Monotonicity Properties of the SIS and SIR Epidemic Models

The dynamics of the SIS and SIR epidemics are modelled by simple, mass action kinetics type, non-linear systems of ordinary differential equations. The signs of derivatives of the populations of susceptible, infective, and removed individuals with respect to each initial population are investigated in this work. For both models, there are derivatives of one sign for all time and derivatives which change sign in time.