Monday, October 7 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 09:30 |
Abba Gumel: Mathematics of malaria transmission dynamics: the renewed quest for eradication ↓ Malaria, a deadly disease caused by protozoan Plasmodium parasites, is spread between humans via the
bite of infected adult female Anopheles mosquitoes. Over 2.5 billion people live in geographies whose local epidemiology permits transmission of P. falciparum, responsible for most of the life-threatening forms of malaria. The wide-scale and heavy use of insecticide-based mosquito control interventions resulted in a significant reduction in malaria incidence and burden in endemic areas, prompting a renewed quest for malaria eradication. Numerous factors, such as Anopheles resistance to the currently-available insecticides used in mosquito control and anthropogenic climate change, potentially pose important challenges to the eradication efforts. In this talk, I will discuss a genetic-epidemiology mathematical modeling framework for assessing the combined impacts of insecticide resistance and climate change on distribution and burden of malaria mosquitoes and disease. If time permits, I will discuss our modeling effort on assessing the impact of sterile insect technique to control the population abundance of malaria mosquitoes, and explore its utility as an alternative pathway for achieving the malaria eradication objective. (TCPL 201) |
09:35 - 10:05 |
Chiu-Yen Kao: Is Maximum Tolerated Dose (MTD) Chemotherapy Scheduling Optimal for Glioblastoma Multiforme? ↓ In this study, we investigate a control problem involving a reaction-diffusion partial differential equation (PDE). Specifically, the focus is on optimizing the chemotherapy scheduling for brain tumor treatment to minimize the remaining tumor cells post-chemotherapy. Our findings establish that a bang-bang increasing function is the unique solution, affirming the MTD scheduling as the optimal chemotherapy profile. Several numerical experiments on a real brain image with parameters from clinics are conducted for tumors located in the frontal lobe, temporal lobe, or occipital lobe. They confirm our theoretical results and suggest a correlation between the proliferation rate of the tumor and the effectiveness of the optimal treatment. Joint work with Seyyed Abbas Mohammadi and Mohsen Yousefnezhad. (TCPL 201) |
10:10 - 10:35 |
Coffee Break (TCPL Foyer) |
10:35 - 11:05 |
Avner Friedman: Free boundary problems in bio-medicine ↓ A free boundary problem (FBP) consists of a system of PDEs in a domain with unknown boundary, which needs to be solved simultaneously with the unknown boundary of the domain. Such problems are increasing arise in models of bio-medical processes, for example: Cancer growth with treatment aimed at decreasing the growing unknown boundary; a growing plaque in cardiac artery which by blocking the artery will result in heart attack; chronic or diabetic dermal wound which, if not healed in proper time, may require amputation; cartilage shrinkage in rheumatoid arthritis; fungal skin infection which, if not treated, may spread over the whole body. Each if these diseases was modeled as a FBP, and numerical simulations of the model were performed and used to gain understanding, and to make recommendations, for effective treatments in experimental studies or in clinical trials. But what about rigorous analysis, e.g. theorems and proofs? In this talk I will briefly review such models and then proceed to describe mathematical results for simplified version of the models, showing that these results actually capture, in some “generalized” sense, those derived by simulations. I will also mention some open questions. (TCPL 201) |
11:10 - 11:40 |
Bei Hu: Periodic Solutions in Free Boundary Problems from Mathematical Biology ↓ Periodic phenomena occur naturally due to periodic intake of food. In this talk we shall present our recent work on periodic solutions on two free boundary models in mathematical biology. (1) Atherosclerosis. Plaque formation is a leading cause of death worldwide; it originates from a plaque which builds up in the artery. We considered a simplified model of plaque growth involving LDL and HDL cholesterols, macrophages and foam cells, which satisfy a coupled system of PDEs with a free boundary, the interface between the plaque and the blood flow. In an earlier work (with Avner Friedman and Wenrui Hao) of an extremely simplified model, we proved that there exist small radially symmetric stationary plaques and established a sharp condition that ensures their stability. In our work with