MFBM Subgroup Contributed Talks

Yifei Li

Queensland University of Technology

"Travelling waves in nonlinear reaction-diffusion equations"

Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are isolated has been proposed, and this approach gives various RDEs where the diffusion term is convex and can become negative (Johnston et al., Sci. Rep. 7, 2017). Numerical simulations suggest these RDEs, under certain choices of the system parameters, support smooth and shock-fronted travelling waves. In this talk, I will formalise these preliminary numerical observations by analysing these two types of travelling wave solutions through a dynamical systems approach.

Juan Carlo Flores Mallari

Ateneo de Manila University, Nara Institute of Science and Technology

"Modeling Collective Behavior of Passengers Boarding and Disembarking from Public Transport in the Philippines"

In this study, we develop a self-propelled particle model of pedestrian motion based on social interaction forces for passengers boarding and disembarking from buses in the Philippines. The forces—attractive, repulsive, and frictional—are derived from positional data acquired by tracking numerous drone videos of a section of a busy highway in Metro Manila. Model validity is tested by simulating passenger trajectories and comparing these simulations with actual data. The model will be used to explore the transmission of COVID-19 through the Philippine public transportation system and to build a framework with which policy interventions and organized crowd control systems (e.g., proper queuing systems and bus stop usage, physical distancing requirements to prevent disease transmission) can be conceptualized and justified. In the future, we will be analyzing the spread of COVID-19 by introducing a variable number of infected passengers to the system and use existing transmission onset data to give particular attention to pre-symptomatic transmission. While the study focuses on bus passengers, the model can be easily modified to be applied to other modes of transportation. In addition, while the study is motivated by COVID-19, the framework to be generated will be usable for analyzing outbreaks of other infectious diseases.

Leo Diaz

University of Melbourne

"Hypergraphs as a tool for automated and reproducible modelling of biochemical systems"

It is becoming obvious that we need better modelling tools as we strive to build larger and more interpretable models of biological systems. Specifically, we cannot keep relying on bespoke, hand-coded models when we want to be able to explore model spaces comprehensively.In this talk I demonstrate that using hypergraphs results in a computationally efficient scheme to represent and generate mathematical models of biological systems. I show that chemical hypergraphs can represent biochemical reaction networks exactly, and that hypergraphs have the potential to represent dynamical systems more generally. This framework allows us to easily manipulate and compose mathematical models, even of large systems, thereby enabling us to explore model spaces automatically. I illustrate the use of chemical hypergraphs using models of gene regulation processes.This framework allows us to construct models that other approaches may be unable to -- considering feedback loops, for instance, is trivial here. Further advantages of this approach are a more accessible, less error-prone and reproducible modelling process.

Shawn Means

Massey University

"A Permutation Method to Assemble Networks"

Networks can represent entities as disparate as genes, computers, infected people, predators and prey or neurons of the brain. Details of underlying structures for given systems amenable to network representations are typically limited to numbers of connections between entities or their node-degree. These degrees may be number of sexual partners, prey species, or synaptic connections in a brain. Realising a network with a given sequence of node-degrees presents a challenge especially if multiple connections or loop-backs for nodes are forbidden — otherwise known as a simple graph. Standard methods of network assembly for sampling a graph space, or all potential realisations of some degree sequence, typically require significant post-processing of initial assemblies to remove multiple connections and loop-backs. We devised an alternative method that not only permits outright exclusion of these edges, but also can target prescribed proportions of them for networks with weighted-edges. These weights may represent multiple interactions, say, between sexual partners, prey species or synaptic connections. We present our method that successfully builds networks with order 10^7 edges on scales of minutes running on a laptop, as well as links to our implementation on the GitHub repository.