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Understanding the regulation of chronic wounds by tissue inhibitors of matrix metalloproteinases through mathematical modelling (2025)
Journal Article
Dari, S., O'Dea, R. D., & Fadai, N. T. (2025). Understanding the regulation of chronic wounds by tissue inhibitors of matrix metalloproteinases through mathematical modelling. Journal of Theoretical Biology, Article 112083. https://doi.org/10.1016/j.jtbi.2025.112083

Understanding the biochemistry and pharmacodynamics of chronic wounds is of key importance, due to the millions of people in the UK affected and the significant cost to the NHS. Chronic wounds are characterised by elevated concentrations of matrix me... Read More about Understanding the regulation of chronic wounds by tissue inhibitors of matrix metalloproteinases through mathematical modelling.

Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model (2022)
Journal Article
Fadai, N. T., & Billingham, J. (2022). Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model. Journal of Physics A: Mathematical and Theoretical, 55(40), Article 405701. https://doi.org/10.1088/1751-8121/ac8ef5

We examine travelling wave solutions of the partial differential equation u_t = u_xx + u(1 − u * φ) on a moving domain x ≤ L(t), where u * φ is the spatial convolution of the population density with a kernel φ(y). We provide asymptotic approximations... Read More about Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model.

Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects (2022)
Journal Article
Fadai, N. T. (2023). Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects. Applied Mathematics Letters, 135, Article 108433. https://doi.org/10.1016/j.aml.2022.108433

We provide new exact forms of smooth and sharp-fronted travelling wave solutions of the reaction–diffusion equation, ∂tu=R(u)+∂xD(u)∂xu, where the reaction term, R(u), employs a Weak Allee effect. The resulting ordinary differential equation system i... Read More about Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects.

Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth (2022)
Journal Article
Jepson, J. M., Fadai, N. T., & O’Dea, R. D. (2022). Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth. Bulletin of Mathematical Biology, 84(8), Article 87. https://doi.org/10.1007/s11538-022-01044-0

We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy’s law to relate the velocity... Read More about Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth.

Inhaled budesonide in the treatment of early COVID-19 (STOIC): a phase 2, open-label, randomised controlled trial (2021)
Journal Article
Ramakrishnan, S., Nicolau, D. V., Langford, B., Mahdi, M., Jeffers, H., Mwasuku, C., Krassowska, K., Fox, R., Binnian, I., Glover, V., Bright, S., Butler, C., Cane, J. L., Halner, A., Matthews, P. C., Donnelly, L. E., Simpson, J. L., Baker, J. R., Fadai, N. T., Peterson, S., …Bafadhel, M. (2021). Inhaled budesonide in the treatment of early COVID-19 (STOIC): a phase 2, open-label, randomised controlled trial. Lancet Respiratory Medicine, 9(7), 763-772. https://doi.org/10.1016/s2213-2600%2821%2900160-0

Infection, inflammation and intervention: mechanistic modelling of epithelial cells in COVID-19 (2021)
Journal Article
Fadai, N. T., Sachak-Patwa, R., Byrne, H. M., Maini, P. K., Bafadhel, M., & Nicolau, D. V. (2021). Infection, inflammation and intervention: mechanistic modelling of epithelial cells in COVID-19. Journal of the Royal Society, Interface, 18(175), Article 20200950. https://doi.org/10.1098/rsif.2020.0950

While the pathological mechanisms in COVID-19 illness are still poorly understood, it is increasingly clear that high levels of pro-inflammatory mediators play a major role in clinical deterioration in patients with severe disease. Current evidence p... Read More about Infection, inflammation and intervention: mechanistic modelling of epithelial cells in COVID-19.

Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics (2020)
Journal Article
Fadai, N. T., Johnston, S. T., & Simpson, M. J. (2020). Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2241), Article 20200350. https://doi.org/10.1098/rspa.2020.0350

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally propose... Read More about Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics.

Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects (2020)
Journal Article
Fadai, N. T., & Simpson, M. J. (2020). Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects. Bulletin of Mathematical Biology, 82(6), Article 74. https://doi.org/10.1007/s11538-020-00756-5

The Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in que... Read More about Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects.

New travelling wave solutions of the Porous–Fisher model with a moving boundary (2020)
Journal Article
Fadai, N. T., & Simpson, M. J. (2020). New travelling wave solutions of the Porous–Fisher model with a moving boundary. Journal of Physics A: Mathematical and Theoretical, 53(9), Article 095601. https://doi.org/10.1088/1751-8121/ab6d3c

We examine travelling wave solutions of the Porous-Fisher model, ϑtu(x,t) = u(x,t)[1 u(x,t)] + ϑx [u(x,t)ϑxu(x,t)], with a Stefan-like condition at the moving front, x = L(t). Travelling wave solutions of this model have several novel characteristics... Read More about New travelling wave solutions of the Porous–Fisher model with a moving boundary.

A Homogenization Approach for the Roasting of an Array of Coffee Beans (2019)
Journal Article
Sachak-Patwa, R., Fadai, N. T., & Van Gorder, R. A. (2019). A Homogenization Approach for the Roasting of an Array of Coffee Beans. SIAM Journal on Applied Mathematics, 79(4), 1550-1580. https://doi.org/10.1137/18m1221904

While the processes underlying the roasting of a single coffee bean have been the focus of a number of recent studies, the more industrially relevant problem of roasting an array of coffee beans has not been well studied from a modeling standpoint. S... Read More about A Homogenization Approach for the Roasting of an Array of Coffee Beans.

Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays (2018)
Journal Article
Eide, R. M., Krause, A. L., Fadai, N. T., & Van Gorder, R. A. (2018). Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays. Journal of Theoretical Biology, 451, 19-34. https://doi.org/10.1016/j.jtbi.2018.04.038

We examine the role of the travel time of a predator along a spatial network on predator-prey population interactions, where the predator is able to partially or fully sustain itself on a resource subsidy. The impact of access to food resources on th... Read More about Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays.

Delayed Reaction Kinetics and the Stability of Spikes in the Gierer--Meinhardt Model (2017)
Journal Article
Fadai, N. T., Ward, M. J., & Wei, J. (2017). Delayed Reaction Kinetics and the Stability of Spikes in the Gierer--Meinhardt Model. SIAM Journal on Applied Mathematics, 77(2), 664-696. https://doi.org/10.1137/16m1063460

A linear stability analysis of localized spike solutions to the singularly perturbed two-component Gierer--Meinhardt (GM) reaction-diffusion (RD) system with a fixed time delay $T$ in the nonlinear reaction kinetics is performed. Our analysis of this... Read More about Delayed Reaction Kinetics and the Stability of Spikes in the Gierer--Meinhardt Model.