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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.

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.