具有B-D非线性传染率的SIQ传染病模型

摘要

为了研究一类具有B-D 非线性传染率的 SIQ传染病模型的稳定性与数值模拟.文中利用分析计算技巧与构造李雅谱诺夫函数的方法,以及计算机数值模拟,得到了阈值R及无病平衡点和地方病平衡点的存在条件,证明了无病平衡点和地方病平衡点的局部与全局稳定性,得到的数值模拟图形结果验证了理论证明结果的正确性.结果表明,具有B-D非线性传染率的传染病模型的平衡解局部稳定性与全局稳定性由含模型参数的阀值来决定的,并说明了该模型种群之间的依赖关系.%The paper studies the stability and numerical simulation of the SIQ epidemics model with the B-D nonlinear incidence rate.By using the analytical calculation technique,the method of constructing Lyapunov function and the computer numerical simulation,the threshold value R and the existence conditions for the disease-free equilibrium point and the endemic equilibrium point are obtained.The local and global stability of the disease-free equilibrium point and the endemic equilibrium point are proved. The obtained numerical simulation results verify the correctness of the theoretical results.The results show that the local stability and global stability of the equilibrium solutions of the infectious disease model with the B-D nonlinear infection rate are determined by the threshold of the model parameters. The dependent relationships between the model population is explained.