Editing Basic reproduction number (section)

=== Epidemic models on networks ===
{{Main|Mathematical modelling of infectious disease}}

Epidemics can be modeled as diseases spreading over [[Complex network|networks]] of contact and disease transmission between people.<ref>{{Cite book |url=http://networksciencebook.com/ |title=Network Science by Albert-László Barabási}}</ref> Nodes in these networks represent individuals and links (edges) between nodes represent the contact or disease transmission between them. If such a network is a locally tree-like network, then the basic reproduction can be written in terms of the [[Degree distribution|average excess degree]] of the transmission network such that:

<math display="block">R_0 = \frac{\beta}{\beta+\gamma} \frac{{\langle k^2 \rangle} -{\langle k \rangle}}{{\langle k \rangle}},</math>

where 
<math> {\beta} </math>
is the per-edge transmission rate, 
<math> {\gamma} </math>
is the recovery rate, 
<math>
{\langle k \rangle}
</math> is the mean-degree (average degree) of the network and <math>
{\langle k^2 \rangle}
</math> is the second [[Moment (mathematics)|moment]] of the transmission network [[degree distribution]].