具有飞沫和直接接触感染的传染病模型分析

Analysis of an Epidemic Model through Droplet Infection and Direct Contact

考虑由飞沫传染和直接接触引发的传染病,建立了具有非线性接触率和非线性治愈率的脉冲时滞SIRS传染病模型.定义了两个正数R1和R2,并且证明了当R1<1时,系统的无病周期解是全局吸引的,当R2>1时系统持久.最后利用数值模拟验证了主要结论.

A disease spreaded by droplet infection and direct contact was considered. And a delayed epi-demic model was established with pulse vaccination and nonlinear transmission nonlinear cure rate. Two positive numbers R1 and R2 were defined. It was proved that there was an infection-free periodic solution which was globally attractive if R1 〈1and the disease was permanent if R2 〉1. Finally, numerical simula-tions were presented to support our main results.