In this work we look at the shapes of pathogen phylogenetic trees derived from the the spread of an infection. The mathematical framework is the general Crump-Mode-Jager branching process. In an exploratory, simulation study we look at how memory affects the general shape of the tree. By general shape we intend measures such as the imbalance of the tree, the average ladder length, and others. Memory is introduced by defining a non-constant infectivity function which, through a non-honogeneous Poisson process, defines the spread of the infection between hosts. We found that memory, in the way we introduced it, has less effect than expected on the overall shape, but has a marked effect on the size of the tree, even if the Malthusian parameter is kept constant. With a more theoretical approach, we investigate the frequency of subshapes in supercritical branching processes. Through characteristic functions we were able to count the number of subshapes within a growing tree. We prove that the ratio between the number of such shapes and the tips converges to a limit as the tree grows. In the case of homogeneous processes, the limit of the cherries to tips ratio depends only on a simple function of the basic reproduction number of the pathogen. We used this relation to develop a new method of inference of the basic reproduction number. This method increase precision for larger sets of taxa, which are becoming more and more available after the advent of next generation DNA sequences. However, the correctness of the tree reconstructed with the methods currently available still remains dubious, thus the number of cherries may be incorrect. To by-pass the reconstruction, we develop an algorithm able to provide an estimate of the number of the cherries directly from the sequences. Its precision is similar or higher than other methods that reconstruct the tree first to provide the cherries estimate. Its high level of parallelisability enables time complexity to be linear, but it is quadratic if not parallelised. This technique combined with the inference of the basic reproduction number constitutes the first phylodynamics method without a tree. On a side project we evaluate the prevalence of tuberculosis mixed infection, which is likely to be twice as high of the detected 15%.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:712896 |
| Date | January 2016 |
| Creators | Plazzotta, Giacomo |
| Contributors | Colijn, Caroline |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/44829 |
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