Discrete and continuous compartmental models of cellular populations

We consider a biological system where several families of cells, differentiated by their activity state and reaction to external factors acting on the system, are present. The dynamics of cell populations is modelled by a compartmental approach, starting from the case of finite number of classes and passing to the continuum range of the variables. In a frame of special attention devoted to the mass balance, the evolution of the system is described by the variation of mass of each species. The well-posedness of the mathematical models is proved.