Long term tree–grass dynamics is an important issue in many places around the world. Especially, if we intend to take into account environmental and human perturbations, like fire events, herbivory, etc. In this paper, we complete and extend temporal models developed in recent papers by Yatat et al. (2014, 2017) and Tchuinte Tamen et al. (2014), using diffusion operators, into spatio-temporal models, in order to study the long term dynamics of a mosaic of forest and grassland in a humid context of Central Africa. We take into account local biomass diffusion, as well as local tree–grass competition for nutrients and light. For this model, we carry out a qualitative analysis that highlights some ecological thresholds shaping the dynamics of the system. In addition, we show that monostable and bistable travelling wave solutions may exist. We illustrate some of our theoretical results with numerical simulations, and, also explore the use of impulsive fires on the dynamics of a mosaic of forest and grassland in a humid savanna. We found that depending on fire-return time as well as difference in diffusion potential of woody and herbaceous vegetation, fire events are able to greatly slow down or even stop the progression of forest in humid regions.