We consider the spread of an infectious disease in a heterogeneous environment, modelled as a network of patches. We focus on the invasibility of the disease, as quantified by the corresponding value of an approximation to the network basic reproduction number, $mathcal{R}_0$, and study how changes in the network structure affect the value of $mathcal{R}_0$. We provide a detailed analysis for two model networks, a star and a path, and discuss the changes to the corresponding network structure that yield the largest decrease in $mathcal{R}_0$. We develop both combinatorial and matrix analytic techniques, and illustrate our theoretical results by simulations with the exact $mathcal{R}_0$.

# Contributed Talk Session - CT04

#### Tuesday, June 15 at 02:15pm (PDT)

Tuesday, June 15 at 10:15pm (BST)

Wednesday, June 16 06:15am (KST)

# Contributed Talk Session - CT04

##### CT04-CBBS:

CBBS Subgroup Contributed Talks

**Xueying Wang***Washington State Univeristy*

"Impact of Varying Networks on Disease Invasion"**Shaza Alsibaai***Department of Mathematics & Statistics, McGill University, Montréal, Canada.*

"The Necessity of Including a Sub-model for Iron Metabolism in Mathematical Modelling of Erythropoiesis"**Gess Iraji***Brandeis University*

"Mathematical Modeling of Clogging in Microfluidic Structures from Simple to Complex Geometries"

##### CT04-CDEV:

CDEV Subgroup Contributed Talks

**Tricity Andrew***North Carolina State University*

"Computational modeling to gain insight into developmental processes shaping stomach curvature"**Amjad Khan***Dalhousie University*

"Modeling the transmission and loss of an important class of mobile genetic elements"**Julio M Belmonte***North Carolina State University*

"Non-Linear Mechanical Response Transforms a Graded Molecular Distribution into a Step-Wise Output in Cell Behavior"**Sarafa Iyaniwura***The University of British Columbia, Vancouver*

"Oscillatory instabilities for a 2-D coupled ODE-PDE Model of Diffusion-Mediated Communication Between Small Signaling Compartments"

##### CT04-ECOP:

ECOP Subgroup Contributed Talks

**Arwa Baabdulla***University of Alberta*

"Homogenization of a Reaction Diffusion Equation can Explain Influenza A Virus Load Data"**Emil Frølich***Ph.D. Student at Technical University of Denmark*

"A new approach to multispecies population games in continuous space and time"**Abdel Halloway***University of Illinois -- Urbana Champaign*

"Unstable Population Dynamics in Obligate Cooperators"**Peter Thompson***University of Alberta Department of Biological Sciences*

"Using movement models to identify spatial memory in animals"

##### CT04-EVOP:

EVOP Subgroup Contributed Talks

**Anthia Le***The University of Queensland*

"The Evolution of Menopause"**Gabriela Lobinska***Weizmann Institute of Science*

"Should you inherit your parent's mutaiton rate?"**Peter Harrington***University of Alberta*

"A framework for studying transients in marine metapopulations"

##### CT04-IMMU:

IMMU Subgroup Contributed Talks

**Gulsah Yeni***Pennsylvania State University*

"Modeling PrEP on Demand for Prevention of HIV"**Esteban Abelardo Hernandez Vargas***UNAM*

"Topological Data Analysis in Infectious Diseases"**Laura Liao***Merck & Co., Inc*

"BUILDING A MECHANISTIC MODELING PLATFORM FOR HIV CURE DRUG DEVELOPMENT"

##### CT04-MEPI:

MEPI Subgroup Contributed Talks

**Tuğba Akman Yildiz***University of Turkish Aeronautical Association*

"Modeling vaccination against COVID-19 in Turkey with effective reproduction number"**Joshua C. Macdonald***University of Louisiana at Lafayette*

"Modeling COVID-19 outbreaks in United States with distinct testing, lockdown speed and fatigue rates"**Aurod Ounsinegad***Tarleton State University Department of Mathematics*

"Dynamics of Eastern Equine Encephalitis Infection Rates: A Mathematical Approach"

##### CT04-MFBM:

MFBM Subgroup Contributed Talks

**Elizabeth Trofimenkoff***University of Lethbridge*

"An algorithm for obtaining parametric conditions for the validity of the steady-state approximation"**Alexander D. Kaiser***Stanford University*

"Design-based models of heart valves and bicuspid aortic valve flows"**Jay Stotsky***University of Minnesota*

"The Impact of Cell-Level Details on Tissue-Scale Properties"**Fawaz K Alalhareth***The University of Texas at Arlington*

"Higher-Order Modified Nonstandard FiniteDifference Methods for Dynamical Systems in Biology"

##### CT04-MMPB:

MMPB Subgroup Contributed Talks

**Ahmed Abdelhamid**

"Computational modeling of external versus internal fibrinolysis in contracted blood clots"**Minseo Kim***Arnold O. Beckman High School*

"Revealing the Effect of Hydration on Kidney Stone Formation Through Singular Perturbation Analysis"**Valeri Barsegov***Department of Chemistry, University of Massachusetts, Lowell*

"Biomechanics, Thermodynamics and Mechanisms of Rupture of Fibrin Clots"

##### CT04-ONCO:

ONCO Subgroup Contributed Talks

**Jeffrey West***Moffitt Cancer Center*

"Antifragile Therapy"**Heiko Enderling***Moffitt Cancer Center*

"Simulating tumor-immune ecosystem evolution during cancer radiotherapy"**Emanuelle Arantes Paixão***Laboratório Nacional de Computação Científica*

"CARTmath: an in silico laboratory to simulate CAR-T immunotherapy in preclinical models"**António Sergio Dias Morais***Universidade de Coimbra*

"Role of prostate gland network structure in early stage prostate cancer"