)≤1;the disease-free equilibrium point is unstable and the endemic equilibrium point is globally asymptotically stable when R_(0)>1.The case data of mumps patients in Jiangsu Province is collected to simulate the epidemic trend of mumps in the next few years.Finally,the sensitivity analysis of parameters shows that the incidence of mumps will continue to increase in recent years.Improving public awareness preventing mumps,developing effective vaccination strategies and strengthening physical exercise can improve the body quality and immune function,so as to prevent the occurrence of mumps,and then control the spread of mumps.

关 键 词：SVEIAR模型 基本再生数 稳定性 数值模拟 

分 类 号：O175.1[理学—数学]