Objectives: To summarize conventional approaches and propose a new one of lymphocyte proliferation description in mathematical models. To compare the different implementations of cell proliferation to characterize pros and cons of their use in large scale QSP models. Results: Three different approaches to describe rate law of lymphocyte proliferation were considered: (1) linear proliferation, (2) saturable proliferation, (3) generation dependent proliferation (GDP). Two types of models imitating in vitro and in vivo conditions and describing lymphocyte proliferation, death and influx (for in vivo only) were constructed. Analytical expressions of model variables at steady states and their stability were studied. Concept of lymphocyte generation was introduced and rate laws GDP were derived via convolution of infinite ODE system describing dynamics of lymphocyte of different generations. It was found that conventional proliferation rate laws (1) and (2) do not allow to describe bell-shaped dependence of cell number on time which might be observed in vitro. Implementation of rate law (1) allows to observe stable steady state only if rate constant of degradation is larger than that of proliferation. Rate law (3) enables us to describe both bell-shaped dependence in vitro and stable positive steady state in vivo at any parameter values.

# Posters-03

#### Tuesday, June 15 at 11:30pm (PDT)

Wednesday, June 16 at 07:30am (BST)

Wednesday, June 16 03:30pm (KST)

# Posters-03

**IMMU**

**IMMU-1 (Session: PS03)**

**Oleg Demin**

*InSysBio*

"Comparison of different implementations of lymphocyte proliferation in QSP models of immune response"

**IMMU**

**IMMU-2 (Session: PS03)**

**Pooja Dnyane**

*PhD student*

"Network motifs in drug - drug interaction"

**IMMU**

**IMMU-3 (Session: PS03)**

**Aparna Ramachandran**

*Academy of Scientific and Innovative Research, CSIR - National Chemical Laboratory*

"Studying the Effects of Anti-Tuberculosis Drugs at Extrapulmonary Sites using a Physiology-based Pharmacokinetic Model"

**MEPI**

**MEPI-2 (Session: PS03)**

**Martin Lopez-Garcia**

*Department of Applied Mathematics, University of Leeds*

"Exact approaches for the analysis of stochastic epidemic processes on small networks"

**MEPI**

**MEPI-32 (Session: PS03)**

**Eva Stadler**

*Kirby Institute, UNSW Sydney*

"Who carries malaria parasites over the dry season?"

**MEPI**

**MEPI-33 (Session: PS03)**

**Helena Stage**

*The University of Manchester*

"Multi-Scale Superinfection Models in Evolutionary Epidemiology"

**MEPI**

**MEPI-34 (Session: PS03)**

**Augustine Okolie**

*Technical University of Munich*

"Phylogenetic Methods for Infectious Models"

**MEPI**

**MEPI-36 (Session: PS03)**

**Bhawna Malik**

*https://math.snu.edu.in/people/researchers/bhawna--malik*

"Emergence of drug-resistant through behavioural interactions: Game theoretic approach"

**MEPI**

**MEPI-37 (Session: PS03)**

**Laxmi**

*Shiv Nadar University, India*

"Game theoretic approach to quantify the impact of ITNs under individuals choice on malaria transmission"

**MEPI**

**MEPI-38 (Session: PS03)**

**Mohamed Khalil Salem**

*GSE Department (Mathematics), Faculty of Engineering, October University for modern sciences and Arts (MSA)*

"Fractional order models of HIV: A Review"

**MEPI**

**MEPI-39 (Session: PS03)**

**Dylan Dronnier**

*Ecole des Ponts*

"Targeted Vaccination Strategies for Infinite-Dimensional Compartmental Models"

**MEPI**

**MEPI-40 (Session: PS03)**

**Chaeyoung Lee**

*Korea university*

"Mathematical modeling for estimating the unidentified infected population of COVID-19"

**MEPI**

**MEPI-41 (Session: PS03)**

**Nicole Cusimano**

*Basque Center for Applied Mathematics*

"COVID-19 dynamics in the Basque Country: towards spatially dependent models"

**MEPI**

**MEPI-42 (Session: PS03)**

**Damián Knopoff**

*Basque Center for Applied Mathematics*

"A multiscale active particle model of epidemic spreading with heterogeneous interactions"

**MEPI**

**MEPI-43 (Session: PS03)**

**Rey Audie S. Escosio**

*Resilience Institute, University of the Philippines*

"Modelling COVID-19 Dynamics with Different Community Quarantine Protocols in National Capital Region, Philippines"

**MEPI**

**MEPI-44 (Session: PS03)**

**Iulia Martina Bulai**

*University of Basilicata*

"Influence of asymptomatic people on malaria transmission: a mathematical model for a low-transmission area case"

**MEPI**

**MEPI-45 (Session: PS03)**

**Hyunwoo Cho**

*Yonsei university*

"Age-structured Pulmonary TB dynamics and cost-effectiveness analysis in Korea"

**MEPI**

**MEPI-46 (Session: PS03)**

**Andrew Bate**

*University of York*

"Biosecurity coalitions in small heterogenous networks"

