Past Seminars

Applying Mathematics to Problems in Virus Transmission and Evolution

Dr Chris Illingworth (University of Glasgow)

Thursday 2nd November 2023  14:00-15:00

Abstract

The evolution of viruses has an extensive influence upon human health, shaping patterns of infection and driving novel pandemics.  Genome sequence data provides a window into the evolution of viruses.  However, methods for analysing sequence data have not always been developed in a way that maximises the insights that can be obtained from data.  Here we describe how relatively simple mathematical concepts can be applied to better understand data from evolutionary experiments and from viral outbreaks, for the benefit of public health.

We describe the use of likelihood methods to understand evolutionary patterns shaping the evolution of potential pandemic viruses, the development of methods to facilitate the real-time analysis of genomic data as part of hospital infection prevention and control, and finally a case where mathematical modelling could provide insights more general than those obtainable from genome sequence data.

 

The effect of Rumor and Hoax in Disease Transmission: A Mathematical Perspective

Asep K. Supriatna (Padjadjaran,University, Indonesia)

Wednesday 6th September 2023 13:00-14:00

Abstract

In this paper, we present a review of mathematical models for the transmission of rumor and hoax. We then explore the effect of disinformation such as rumor and hoax and their effect on the spread of disease infection. This phenomenon is not uncommon to occur, such as in the case of the COVID-19 pandemic. There is so much misinformation or even disinformation regarding the nature of the disease and how people should behave toward the disease. In many countries, this led to mismanagement of the disease, in particular, many people exhibited poor behavior or poor disease awareness in responding to the disease. We explore the effect of rumor and hoax in a mathematical model of disease transmission in the form of differential. By modifying the known SIR model, we divide the population into different categories depending on their health status, such as susceptibles, infected, and immune individuals. Furthermore, we also divide the susceptibles into different categories according to the knowledge of the rumor and hoax. We give a numerical example to show the effect of rumors or hoaxes in the disease dynamics.

 

MODELING ANTHRAX-RABIES INTERACTIONS IN THE AFRICAN SAVANNA

Christopher Kribs (The University of Texas at Arlington, USA)

Wednesday 1st June 2023 13:00-14:00 Room LT907 University of Strathclyde

Abstract

Ungulates like zebras suffer from outbreaks of anthrax, disrupting the food supply of scavengers like jackals.  Rabies outbreaks among jackals depends on zebra carcass density in a complex way, as they spread rabies only when feeding.  Following work by Borchering et al. in modeling the jackals' contact rate using data from Etosha National Park in Namibia, we develop and analyse a dynamical systems model to show how the transmission dynamics of each disease affect those of the other, revealing the potential for sustained oscillations in addition to traditional threshold behavior.

Modelling and Validating Device-Induced Thrombosis and Thromboembolization

Prof Keefe Manning (The Pennsylvania State University, USA)

Tuesday 13th December 2022 15:00-16:00

Abstract

Thrombosis remains a significant clinical issue manifesting in heart attacks and strokes. However, the challenges extend to the success of cardiovascular devices. Given the complex process associated with thrombosis, developing an accurate computational model is challenging particularly validating the model that encompasses a range of flow and surface interactions and occurs at different temporal and spatial scales. Leveraging canonical experiments that acquire a breadth of data will be crucial to validate the computational model. Furthermore, there are different mathematical approaches that may be used to model thrombosis with some ideally suited for predicting embolization. This presentation will cover the development and experimental validation of the model and ongoing methods that add more complexity and accuracy to the model. Ultimately, the goal of the model is to be sensitive to different material surfaces and respond to low and high shear environments to predict thrombus formation and potential embolization.

Mathematical approaches for studying form and function of vascular tumours

Prof Helen Byrne (University of Oxford)

Thursday 17th March 14:00-15:00 ZOOM (ID: 924 6361 4209)

Abstract

Over the past twenty-five years we have witnessed an unparalleled increase in understanding of cancer. This transformation is exemplified by Hanahan and Weinberg's decision in 2011 to expand their original Hallmarks of Cancer from six traits to ten and, very recently, to fourteen! At the same time, mathematical modelling has emerged as a natural tool for unravelling the complex processes that contribute to the initiation and progression of tumours, for testinghypotheses about experimental and clinical observations, and assisting with the development of new approaches for improving its treatment. 

Following Hanahan and Weinberg's lead, in this talk I will reflect on how increased access to experimental data is stimulating the application of new theoretical approaches for studying tumour growth. I will focus on three case studies which illustrate how mathematical approaches can be used to characterise and quantify tumour vascular networks, to understand how microstructural features of these networks affect tumour blood flow, and to study the impact of unsteady blood flow on tumour growth. 

Asymptotic modeling of nonlinear imperfect solid/solid interfaces

Frederic Lebon (Aix Marseille Universite, France)

Thursday 3rd February 2022 14:00-15:00 

Abstract

Our work focuses on the theoretical and numerical modelling of interfaces between solid structures (contact, friction, adhesion, bonding, etc.). We will present a general methodology based on matched asymptotic theory to obtain families of models including the relative rigidity of the interphase (soft or hard), geometrical or material non-linearities, damage and multiphysics couplings.  Numerical results will be presented.

MODELS FOR CELL MIGRATION ASSAYS, INCLUDING PDES WITH NONLINEAR DIFFUSION

Scott McCue (QUT, Brisbane, Australia)

Monday 6th December 2021 11:00-12:00 

Abstract

Experimentalists who study cancer invasion and wound repair often employ simple assays such as the in vitro scratch assay to quantify the combined effects of cell proliferation and cell migration on the collective motion of cells in two dimensions.  In turn, these experiments prove to be fruitful for researchers in mathematical biology to test and explore mathematical models for collective cell motion.  I will discuss some of these ideas from the perspective of an applied mathematician, making reference to PDE models such as the Fisher-KPP equation as well as discrete processes based on random walk models.  Then I will spend some time on a hole-closing model for a two-dimensional wound assay that is based on a PDE with nonlinear degenerate diffusion.  The mathematics here is interesting as it involves similarity solutions of the second kind.  Finally, I will touch on slightly more complicated PDE models with nonlinear diffusion that can be used to study problems in similar geometries, such as thin tissue growth in printed bioscaffolds.

MODELING THE SKELETAL MUSCLE TISSUE AS AN ANISOTROPIC ACTIVE MATERIAL

Alessandro Musesti (Università Cattolica del Sacro Cuore, Italy)

Thursday 22nd July 2021 14:00-15:20 

Abstract

Abstract: Skeletal muscle tissue is a paradigmatic example of an active
material, for which deformations can occur in absence of loads, given an
external stimulus. After reviewing its main properties, in the talk I
will compare the two main methods used to model such materials, namely
active stress and active strain. In a hyperelastic setting, it will be
shown that a simple shear produces different stresses in the two
approaches; hence, active stress and active strain produce contrasting
results in shear, even if they both fit uniaxial data. Our results show
that experimental data on the stress-stretch response on uniaxial
deformations are not enough to establish which activation approach
better capture the activation mechanics. A further study of other
deformations, such as simple shears, would be important in order to
develop a realistic model of an active material.