5. Properties of the individual-based SIR approach
In this section, we derive some useful properties from the individual-based SIR approach. Those properties describe the
infection process more fully, and they relate the infection process with the contact network topology over which an outbreak takes place. First, we derive the epidemic threshold, and we show how it is related to the network topological properties. We also derive the condition under which the infection reaches its peak value with time, and how the peak infection value is related to the epidemic threshold. Moreover, we study the role of the network topology on the spread of epidemics.