**NEUR**

**NEUR-3 (Session: PS03)**

**Hammed Olawale Fatoyinbo**

*Massey University, New Zealand*

"Stability of Travelling Waves in Electrically Coupled Smooth Muscle Cells"

**NEUR**

**NEUR-4 (Session: PS03)**

**Zakaria Shams Siam**

*North South University*

"Estimation of Motor Nerve Conduction Velocity Distribution: A Frequency Domain Approach"

**NEUR**

**NEUR-5 (Session: PS03)**

**Rubyat Tansnuva Hasan**

*North South University*

"Estimation of Motor Nerve Conduction Velocity Distribution: A Continuous Approach"

**NEUR**

**NEUR-6 (Session: PS03)**

**Zeinab Tajik Mansoury**

*University of Tehran*

"Dynamical Analysis of Hippocampal Circuitry under Opioid Addiction Suggests the Mechanism of the Relapse"

**NEUR**

**NEUR-7 (Session: PS03)**

**Seokjoo Chae**

*Korea Advanced Institute of Science and Technology*

"The data-based inference method reveals the network structure of the SCN"

**OTHE**

**OTHE-1 (Session: PS03)**

**Sophie Fischer**

*University of Bergen*

"A mechanistic model for endocrine profiles of female puberty maturation"

**OTHE**

**OTHE-2 (Session: PS03)**

**Indrani Madhugiri**

*Chemical Engineering and Process Development Division, CSIR-National Chemical Laboratory, Pune-411008, India*

"Unintuitive effects of substrate competition on steady state concentration of product of reversible enzymatic transformations"

**OTHE**

**OTHE-3 (Session: PS03)**

**Kaniz Fatima Lima**

*Lecturer, University of Science and Technology Chittagong*

"Impact of Mutation on the Invasion Potential of Chikungunya Outbreak"

**OTHE**

**OTHE-4 (Session: PS03)**

**Manisri**

*Centre for Computational Natural Sciences and Bioinformatics, IIIT Hyderabad*

"Mathematical modelling of transcriptional network of liver regeneration"

**OTHE**

**OTHE-5 (Session: PS03)**

**Souvadra Hati**

*BSSE, Indian Institute of Science*

"Operating Principles of Circular Toggle Polygons"

**OTHE**

**OTHE-6 (Session: PS03)**

**Shama Javeed**

*Pusan National university*

"Numerical study of blood flow through catheterized artery"

**OTHE**

**OTHE-7 (Session: PS03)**

**Ashley Sreejan**

*Chemical Engineering and Process Development Division, CSIR-National Chemical Laboratory*

"Mathematical model of the multi-amino acid multi-transporter system in CHO cells"

**POPD**

**POPD-26 (Session: PS03)**

**Vitor De Oliveira Sudbrack**

*DEE - UniL*

"Population dynamics in highly fragmented landscapes"

**POPD**

**POPD-27 (Session: PS03)**

**Simon Syga**

*TU Dresden*

"Studying the interplay of spatio-temporal interactions and evolutionary dynamics during cancer cell invasion"

**POPD**

**POPD-28 (Session: PS03)**

**Peter Nabutanyi**

*Bielefeld University, Germany*

"Modelling Interaction of Genetic Problems in Small Populations and Minimum Viable Population Size"

**POPD**

**POPD-29 (Session: PS03)**

**Martin Pontz**

*Tel Aviv University*

"Aneuploidy as a transient evolutionary step to adaptation"

**POPD**

**POPD-30 (Session: PS03)**

**Ayan Das**

*Center for Ecological Sciences, Indian Institute of Science, Bengaluru*

"Demographic noise can promote abrupt transitions in ecological systems"

**POPD**

**POPD-31 (Session: PS03)**

**Wissam Barhdadi**

*Ghent University*

"Analyzing eco-evolutionary dynamics under environmental change in a physiologically-structured individual-based model"

**POPD**

**POPD-32 (Session: PS03)**

**Connah Johnson**

*University of Warwick*

"ChemChaste: Modelling chemical dynamics in spatially distributed bio-films"

**POPD**

**POPD-33 (Session: PS03)**

**Sou Tomimoto**

*Mathematical Biology Laboratory, Department of Biology, Faculty of Sciences, Kyushu University*

"Modeling mutation accumulation and expansion in long-lived trees with complex branching structure"

**POPD**

**POPD-34 (Session: PS03)**

**Baeckkyoung Sung**

*KIST Europe / UST Korea*

"Endocrine dynamics modelling on the hypothalamic-pituitary-gonadal axis of the aquatic lower vertebrates"

**POPD**

**POPD-35 (Session: PS03)**

**Samuel Dijoux**

*Dept. of Ecosystem Biology, Faculty of Science, University of South Bohemia, České Budejovice, Czech Republic*

"'Symmetry in asymmetries' of body sizes and productivities drives consumer coexistence in multi-channel food webs"