· Spring 2023: Online Math 2318
· Fall 2022: Online Math 4364 and 5344
· Spring 2022: Online Math 4364 and 5344
· Fall 2021: Online Math 2318 (formerly 2331).
· Spring 2021: Online Math 5386.
· Fall 2020: Online Math 4335 and 5397.
Projects and Positions:
Research Interests: Reaction-Diffusion Systems and Mathematical Biology. Google Scholar list of publications. Selected Work since 2016:
· Global existence for reaction-diffusion systems on multiple domains, with William E. Fitzgibbon and John Ryan, Axioms 2022, 11, 335. https://doi.org/10.3390/axioms11070335.
· A Diffusive SEIR Model for Community Transmission of Covid-19 Epidemics: Application to Brazil, with W.E. Fitzgibbon, Glenn F. Webb and Yixiang Wu, Mathematics in Applied Sciences and Engineering, Vol. 2 No. 4 (2021): pp. 219-309, DOI: https://doi.org/10.5206/mase/14150.
· Reaction-Diffusion-Advection Systems With Discontinuous Diffusion and Mass Control, with W.E. Fitzgibbon, Bao QuocTang and Hong-Ming Yin, SIAM Math Anal, 2021, Vol. 53, No. 6, pp. 6771-6803.
· Global Well-posedness For Volume-Surface Reaction-Diffusion Systems, with Bao Quoc Tang, Communications in Contemporary Mathematics, February 2022, https://doi.org/10.1142/S021919972250002X.
· New Insights into a Pandemic SIR Model for Control and Public Health Intervention, with Enrique Barbieri and William E. Fitzgibbon, 2021 IEEE Conference on Control Technology and Applications (CCTA), DOI: 10.1109/CCTA48906.2021.9659144. Added to IEEE Xplore: January 2022.
· Global well-posedness and nonlinear stability of a chemotaxis system modeling multiple sclerosis, with Laurent Desvillettes, Valeria Giunta and Bao Quoc Tang, Proc. A Royal Soc. Edinburgh, 152, 826–856, 2022, DOI:10.1017/prm.2021.33.
· Uniform Boundedness for Reaction-Diffusion Systems with Mass Dissipation, with B.P. Cupps and Bao Quoc Tang, SIAM J. Math. Anal., 53(1), 2021, 323–350.
· Analysis of a Reaction-Diffusion Epidemic Model with Asymptomatic Transmission, with W.E. Fitzgibbon, G.F. Webb and Y. Wu, Journal of Biological Systems, Vol. 28, No. 3 (2020), 561-587.
· Predicting the end-stage of the COVID-19 epidemic in Brazil, with W.E. Fitzgibbon, G.F. Webb and Y. Wu, medRxiv, May 28, 2020.
· Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems, with Amit Einav and Bao Quoc Tang, Accepted to SIAM Math Anal., April 2020.
· A Coupled System Modelling the Aqueous Transport of an Infectious Pathogen to Regional Communities, with W.E. Fitzgibbon, G.F. Webb and Y. Wu, Accepted to Journal of the Royal Society Interface, July 2020.
· Maritime Transport and the Threat of Bio Invasion and the Spread of Infectious Disease, with W.E. Fitzgibbon, G.F. Webb and Y. Wu, in Computation and Big Data for Transport, Digital Innovations in Surface and Air Transport Systems, Editors: P. Diez, P. Neittaanmäki, J. Periaux, T. Tuovinen, J. Pons-Prats, Springer 2020.
· Boundedness for reaction-diffusion systems with Lyapunov functions and intermediate sum conditions, with Bao Quoc Tang, Accepted to Nonlinearity, April 2020.
· Global Existence of Solutions to Volume-Surface Reaction-Diffusion Systems with Dynamic Boundary Conditions, with V. Sharma, Differential and Integral Equations, Volume 33, Number 3-4 (2020), 113-138.
· Uniform-in-time Bounds for Quadratic Reaction-Diffusion Systems with Mass Dissipation in Higher Dimensions, with Klemens Fellner and Bao Quoc Tang, Discrete and Continuous Dynamical Systems Series S, Vol 14, Number 2, February 2021, 635-651.
· Global Classical Solutions to Quadratic Systems with Mass Control in Arbitrary Dimensions, with Klemens Fellner and Bao Quoc Tang, Annales de l'Institut Henri Poincaré, Volume 37, Issue 2, March-April 2020, 281-307.
· Spatial Models of Vector-Host Epidemics with Directed Movement of Vectors Over Long Distances, with W.E. Fitzgibbon, G.F. Webb and Y. Wu, 2019, Mathematical biosciences 312, 77-87.
· Analysis of a Reaction Diffusion Model for a Reservoir Supported Spread of Infectious Disease, with W.E. Fitzgibbon, Discrete and Continuous Dynamical Systems-B, November 2019 (11), 6239-6259.
· A Vector-Host Epidemic Model with Spatial Structure and Age of Infection, with W.E. Fitzgibbon, G.F. Webb and Y. Wu, 2018, Nonlinear Analysis: Real World Applications 41, 692-705.
· An Outbreak Vector-host Epidemic Model with Spatial Structure: The 2015 Zika Outbreak in Rio de Janeiro, with W.E. Fitzgibbon and G.F. Webb, 2017, Theoretical Biology and Medical Modelling 14 (1), 7.
· Uniform Bounds for Solutions to Volume-Surface Reaction Diffusion Systems, with V. Sharma, 2017, Differential and Integral Equations 30 (5/6), 423-442.
· Finite Element Approximation of a Spatially Structured Metapopulation with PDE Model, with Marcus R. Garvie and V. Sharma, Computers & Mathematics and Applications, Vol, 74, No. 5, 2017, 934-947.
· Global Existence of Solutions to Reaction Diffusion Systems with Mass Transport Type Boundary Conditions, with V. Sharma, 2016, SIAM Journal on Mathematical Analysis 48 (6), 4202-4240.