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. © 2008 Elsevier Inc. All rights reserved.