基于Logistic增长和心理作用的SIR传染病模型的渐近分析

根据传染病动力学原理,考虑到传染病的发生,人们将采取相应的预防和控制措施,建立了基于Logistic增长和心理作用的SIR传染病模型.综合利用常微分方程定性与稳定性理论和极限系统理论,分别获得了该模型的无病平衡点和地方病平衡点全局渐近稳定的充分条件.研究结果表明:人们心理作用的积极影响,能够将疾病的传播和流行控制在一定范围内,加上有效的治疗措施,甚至能够加快疾病的绝灭.

Asymptotic Analysis of an SIR Epidemic Model with Psychology Effect and Logistic Grow

By using epidemic dynamic theory,considering the occurrence of infectious diseases,people will take corresponding measures to prevent and Logistic grow,a class of SIR epidemic model with psychology effect and treatment is established.By using some methods,including qualitative and stability theory of ordinary differential equations,limit system theory,sufficient conditions are obtained for the global asymptotic stability of each of disease-free equilibrium and endemic equilibrium to the proposed model. The results show that the positive influence of people's psychological function can control the spread and prevalence of disease within a certain range,together with effective treatment measures,can even accelerate the extinction of the disease.