Quasimonotone systems. Positive feedback systems. Cooperative systems

In the previous chapters we have been trying to identify the general structure of epidemic systems and we discovered that they fall essentially in two classes depending on the structure of the interacting matrix in bilinear forces of infection.

Applications of this theory to epidemic systems can be found in [142, 18], among others. In [57, 59, 46, 55] large attention has been devoted to positivefeedback epidemic systems also checking the robustness of the basic model with respect to modifications which take into account realistic features of the system: space structure, periodicity of the parameters, boundary feedback, etc.

This kind of robustness is of great interest for a modeler in that it may imply a structural stability of the model with respect to features that have not been analyzed yet or else that cannot be identified for lack of available data.

We shall start our analysis by listing a series of epidemic systems that may fall in this class. In Appendices A and B, Sections A.4 and B.2.1 respectively, we shall include the main mathematical theorems, that allow the analysis of positive feedback epidemic systems.