In this paper, we study deterministic limits of Markov processes made of several interacting objects. While most classical results assume that the limiting dynamics has Lipschitz properties, we show that these conditions are not necessary to prove convergence to a deterministic system. We shows that under mild assumptions, the stochastic system convergences to the solution of a differential inclusion and we provide simple way to compute the limit inclusion. When this differential inclusion satisfies a one-sided Lipschitz condition (often satisfied in practice), there exists a unique solution of this differential inclusion and we show convergence in probability with explicit bounds. This extends the applicability of mean field techniques to system exhibiting threshold dynamics such as queuing systems with boundary conditions. This is illustrated by applying our results to push-pull queues with a large number of incoming sources and a large number of servers that are natural models of volunteer computing systems.