Global dynamics of a coupled epidemic model

Abstract

In this paper, we propose a novel epidemic model coupling direct and indirect transmission of disease and study the global dynamic of the model system. Despite the nonlinearity and complexity of the system, the basic reproduction number exhibits a nice linear property: it is simply the sum of two basic reproduction numbers for direct and indirect disease transmissions respectively. We further demonstrate that the local and global dynamics of the system are related to the basic reproduction number. The new model has the advantage that it generalizes or connects to various disease models on HIV, Zika virus, avian influenza, H1N1 and so on.

Feedback stabilization of bilinear coupled hyperbolic systems

“…Second order infinite dimensional coupled systems are frequently encountered in practical engineering problems, for example in civil engineering structures (suspension bridges models [24]) and in many problems coming from elasticity (see for instance Lions [17] and references therein). In recent years, the study of this kind of systems has become fairly common and is now an established area of research with an extensive and long list of publications and conference communications (see [25], [10], [1], [2], [3], [4], [16], [12], [5] and the references therein). In this paper we are interested in the problem of stabilization of a class of coupled systems where the control acts only on the first equation of these systems, by using a technique that links the stabilization with a property of controllability for the undamped system.…”