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Most epidemic models for the spread of diseases in contact networks take the assumption of the infected probability of a susceptible agent dependent on its absolute number of infectious neighbours. We introduce a new epidemic model in which the infected probability of a susceptible agent in contact networks depends not on its degree but on its exposure level. We find that effective average infection rate (λ) (i.e., the average number of infections produced by a single contact between infected individuals and susceptible individuals) has an epidemic threshold (λ)c = 1, which is related to recovery rate, epidemic mechanisms and topology of contact network. Furthermore,we show the dominating importance of epidemic mechanisms in determining epidemic pattes and discussed the implications of our model for infection control policy.