Grant Lythe, mathematical immunology, mathematical modelling

Stochastic modelling and mathematical immunology

PhD studentships:
Mathematical Immunology and Quantitative Immunotherapy, MedImmune Develop novel computer models describing the dynamics of immune cells, especially T-cells, their interactions with tumour cells and the influence of pharmacotherapies targeting tumour-immune cell interactions. Participate in QuanTII activities, including attending network-wide training events, group meetings, seminars, workshops and training courses, and taking part in collaborations, research visits and secondments.
Within-host mathematical models of Yersinia pestis infection
A within-host, mechanistic, stochastic model of the infection process of Yersinia pestis within humans will be developed. This module will predict the probability of infection and the time to symptoms for an individual exposed to a given dose of Yersinia pestis. Published data from animal models (primarily primate) will be leveraged, together with available human clinical case data. A within-host mechanistic model of the effect of a range of treatments (e.g., different varieties of antibiotic) will be developed, allowing different dosing strategies to be tested.
Models of adaptive immune responses following exposure to Ebola virus
This project is based on the hypothesis that a specific adaptive immune response in lethal Ebola Virus (EBOV) infection can be protective upon transfer to naive EBOV infected recipients. That is, that the timing and characteristics of the specific adaptive immune response initiated in an EBOV infected individual are predictors of survival or death. The aim of the project, in collaboration with Public Health England (PHE), is to develop mathematical models of adaptive immune responses following exposure to Ebola virus disease. The mathematical models, together with clinical data, provided by Professor Miles Carroll (PHE), of innate and adaptive immune responses to EBOV, as well as with Bayesian methods, will allow us to characterise and quantify the temporal dynamics of host adaptive cells during an infection, and in doing so, identify the differences in host adaptive immune responses that lead to survival or death.

First passage events in biological systems with non-exponential inter-event times Mario Castro, Martín López-García, Grant Lythe and Carmen Molina-Parí
Scientific Reports 8 15054 (2018)
Some deterministic and stochastic models of naive T-cell homeostasis
Grant Lythe and Carmen Molina-París
Immunological reviews 285 (2018)
The T Cells in an Ageing Virtual Mouse
Mario Castro, Grant Lythe and Carmen Molina-París
Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology pp 127-14 (2017)
A new mechanism shapes the naive CD8+ T cell repertoire Pedro Goncalves, Marco Ferrarini, Carmen Molina-París, Grant Lythe, Florence Vasseur, Annik Lim, Bendita Rocha and Orly Azogui
Molecular Immunology 85 66 (2017)
Sampling from T cell receptor repertoires Marco Ferrarini, Carmen Molina-París and Grant Lythe.
Contributions in Mathematical and Computational Sciences
Continuous Effector CD8+ T Cell Production in a Controlled Persistent Infection Is Sustained by a Proliferative Intermediate Population H. Hamlet Chu, Shiao-Wei Chan, John Paul Gosling, Nicolas Blanchard, Alexandra Tsitsiklis, Grant Lythe, Nilabh Shastri, Carmen Molina-París, Ellen A. Robey
How many TCR clonotypes does a body maintain? Grant Lythe, Robin E. Callard, Rollo L. Hoare and Carmen Molina-París
Journal of Theoretical Biology
Mathematics in modern immunology Mario Castro, Grant Lythe, Carmen Molina-París and Ruy M. Ribeiro. Interface focus
Modelling early events in Francisella tularensis pathogenesis Grant Lythe, Joseph Gillard, Thomas Laws and Carmen Molina-París
Frontiers in Cellular and Infection Microbiology
Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations Kevin Burrage and Grant Lythe
Stochastic Partial Differential Equations: Analysis and Computations
A mathematical perspective on CD4+ T cell quorum-sensing Joseph Reynolds, InĂªs F. Amado, Antonio A. Freitas, Grant Lythe and Carmen Molina-París
Journal of Theoretical Biology
Mathematical model of naive T cell division and survival IL-7 thresholds Joseph Reynolds, Mark Coles, Grant Lythe and Carmen Molina-París
Frontiers in Immunology
A stochastic T cell response criterion James Currie, Mario Castro, Grant Lythe, Ed Palmer and Carmen Molina-París
Royal Society Interface
T-cell movement on the reticular network Graham Donovan and Grant Lythe

Accurate Stationary Densities with Partitioned Numerical Methods for Stochastic Differential Equations Kevin Burrage and Grant Lythe
Numerical experiments on noisy chains: from collective transitions to nucleation-diffusion Mario Castro and Grant Lythe
Kink Stochastics Grant Lythe and Salman Habib
Diffusion-limited reaction in one dimension Grant Lythe