Integrability of a SIS model

We prove that the classical model of an infectious disseise, which never kills and which does not induce autoimmunity, is integrable. This model can be written as x′=−bxy−mx+cy+mk, y′=bxy−(m+c)y with parameters b,c,k,m∈R. We provide the explicit expression of its first integrals and of the set of all its invariant algebraic curves.