On the Carrying and Evolution Matrices in Epidemic Models

Abstract

This study presents a technical characterization of classical epidemic models of compartments by decomposing the state into an infectious sub-state (or infective compartment) and a non-infective sub-state (or non-infective compartment). Then, the linearized infective part of the model is discussed through a positivity/stability viewpoint from linear algebraic tools. Some relevant properties of the transition and transmission matrices are described in a general context. The main advantage of the given formalism is that the linearized behavior about the equilibrium steady-state is general in the sense that it is independent of the particular epidemic model due to the compartmental structure performed analysis. The performed study is made in the absence and in the presence of delayed dynamics.