一类埃博拉病毒的传染病模型分析

Analysis of an Epidemic Model with Ebola Virus

为控制高死亡率的埃博拉病毒的传播,建立了具有接种疫苗、感染者死亡后病毒传播的埃博拉传染病模型,运用下一代生成矩阵法得到基本再生数R0。应用Lyapunov函数证明了当R0<1时无病平衡点的全局稳定性,疾病最终灭绝;当R0> 1时,地方病平衡点的存在性以及全局稳定性。通过对模型进行数值模拟,发现提高疫苗的接种率或提高合理的殡葬率可缩短疾病消亡或趋于稳定的时间,且可有效控制疾病的传播,对于治愈率极低的埃博拉病毒的研究有着重要的参考意义。

In order to control the transmission of Ebola virus with high mortality rate,an Ebola infectious disease model with vaccination and viral transmission after death is established,and the basic reproduction number R0 is obtained by using the next generation of generator matrix. By using of Lyapunov function,the global stability of disease-free equilibrium point is proved when R0< 1 and the disease eventually extinct and existence and global stability of endemic equilibrium point when R0> 1.Through numerical simulation of the model studied,it is found that increasing vaccination rate and reasonable burial rates of disease shorten the time it takes for the disease to die or stabilize,and effectively control the spread of the disease. For Ebola virus with low cure rate,it has important research value,and provide a scientific and rational theoretical basis.