A new software reliability model based on the Polya contagion stochastic process is proposed. We model the failure detection process as a pure birth process with a failure rate that depends not just on time but on the number of failures previously detected, as it happens in the Polya process obtained as the asymptotic limit of the Polya urn model for contagion. Since the contagion proposes an increasing failure (birth) rate, this model is suitable to be applied at the beginning of the testing process or when some code has been added to the project, situations where the S-shaped model is usually used. The result of applying our model to real data is also shown.