Integrability of a SIS model

Abstract

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′ = - b x y - m x + c y + m k, y′ = b x y - (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.