医院内媒介交叉感染的数学建模及稳定性分析

Mathematical Modeling and Stability Analysis of Media Cross-Infection in Hospitals

结合医院内媒介交叉感染的实际问题,建立了医院内以医生和护士为传染媒介引起的抗生素耐药性交叉感染模型,得到了控制疾病流行与否的阈值R_0,分析了阈值条件下无病平衡点和正平衡点的稳定性等动力学性态,得到了R_0<1时无病平衡点是全局稳定的,且医院携带耐药菌的医护人员和病人数都为零,不会发生交叉感染,R_0>1时有且仅有一个正平衡点E*,且全局稳定,医院内抗生素耐药性的交叉感染将趋于平稳流行.

Combined with media-cross infection in hospitals, the mathematical model es- tablishes cross infection model with antibiotic-drug resistance that caused by healthcare workers, who play as vector of infection; getting threshold R0 that controls popularity of disease; analyzing the stability of disease-free equilibrium and positive equilibrium under threshold Ro condition. Furthermore, when R0 〈 1, the disease-free equilibrium is globally stable and there is no cross infection when the number of healthcare workers and patients with drug-resistance bacteria is zero, and there is only one positive equilibrium E＊ when the mathematia model makes certain that threshold R0 〉 1 is in globally stable situation and cross functiorL of antibiotics-drug resistance is in smoothly development.