公共教育影响的SIR传染病斑块模型性态分析

Dynamic Behaviors of an SIR Patch Model with Public Education

建立了考虑公共卫生教育影响的SIR斑块模型.通过分析模型动力学性态,给出模型平衡点存在条件,并证明了无病平衡点和地方病平衡点的稳定性.通过数值模拟分析公共卫生教育和斑块间的传播对模型疾病传播的影响,发现媒体的传播和公众之间的交流可以促进疾病防护意识,进而降低传染及传播疾病的几率.当疾病爆发时,应尽量减少人口流通,当疾病爆发后,应加强疾病防护意识的传播,尤其是医疗水平较低的地区.

In this paper,We foriulated an SIR model with public health education on two patches.By analyzing the dynamic behaviors of the model,we gave the conditions of the existence of the equilibrium for the model,and proved the stability of the diseasefree equilibrium and the endemic equilibrium.By numerical simulation,we analyzed the influence of public health education and migration between patches on the spread of disease for the model.It is found that the spread of the media and the communication between the public can promote disease prevention awareness,and reduce the probability of infection and the chance of spreading the disease.Therefore,When disease outbreaks,the circulation of the population should be minimized.After the outbreak of disease,awareness of disease prevention should be strengthened in some areas with low levels of medical care.