具有交叉感染的2种菌株对逼近模型分析

为了研究具有一般接触率和用于治疗的SIS对逼近模型及其动力学性质,针对2种菌株是否可以独立生存,建立了一个在规则网络上2种菌株有交叉感染的SIS对逼近传染病模型。根据二项分布,利用节点的状态相关系数得到一个12维系统,计算出模型的基本再生数,得出无病平衡点的局部稳定性,进而获得了无病平衡点不稳定的阀值。通过理论分析和数值模拟得出模型的无病平衡点无条件存在,即不稳定。在研究了2种菌株独立存在以及共同生存的条件后,可以看出2种菌株可以独立生存,也可以相互感染。高维(12维)系统的引入,使得对逼近模型既能模拟疾病的传播机制又能捕捉到疾病传播所在种群的网络结构,因此将对逼近模型应用到多菌株疾病的传播中具有一定价值。

Analysis of pair approximation model of two strains with the cross infection

To study the dynamics of pair approximation SIS model with general comtact rate and treatment.The pair approximation SIS model with a cross infection two strains are established in this paper in view of the two strains could live independently. We got a 12d system using the node status correlation coefficient based on the binomial distribution. In addition, we concluded that the local stability of the disease-free equilibrium by calauating the model of the basic reproductive number, and then, the unstable threshold of disease-free equilibrium is found. Finally, model of the disease-free equilibrium existenced unconditionally and it namely is not stable through theoretical analysis and numerical simulation. The conditions of two strains exist independently and the common survival are studied in this paper, and then, we concluded that two strains can live independently, and also be infected with each other. The high dimensionality (12) system is studied. The approximation model not only simulate the spread of disease mechanism but also capture the spread of disease in populations of network structure. So it has a certain value that applying the approximation model to many strains of the spread of disease.