# R0-Adjusted Centrality

#### Definition

This method is a new epidemic centrality measure and applied as an extension of topological centrality methods which obtained by incorporating the basic reproduction number $R0$ of each city into the weighted centrality measures. When assessing disease spreading centrality of a node on a network and edge weights. The logic behind this concept is that node’s intrinsic property plays a role in the dynamics of disease spreading in a network.

R0-adjusted degree centrality is defined as one type of this extension applications and defined by following relation:

$$C_D^{w,\beta}(i)=R0(i)^\beta \times C_D^ w(i)$$

where $R0$ is the basic reproductive number, $\beta$ is contact rate, $w$ is weight of each link, and $D$ is degree of node $i$.

The proposed R0-adjusted centrality incorporates $R0$ value of a node to the existing network centrality measure to quantify a node’s importance in two aspects, network topology and amplifying/attenuating the intensity of disease spreading.

For this epidemic degree based centrality measures, these additional considerations have a relatively clear interpretation. Including edge weights reflects the volume of population exchange between cities, and thus seems a more accurate representation for disease transmission on an air travel network. It can be further refined by estimating the volume of infective population exchange along the edges. This is done by using $R0$ of each city as a proxy for the fraction of infective population during the disease spreading.

R0-adjusted degree centrality is defined as one type of this extension applications and defined by following relation:

$$C_D^{w,\beta}(i)=R0(i)^\beta \times C_D^ w(i)$$

where $R0$ is the basic reproductive number, $\beta$ is contact rate, $w$ is weight of each link, and $D$ is degree of node $i$.

The proposed R0-adjusted centrality incorporates $R0$ value of a node to the existing network centrality measure to quantify a node’s importance in two aspects, network topology and amplifying/attenuating the intensity of disease spreading.

For this epidemic degree based centrality measures, these additional considerations have a relatively clear interpretation. Including edge weights reflects the volume of population exchange between cities, and thus seems a more accurate representation for disease transmission on an air travel network. It can be further refined by estimating the volume of infective population exchange along the edges. This is done by using $R0$ of each city as a proxy for the fraction of infective population during the disease spreading.