具有无症状感染者的SEIAC模型动力学研究
Dynamics Study of a SEIAC Model with Asymptomatic Patient

本文基于无症状感染者在疾病传播过程中的作用，建立了一类具有无症状感染者的SEIAC动力学模型，利用下一代矩阵得到决定疾病存在与否的基本再生数R0，通过构造Lyapunov函数得到当R0 < 1时，无病平衡点是全局渐近稳定的，即疾病最终趋于灭绝；而当R0 > 1时，地方病平衡点是全局渐近稳定的，即疾病将持续存在成为地方病。最后借助Mathematica软件对基本再生数进行敏感性分析及模型数值模拟。结果表明：提高治疗水平有利于疾病的防控，忽视无症状感染者的影响将低估疾病的传播情况。该结果将为具有无症状感染者的传染病的防控提供一定的理论支撑。
Based on the role of asymptomatic patient in the process of disease transmission, this paper estab-lishes a SEIAC dynamic model with asymptomatic patient. The next generation matrix is used to obtain the basic reproduction number R0 that determines the existence of the disease. By con-structing the Lyapunov function, it is obtained that when R0 < 1, the disease-free equilibrium is globally asymptotically stable, that is, the disease eventually tends to extinction, when R0 > 1, the endemic equilibrium is globally asymptotically stable, in other words, the disease will persist and become endemic. Finally, the sensitivity analysis and model numerical simulation of the basic re-production number are carried out by Mathematica. The results show that improving the treatment level is conducive to the prevention and control of the disease, and ignoring the impact of asymp-tomatic patient will underestimate the spread of the disease. The results will provide some theo-retical support for the prevention and control of infectious diseases with asymptomatic patient.