CBBS Subgroup Contributed Talks

Anushaya Mohapatra

BITS, Pilani, Goa Campus, India

"The ideal free distribution and the evolution of partial migration"

In this talk, we will discuss how the ideal free distribution (IFD) arises in the context of a partially migrating population using a stage-structured matrix model. Partial migration is a unique form of phenotypic diversity wherein migrant and non-migrant individuals coexist together. We show that the ideal free distribution is evolutionary stable in a global sense, assuming that both migrants and non-migrants experience density dependent competition with each other during reproduction. We also establish that the partially migrating species satisfies a dichotomy: Either both morphs have the same fitness, a scenario that corresponds to an IFD. Or, one morph has a higher fitness than the other. Evolutionary process however, will drive the population to the IFD.

Debasmita Mukherjee

Sunandan Divatia School of Science, SVKM's NMIMS Deemed to be University, Mumbai, India

"Atherosclerosis: A Mathematical Model for Early Prognosis"

Atherosclerosis, an arterial disease that causes malfunction of the cardiovascular system, occurs due to the accumulation of plaque in the intima, the innermost layer of artery. A suitable mathematical model is presented here in terms of a nonlinear autonomous system of ten Ordinary differential equations that incorporate various cellular components such as low-density lipoproteins (LDL) high-density lipoproteins (HDL), free radicals, oxidized LDL, chemoattractant, monocytes, macrophages, T-cells, smooth muscle cells (SMCs) and necrotic core (or plaque cells) as dependent variables. The present model is found to be globally stable theoretically and numerically under certain conditions. Since the model system is large in size, the concept of global stability can be physically visualized through appropriate projections of specific subsystems into three- and two-dimensional subspaces. Since the present model is globally stable, it can resist to some extent any wider arbitrary range of assumed parameter values not found in the literature. The aim of the model under study is to provide a computational framework that allows searching for important parameters that are likely to aid in clinical investigations of this malignant disease.

Michael Getz

Indiana University, Bloomington

"Continuum to Discrete event modeling within PhysiCell"

Agent based modeling frameworks such as PhysiCell contain many discrete and continuum components such as the cells and tissue microenvironment. These components events require use of uncoupled solvers to evaluate the problem across simulation time. At the interface between solvers special cases must be defined as low concentrations can become a source of error where fractions of objects are consumed by many discrete cells- similarly when a discrete (Cell) object is translated to a continuum framework (ODE) attention must be also payed to reduce error in the event. Better reduction of error allows for larger simulations for a cheaper cost, such as if an epithelium model (spatially simulated) is coupled to the lymph node (ODE). Examples with an infection model of COVID are shown including lymph node recruitment of immune cells.

Raneem Aizouk

City, university of London

"Modelling conflicting individual preferences: target sequence and graph realization"

we will consider a group of individuals, who each have a target number of contacts they would like to have with other group members. We are interested in how close this can some to being realized, and consider the long term outcome for the group under a reasonable dynamics on the number of contacts. The individuals will be represented as vertices, and the number of contacts as the vertex degree. It is well known that not all degree sequences can be realized as undirected graphs and the Havel-Hakimi algorithm characterizes those that can. Our main concern is to reach graphs that minimize the total deviation between what is desired and what is possible. The set of all such graphs and the set of all such associated sequences are termed the minimal sets. This problem has previously been considered by Broom and Cannings, and it is a hard problem to tackle for general target sequences. We consider the n-element arithmetic sequence for general n, including obtaining a formula which generates the size of the minimal set for a given arithmetic sequence. We also consider a strategic version of the model where the individuals are involved in a multiplayer game.