Hybrid models based on state space quantisation and providing a nondeterministic nature are a convenient framework for the study of behaviour prediction and control of various complex biological processes with incomplete knowledge. Starting from a model of a tumour growth process, in the literature, the paper proposes an abstract quasi-random invasion process in a partitioned state space with a lattice structure. The invader is a relative nutrient concentration. An event occurs whenever the numerical gradient of the invader in an occupied cell reaches a threshold limit, thus allowing the growth process to randomly occupy a new adjacent cell or position in the lattice. Simulations of the system are performed, for different scenarios and a control mechanism of the growth process is also proposed, incorporating feedback and exogenous nutrient inhibitors.

Keywords: Complex systems, Hybrid systems, State space partition, Biological modelling, Difference equation, Simulation