Supporting Code (2015, 2016 UNLICENSED by Raazesh Sainudiin) for The Transmission Process: A Combinatorial Stochastic Process for the Evolution of Transmission Trees over Networks, UCDMS Research Report 2016/1, Raazesh Sainudiin and David Welch, July 2016
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Transmission Process
2015 Raazesh Sainudiin
This is code accompanying the technical report 'The Transmission Process' by Raazesh Sainudiin and David Welch. The code is for clarity and simplicity of implementation (it is not efficient for large scale simulations).
Three example host contact networks
SI Contact Network is the Complete Graph
Let the SICN be the complete graph. We get the distribution of transmission trees at various resolutions next.
SI Contact Network is the Path Graph
Let the SICN be the path graph. We get the distribution of transmission trees at various resolutions next.
SI Contact Network is the Star Network
Let the SICN be the star network. We get the distribution of transmission trees at various resolutions next.
Likelihood Functions & Sufficient Statistics
based on tree topology without labels or branch-lengths
Note one can include branch-lengths into the likelihood easily via the exponential rates for the continuous time Markov processes that the discrete jump chains studied here. This will be necessary to conduct statistical inference for applied epidemiological models.
Demo of the mle for a complete graph with 50 nodes and 10 sampled trees
Sufficient Statistics of the parameters specifying the distribution for Beta-splitting Transmission Tree topologies
Let's save these plots
Let's do a more exhaustive simulation next
Let's plot the sufficient stats for this longer run.
Some Deterministic Contact Networks
Bidirectional Circular Network
To Make Latex tikz-graph see http://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_latex.html.
Just checking that the trees are uniformly distributed over 2^{n-1} ORBOR trees := Only-Right-Branching-subtrees-Of-Root-node trees (for peace of mind 😃.
MLE of transmission trees from the bidirectional circular network.
Let us repeat the same computation over the relative frequency of split-pairs as opposed to the frequency over a larger number of replicate transmission trees.
Balanced Tree Network
To Make Latex tikz-graph see http://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_latex.html.
Just checking prob for left-branching d-shark transmission trees (ignoring all labels) under balanced tree network - for peace of mind 😃
The unlabelled transmission tree is unique.
Toroidal Grid Network
Let us see graph in latex.
3D Toroidal Grid
Some Random Contact Networks
Erdos-Renyi
Random Regular Network
Small World Random Network
demo of the mle - needs numerical TLC...
Preferential Attachment Random Network
Now let us initialize randomly from one of the first m nodes at the beginning of the preferential attachment algorithm
Drawing some figures