Models arising in biology are often written in terms of Ordinary Differential Equations. The celebrated paper of Kermack-McKendrick (1927), founding mathematical epidemiology, showed the necessity to include parameters in order to describe the state of the individuals as time elapsed after infection. During the 70s, many mathematical studies where developed when equations are structured by age, size or a physiological trait. The talk will present some structured equations, show that a universal relative entropy structure is available in the linear case. In the nonlinear cases it might be that periodic solutions occur, which can be interpreted, e.g., as network activity in the neuroscience. When the equations are conservation laws, a variant of the Monge-Kantorovich distance also gives a general control of solutions.