%0 Journal Article
%T 一类具有随机扰动的SEIR传染病随机模型的稳定性分析<br>Stability Analysis of a Stochastic SEIR Epidemic Model with Random Perturbations
%A 黄毅
%A 廖新元
%J Advances in Applied Mathematics
%P 3400-3406
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.137325
%X 本文提出了一类非线性微分方程组成的SEIR传染病随机模型，该模型考虑了系统受到的白噪声随机扰动的影响，并且假定扰动与系统偏离平衡点的程度成正比。应用线性矩阵不等式(Linear Matrix Inequalities, LMI)等方法，结合MATLAB找到符合矩阵不等式的矩阵，验证了平衡点的概率稳定性，并进行数值模拟验证结果。<br />
We propose a stochastic SEIR epidemic model composed of a set of nonlinear differential equations. This model takes into account the effect of white noise stochastic perturbations on the system, and it is assumed that the perturbations are proportional to the degree of deviation of the system from the equilibrium point. By applying the Linear Matrix Inequality (LMI) method and using MATLAB to find matrices that satisfy the matrix inequalities, we verify the probabilistic stability of the equilibrium point and conduct numerical simulations to validate the results.
%K 传染病模型，随机扰动，概率稳定性，数值仿真<br>Epidemic Model
%K Stochastic Perturbations
%K Probabilistic Stability
%K Numerical Simulation
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=92064