On the Role of the Basic Reproduction Number in Systems Modeling Disease Propagation

The aim of this chapter is to show how the basic reproduction number can be calculated regarding dynamical systems. To illustrate the presented methods, we apply them to a system modelling disease propagation coming from the literature. These systems are autonomous ordinary differential equation, difference equations, and reaction-diffusion system modeling the situation when the susceptibles and the infecteds react to each other and diffuse in a two-dimensional bounded, connected spatial domain with piecewise smooth boundary.