Speakers
Mingxin Wang （Harbin Institute of Technology, China）
Mainul Haque （University of Nottingham Ningbo China）
Yongmei Cai （University of Nottingham Ningbo China）
Philip Maini （University of Oxford, UK）
Program (Beijing time)
Date: 16th September 2021.
Time: 3 PM-4 PM
Venue: PB-311 or
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Speaker: Dr. Mingxin Wang, Professor in Applied Mathematics, School of Mathematics, Harbin Institute of Technology, PRC.
Title: Applications of partial differential equations (PDEs) in Turing stationary patterns.
Abstract: In 1952 Alan Turing showed that in a reaction-diffusion system of two or more components, the presence of diffusion can destabilize a uniform state, and produce nonhomogeneous steady state distributions known as patterns. In this talk, we introduce the methods dealing with Turing stationary patterns with specific examples of partial differential equations (PDEs). The main contents include calculations of indexes, the a priori estimation and determination of polynomial roots.
Time: 4 PM-5 PM
Venue: PB-311 or
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Speaker: Dr. Mainul Haque, Associate Professor in Applied Mathematics, School of Mathematical Science, University of Nottingham Ningbo China, PRC.
Title: Existence of complex patterns in a modified Beddington–DeAngelis partial differential equations (PDEs) model.
Abstract: The study of reaction–diffusion PDEs (partial differential equations) system constitutes some of the most fascinating developments of late twentieth century mathematics and biology. We investigate complexity and chaos in the complex patterns dynamics of the original Beddington-DeAngelis predator–prey model under the influence of intra species competition among predators. We investigate the emergence of complex patterns through reaction–diffusion equations in this system. We derive the conditions for the codimension-2 Turing-Hopf, Turing-Saddle-node, and Turing-Transcritical bifurcation, and the codimension-3 Turing-Takens-Bogdanov bifurcation. These bifurcations give rise to very complex patterns that have not been observed in previous predator-prey models; however similar patterns are observed in real ecological scenarios such as in the Kielder Forest (Kielder Forest is a large forestry plantation in Northumberland, UK) for field voles. A large variety of different types of long-term behavior, including homogenous distributions and stationary spatial patterns are observed through extensive numerical simulations (using Finite Element Method) with experimentally-based parameter values. Finally, a discussion which includes the ecological implications of the analytical and numerical results is provided.
Date: 17th September 2021.
Time: 3 PM-4 PM
Venue: PB-311 or
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Speaker: Dr. Yongmei Cai, Assistant Professor in Applied Mathematics/Statistics, School of Mathematical Science, University of Nottingham Ningbo China, PRC.
Title: Positivity and Boundedness Preserving Numerical Scheme for the Stochastic Epidemic Model with Square-root Diffusion Term
Abstract: This talk concerns with the numerical solution to the stochastic susceptible-infected-susceptible epidemic model with square-root diffusion coefficient. The typical features of the model including the positivity and boundedness of the solution and the presence of the square-root diffusion term make this an interesting and challenging work. By modifying the truncated Euler-Maruyama (EM) scheme, we generate a positivity and boundedness preserving numerical scheme, which is proved to have a strong convergence to the true solution over finite time intervals. We also demonstrate that this method is applicable to a bunch of popular SDE models, e.g. the mean-reverting square-root process, an important financial model, and the stochastic SIR epidemic model.
Time: 4 PM-5 PM
Venue: PB-311 or
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Speaker: Dr. Philip Maini, Professor in Mathematical Biology, Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK.
Title: Using partial differential equations (PDEs) to model collective cell behaviour in cancer.
Abstract: Collective cell behaviour is a common occurrence in many areas in biology and medicine. Here, I will review recent work we have carried out in two areas of collective behaviour in solid tumours: (i) We revisit the classical "snail-trail" model for tumour angiogenesis and find that deriving a PDE description of this process from first principles using coarse-graining leads to a different set of equations to those classically used. We analyse this new model and compare and contrast its behaviour with the classical model. (ii) We develop a new model for cancer cell invasion which hypotheses that cell-cell co-operation is crucial for collective migration.