Network Firewall Dynamics and the Subsaturation Stabilization of HIV

Listing 5

Procedure AddEdge.

 Input: individual 𝑣.

(1) //Determine candidate new neighbors for v.

(2) 𝐶^𝑡(𝑣)∶=𝑉^𝑡⧵𝑁^𝑡(𝑣)∪{𝑣}.

(3) if  𝐶^𝑡(𝑣)>0  then

(4)   foreach  𝑐 in 𝐶^𝑡(𝑣)  do

(5)   Compute the bias due to degree constraints:

         𝑎_𝛿𝑒(𝑐)∶=^{−1/(𝑑(𝑐)−|𝑁(𝑐)|)}|𝑁(𝑐)|<𝑑(𝑐)0otherwise.(7)

(6)   Compute the bias due to the bivariate degree distribution:

         𝑎^𝑡_𝜒(𝑣,𝑐)∶=𝜒𝑁^𝑡(𝑣)−𝜀,𝑁^𝑡(𝑣)+𝜀,𝑁^𝑡(𝑐)−𝜀,𝑁^𝑡(𝑐)+𝜀.(8)

(7)    Compute the bias due to bivariate attribute distributions:

         𝑎^𝑡_𝛽(𝑐)∶=∏^𝑚_𝑖=1𝛽_𝑖𝑥_𝑖(𝑣),𝑥_𝑖(𝑐).(9)

(8)   Compute propensity of edge (𝑣,𝑐) as the product of the above three biases:

         𝜔^𝑡(𝑐)∶=𝑎_𝛿(𝑐)⋅𝑎^𝑡_𝜒(𝑐)⋅𝑎^𝑡_𝛽(𝑐).(10)

(9)   Normalize propensity to obtain a distribution over 𝐶^𝑡(𝑣):

         𝑞^𝑡(𝑐)𝜔∶=^𝑡(𝑐)∑_{𝑐′∈𝐶𝑡(𝑣)}𝜔^𝑡𝑐^′.(11)

(10) 𝑤∶= choose from 𝐶^𝑡(𝑣) randomly according to distribution 𝑞^𝑡.

(11)  //Add the edge connecting 𝑣 to 𝑤.

(12)   𝑁^𝑡(𝑣)∶=𝑁^𝑡(𝑣)∪{(𝑣,𝑤)}