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This paper studies a Distributed computing (DC) system under virus epidemics,the reliability of which is defined as the probability of fulfilling a task before a specified time.Firstly,the DC system architecture is modeled by an undirected graph whose nodes (i.e.computers) have a continuous-state model representing its computational capability.Then a set of epidemic differential equations are formulated and solved to obtain the state dynamics of each node under the virus epidemics,based on which the reliability of DC system can be calculated.Numerical results show the effectiveness of the proposed method.