MS02 - ECOP-1
Barbie Tootle Room (#3156) in The Ohio Union

Applications of Reaction-Diffusion Models in Biological Systems

Monday, July 17 at 04:00pm

SMB2023 SMB2023 Follow Monday during the "MS02" time block.
Room assignment: Barbie Tootle Room (#3156) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS01-ECOP-1 (click here).

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Yu Jin, Daniel Gomez, King Yeung (Adrian) Lam


The application of reaction-diffusion-advection models is prevalent throughout biological problems ranging from intracellular to ecological phenomena. The analysis of such models often leads to biological insights while simultaneously being of mathematical interest. Recently, we have seen novel applications in epidemiology, evolutionary and population dynamics, cell physiology, and conservation biology. In this mini-symposium we will gather speakers working on a variety of biological problems in which reaction-diffusion-advection models play a prominent role. Speakers will communicate the latest advances in their respective fields, and identify emerging directions for future research efforts. Moreover, by gathering speakers studying distinct biological phenomena but using similar mathematical tools, we hope to promote collaborations between researchers working on different biological problems.

Xingfu Zou

University of Western Ontario (Mathematics)
"On a predator-prey model with fear effect, predator-taxis and degeneracy in spatially heterogeneous environmen"
I will present a diffusive predator-prey model that includes fear effect, predator-taxis, spatial heterogeneity and degeneracy on some space dependent model parameters. I will report some recent results on local and global bifurcations of steady state solutions of the model system. This is a joint work with Dr. Jingjing Wang.
Additional authors: Jingjing Wang, Shaanxi University of Finance and Economics

Yu Jin

University of Nebraska-Lincoln (Mathematics)
"The influence of a protection zone on population dynamics"
Protecting native species or endangered species has been an important issue in ecology. Differential equations have been applied to incorporate protection zones in the habitat of species to investigate the influence of protection zones on long-term population dynamics. We derive a reaction-diffusion model for a population in a one-dimensional bounded habitat, where the population is subjected to a strong Allee effect in its natural domain but obeys a logistic growth in a protection zone. We establish threshold conditions for population persistence and extinction via the principal eigenvalue of an associated eigenvalue problem, and then propose strategies for designing the optimal location of the protection zone under different boundary conditions in order for the population to persist in a long run.
Additional authors: Rui Peng, College of Mathematics and Computer Science, Zhejiang Normal University, China; Jinfeng Wang, School of Mathematical Sciences and Y.Y. Tseng Functional Analysis Research Center, Harbin Normal University, China

Arwa Abdulla Baabdulla

University of Alberta (Department of Mathematical and Statistical Sciences)
"Mathematical Modelling of Reovirus in Cancer Cell Cultures"
Reovirus is a nonpathogenic virus that inhabits the enteric tract of mammals. It is a double-stranded RNA virus that showed the ability to naturally infect and lyse tumors under in vitro and in vivo conditions. Unmodified reovirus (T3wt) is currently being evaluated as an anti-cancer therapy in more than 30 clinical trials in different types of cancer such as metastatic breast cancer, prostate cancer, and colorectal cancer. Dr. Maya Shmulevitz from Li-Ka Shing Institute of Virology, University of Alberta and her PhD student Francisca Cristi focus in their laboratory to improve reovirus as a cancer therapy. In collaboration with them, we are trying to answer the following questions via mathematical modelling: How far does the virus spread depending on the binding rate? How does the viral invasion speed depend on the binding rate? How does reducing the binding rate affect the plaque size?
Additional authors: Thomas Hillen; University of Alberta

Domènec Ruiz-Balet

Imperial College London (Mathematics)
"The tragedy of the commons via traveling waves in mean-field games"
The main topic of the talk is to observe mathematically the tragedy of the commons in spatial models. Garret Hardin, in 1968, exposed in his seminal paper, several situations in which the uncoordinated action of selfish individuals can lead to the depletion of a common resource, the so-called tragedy of the commons. We will consider a population model that consists of the most basic reaction-diffusion equations and we will formulate a harvesting game. Making use of a mean-field game (MFG) formulation, we will observe how the MFG “reversed” travelling wave solutions in the sense that, in the absence of players the population would invade the whole domain but in the aforementioned Nash equilibria the population gets extinguished. We will also briefly discuss other population models in which this situation arises.

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