中文摘要：

本文主要研究一类具标准发生率和空间扩散项的计算机病毒S IR 模型的传播动力学.分 析了当模型的阈值小于1时无病平衡点是局部渐近稳定的,也即计算机病毒趋于消亡;当阈值大于 1时染病平衡点是局部渐近稳定的,说明计算机病毒将逐渐蔓延开来.然后,运用上下解的方法,进 一步证明了上述的局部稳定性在一定条件下会是全局稳定的.最后,根据已有的动力学结论,给出 了病毒的传染病学解释.

英文摘要：

This paper deals with the transmission dynamics of a SIR model for the computer virus with standard incidence rate and spatial diffusion. We show that if the threshold value for the model is less than 1 ,the disease- free equilibrium is locally asymptotically stable, which implies that the virus tends to vanish; otherwise, the epidemic equilibrium is locally asymptotically stable, which means that the virus will gradually spread. Moreover, we prove that the above local stability can extend to be globally stable under certain conditions by using the upper and lower solutions method. A brief epidemiological explanation for our theoretical results is also given.