Outputs (55)

Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response (2024)
Journal Article
Franks, S. J., Dunster, J. L., Carding, S. R., Lord, J. M., Hewison, M., Calder, P. C., & King, J. R. (2024). Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response. Mathematical Medicine and Biology, 41(4), 304-345. https://doi.org/10.1093/imammb/dqae017

The intestinal microbiota play a critical role in human health and disease, maintaining metabolic and immune/inflammatory health, synthesizing essential vitamins and amino acids and maintaining intestinal barrier integrity. The aim of this paper is t... Read More about Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response.

Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation (2024)
Journal Article
Fasondini, M., King, J. R., & Weideman, J. A. (2024). Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation. Nonlinearity, 37(10), Article 105005. https://doi.org/10.1088/1361-6544/ad700b

Blow-up solutions to a heat equation with spatial periodicity and a quadratic nonlinearity are studied through asymptotic analyses and a variety of numerical methods. The focus is on tracking the dynamics of the singularities in the complexified spac... Read More about Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation.

Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain (2024)
Journal Article
Franks, S. J., Gowler, P. R., Dunster, J. L., Turnbull, J., Gohir, S. A., Kelly, A., Valdes, A. M., King, J. R., Barrett, D. A., Chapman, V., & Preston, S. (2024). Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain. Mathematical Biosciences, 374, Article 109228. https://doi.org/10.1016/j.mbs.2024.109228

Chronic pain is a major cause of disability and suffering in osteoarthritis (OA) patients. Endogenous specialised pro-resolving molecules (SPMs) curtail pro-inflammatory responses. One of the SPM intermediate oxylipins, 17-hydroxydocasahexaenoic acid... Read More about Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain.

Mathematical models of coagulation—are we there yet? (2024)
Journal Article
Owen, M. J., Wright, J. R., Tuddenham, E. G., King, J. R., Goodall, A. H., & Dunster, J. L. (2024). Mathematical models of coagulation—are we there yet?. Journal of Thrombosis and Haemostasis, 22(6), 1689-1703. https://doi.org/10.1016/j.jtha.2024.03.009

Background
Mathematical models of coagulation have been developed to mirror thrombin generation in plasma, with the aim of investigating how variation in coagulation factor levels regulates hemostasis. However, current models vary in the reactions t... Read More about Mathematical models of coagulation—are we there yet?.

Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport (2023)
Journal Article
Bellows, S., Janes, G., Avitabile, D., King, J. R., Bishopp, A., & Farcot, E. (2023). Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport. PLoS Computational Biology, 19(11), Article e1011646. https://doi.org/10.1371/journal.pcbi.1011646

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling... Read More about Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.

Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties (2023)
Journal Article
King, J. R., Richardson, G. W., & Foster, J. M. (2023). Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties. European Journal of Applied Mathematics, 34(5), 1099-1132. https://doi.org/10.1017/S0956792523000098

The dynamics of interfaces in slow diffusion equations with strong absorption are studied. Asymptotic methods are used to give descriptions of the behaviour local to a comprehensive range of possible singular events that can occur in any evolution. T... Read More about Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties.

Burgers’ equation in the complex plane (2023)
Journal Article
VandenHeuvel, D. J., Lustri, C. J., King, J. R., Turner, I. W., & McCue, S. W. (2023). Burgers’ equation in the complex plane. Physica D: Nonlinear Phenomena, 448, Article 133686. https://doi.org/10.1016/j.physd.2023.133686

Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers' equation in the... Read More about Burgers’ equation in the complex plane.

Blow up in a periodic semilinear heat equation (2023)
Journal Article
Fasondini, M., King, J., & Weideman, J. (2023). Blow up in a periodic semilinear heat equation. Physica D: Nonlinear Phenomena, 446, Article 133660. https://doi.org/10.1016/j.physd.2023.133660

Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition. Novel res... Read More about Blow up in a periodic semilinear heat equation.

Cauchy-Dirichlet problems for the porous medium equation (2022)
Journal Article
Bowen, M., King, J. R., & Witelski, T. P. (2023). Cauchy-Dirichlet problems for the porous medium equation. Discrete and Continuous Dynamical Systems - Series A, 43(3&4), 1143-1174. https://doi.org/10.3934/dcds.2022182

We consider the porous medium equation subject to zero-Dirichlet conditions on a variety of two-dimensional domains, namely strips, slender domains and sectors, allowing us to capture a number of different classes of behaviours. Our focus is on inter... Read More about Cauchy-Dirichlet problems for the porous medium equation.

Metabolic modeling-based drug repurposing in Glioblastoma (2022)
Journal Article
Tomi-Andrino, C., Pandele, A., Winzer, K., King, J., Rahman, R., & Kim, D.-H. (2022). Metabolic modeling-based drug repurposing in Glioblastoma. Scientific Reports, 12, Article 11189. https://doi.org/10.1038/s41598-022-14721-w

The manifestation of intra- and inter-tumor heterogeneity hinders the development of ubiquitous cancer treatments, thus requiring a tailored therapy for each cancer type. Specifically, the reprogramming of cellular metabolism has been identified as a... Read More about Metabolic modeling-based drug repurposing in Glioblastoma.