对两菌株SIJS传染病数学模型的分析

Analysis of the SIJS Mathematical Epidemic Model with Two Strains

主要研究了带两菌株的SIJS传染病数学模型,通过对数学模型的分析,讨论了传染病的传播与消亡原理。首先,根据传染病的传播规律,建立带两菌株的SIJS传染病的数学模型;其次,给出基本再生数R0,并证明当R0<1时无病平衡点的渐近稳定性;最后,证明了当R0>1时,地方病平衡点局部渐近稳定。

In this paper, the epidemic mathematical SIJS model with two strains is studied, by analyzing the mathematical model, the principle of the demise and the spread of infectious diseases are discussed. Firstly, according to the propagation of infectious diseases, a epidemic mathematical SIJS model is established with two strains to the infectious diseases. Secondly, the basic reproductive number is established, and it is proved that if R0〈1, the disease-flee equilibrium is locally asymptotically stable and the disease dies out eventually. Finally, if Roll, a unique endemic equilibrium is locally asymptotically stable.