Local stability of a delayed computer virus propagation model with graded infection rate was in-vestigated by regarding the delay due to the period that anti-virus software use to clean viruses as a bifur-cation parameter.The critical value of the delay for local stability and existence of Hopf bifurcation of the model was obtained by analyzing distribution of roots of the corresponding characteristic equation.The re-search showed that the model was local stability when the delay value is lower than the critical value, while it would lose the stability and come into being the Hopf bifurcation when the delay value is higher than the critical value.Finally,a numerical example was presented to testify the effects of theoretical re-sults.%以反病毒软件查杀网络病毒所需要的时间周期时滞为分支参数，研究了一类具有分级感染率的时滞SLARS 网络病毒传播模型的局部稳定性。通过讨论模型相应特征方程根的分布，得到模型的局部稳定和产生 Hopf分支的时滞临界点。研究表明，当时滞的值低于临界点时，模型是局部渐近稳定的。而一旦时滞的值超越临界点时，模型将失去稳定性并产生 Hopf 分支。最后，给出一个仿真示例，对所得到的理论结果进行了数值模拟。
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