Infection with Mycobacterium tuberculosis (Mtb) is characterized by localized, roughly spherical lesions within which the pathogen interacts with host cells. Containment of the infection or progression of disease depends on the behavior of individual cells, which, in turn, depends on the local molecular environment and on contact with neighboring cells. Modeling can help us understand the nonlinear interactions that drive the overall dynamics in this system. Early events in infection are particularly important, as are spatial effects and inherently stochastic processes. We describe a model of early Mycobacterium infection using the CyCells simulator, which was designed to capture these effects. We relate CyCells simulations of the model to several experimental observations of individual components of the response to Mtb.