具有季节性和接种疫苗的元胞自动机传染病模型

为了研究基于二维元胞自动机的一类具有季节性和疫苗接种的SIR传染病模型对控制传染病的影响,利用平均场近似方法建立了非线性离散模型。对模型进行了数学分析,通过计算无病平衡点的Jacobian矩阵的谱半径,得到了无病平衡点的局部稳定性,通过数值模拟,找出了在正平衡点处染病者与元胞邻居结构δ的关系,并且考虑了不同的初始患者设置对疾病传播速度的影响,不同的接种疫苗率对疾病传播速度的影响。通过研究可知:当疾病的初始患者为中心分布时,传染病的传播速度小于初始患者为随机分布时的速度;随着接种疫苗率的增大,传染病的传播速度会减小,对初始患者为中心分布的元胞自动机影响较大。研究模型在控制传染病传播的动力学研究方面具有一定的参考价值。

A cellular automata model for epidemics with seasonal and vaccination

In order to study the influence on the infectious desease control of a class of SIR epidemic models with seasonal and vaccination based on two-dimensional cellular automaton, a nonlinear discrete model is established by means of mean-field approximation. The model is analyzed mathematically. By calculating the spectral radius of the Jacobian matrix with the disease-free equilibrium, the local stability of the disease-free equilibrium is obtained. The relationship between the number of infected persons at the positive equilibrium point and the structure of the cell neighborhood is obtained by numerical simulating. And the effects of different initial patient settings on the disease transmission speed and the different vaccination rates on disease spread are considered. Through numerical simulation, the conclusion is gotten that when the initial patient is distributed at a central distribution, the speed of transmission is less than the velocity of the infectious disease when the initial patient is randomly distributed; with the increase of vaccination rate, the infectious disease transmission speed will decrease, which has greater impact on the initial distribution of patients as the center of cellular automaton. The study model has reference value in the dynamic research of controlling infectious disease transmission.