Education

Doctor of Philosophy in Applied Mathematics

Adelaide University · 2022–2026

I completed my PhD in Applied Mathematics at Adelaide University in 2026 under the incredible supervision of Dr Andrew Black (principal supervisor) and Dr Lauren Kennedy.

My PhD looked at modelling what happens once a virus enters a host and how this translates to outbreak dynamics. Within-host models seek to explain the dynamics of dynamics of viral infections inside an individual (tracking cells and virions, and their interactions), while between-host models describe transmission between individuals. Compared with between-host modelling, both our understanding of within-host dynamics and the computational tools available for analysing them are less developed. This is in part due to the massive number of cells involved as stochastic simulations at this scale are computationally expensive, so simpler deterministic approximations are typically used instead. These tend to be piecewise linear models that obscure much of the underlying biology.

The first paper from my PhD addresses the challenge of using stochastic within-host models by developing methods that exploit the natural structure of these models, incorporating stochasticity into a large population model without requiring full stochastic simulations. This improves computational efficiency while preserving the biological realism of within-host dynamics through a system of ODEs. The second and third papers from my PhD leverage this framework to develop inference frameworks for estimating model parameters from observed data in stochastic within-host and multi-scale models. The second paper builds an efficient approximation to the likelihood for stochastic within-host models, enabling a method that captures key macroscopic stochastic dynamics accurately and allows for computationally feasible parameter estimation. In the final paper, we extend this framework to multi-scale models, utilising a cut-inference framework, to use stochastic within-host dynamics to inform between-host transmission dynamics in household settings. The resulting method is embedded within household settings as they provide the natural context for collecting detailed individual level data (symptoms, viral load measurements, etc.), which is crucial for accurately linking within-host dynamics to between-host transmission.

The papers that arose from, and collectively form, my PhD are:

1. Dylan J. Morris, Lauren Kennedy, Andrew J. Black, 2025. Bayesian inference for disease transmission models informed by viral dynamics. arXiv: arXiv:2604.20069v1.
2. Dylan J. Morris, Lauren Kennedy, Andrew J. Black, 2025. Random time-shift approximation enables hierarchical Bayesian inference of mechanistic within-host viral dynamics models on large datasets. PLoS Computational Biology 20(12): e1013775. 10.1371/journal.pcbi.1013775.
3. Dylan Morris, John Maclean and Andrew J. Black, 2024. Computation of random time-shift distributions for stochastic population models. Journal of Mathematical Biology, 89, 33, 10.1007/s00285-024-02132-6.

Master of Philosophy in Applied Mathematics

The University of Adelaide · 2019–2021

I completed my M.Phil in 2021 with my thesis:

• Dylan J. Morris. Inference on historical Ebola outbreaks using hierarchical models: a particle filtering approach (2021). MPhil Thesis. hdl.handle.net/2440/132642

This work looked at how we can model outbreaks of Ebola efficiently by using importance sampling in particle filters. This methodology allows realisations of a continuous-time Markov chain to be simulated that are consistent with two time-series of (partial) observations of the outbreak. Ebola served as a great case study since it is a disease where it’s relatively easy to link when someone becomes infectious and subsequently dies (or recovers).

Bachelor of Mathematical Sciences

The University of Adelaide · 2016–2018

Majors:

• Applied Mathematics
• Statistics