A SIR-model with square-root dynamics: An NSFD scheme

We present a SIR-model for which the interaction term is expressed as the square-root of the S and I variables. General results on the behaviour of the solutions are discussed and a discrete-time, finite difference scheme is constructed using the NSFD methodology of Mickens. An important feature of the scheme is that both the positivity and a conservation law for the system of differential equations are maintained by the discretization.