Evelyn Zhao, we look for the existence of non-radially symmetric stationary solutions. The absence of an explicit radially symmetric stationary solution presents a big challenge to verify the Crandall-Rabinowitz theorem; through asymptotic expansion, we extend the analysis to establish a finite branch of symmetry-breaking stationary solutions which bifurcate from the radially symmetric solutions. This work is further extended (with Xiaohong Zhang, Zhengce Zhang) to include to allow reverse cholesterol transport in the model. Extension in the longitude direction and combined longitude-latitude direction is recently carried out (with Yaodan Huang). A periodic small plaque solution was recently found (with Yaodan Huang). This solution is linearly stable under certain conditions (with Jingyi Liu). (2) Tumor growth. Many models assume tumor cells are immersed in a constant supply of nutrient, for simplicity. We shall present the periodic solution and stability for the radially symmetric case. In particular, we shall establish the existence and uniqueness of the periodic solution in the biologically reasonable case and establish a global attractor in the class of radially symmetric initial data (with Yaodan Huang, Jingyi Liu). (TCPL 201) |
11:45 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
14:20 - 14:40 |
Bo Zhang: Movement alters ecological dynamics in heterogeneous environments ↓ Understanding mechanisms of coexistence is a central topic in ecology. Mathematical analysis of models of competition between two identical species moving at different rates of symmetric diffusion in heterogeneous environments show that the slower mover excludes the faster one. The models have not been tested empirically and lack inclusions of a component of directed movement toward favorable areas. To address these gaps, we extended previous theory by explicitly including exploitable resource dynamics and directed movement. We tested the mathematical results experimentally using laboratory populations of the nematode worm, Caenorhabditis elegans. Our results not only support the previous theory that the species diffusing at a slower rate prevails in heterogeneous environments but also reveal that moderate levels of a directed movement component on top of the diffusive movement allow species to coexist. Additionally, we have expanded our work to test the outcomes of different movement strategies in a various of fragmented and toxincant environments. For instance, we combine mechanistic mathematical modeling and laboratory experiments to disentangle the impacts of habitat fragmentation and locomotion. Our theoretical and empirical results found that species with a relatively low motility rate maintained a moderate growth rate and high population abundance in fragmentation. Alternatively, fragmentation harmed fast-moving populations through a decrease in the populations’ growth rate by creating mismatch between the population distribution and the resource distribution. Our study will advance our knowledge of understanding habitat fragmentation's impacts and potential mitigations, which is a pressing concern in biodiversity conservation. (TCPL 201) |
14:40 - 15:00 |
Olga Turanova: Effect of Repelling Chemotaxis on Propagation ↓ This talk concerns an equation of Fisher-KPP type with a Keller-Segel chemotaxis term. The goal is to determine the effect of strong repelling chemotaxis on propagation. We provide an almost complete picture of the asymptotic dependence of the traveling wave speed on parameters representing the strength and length-scale of chemotaxis. Our study is based on the convergence, in certain asymptotic regimes, to traveling waves of the porous medium Fisher-KPP equation and to those of a hyperbolic Fisher-KPP-Keller-Segel equation. The talk is based on joint work with C. Henderson and Q. Griette. (TCPL 201) |
15:00 - 15:30 |
Coffee Break (TCPL Foyer) |
15:30 - 15:50 |
Xinyue Zhao: Bifurcation Analysis in a Free Boundary Model for Early Atherosclerotic Plaque Development ↓ Atherosclerosis, the hardening of arteries due to plaque accumulation, is a leading cause of disability and premature death in the United States and worldwide. In this talk, I will present a highly nonlinear and highly coupled PDE model that describes the growth of arterial plaque in the early stage of atherosclerosis. The model incorporates LDL and HDL cholesterols, macrophage cells, and foam cells, with the interface separating the plaque and blood flow regions being a free boundary. I will discuss our findings on the existence of finite branches of symmetry-breaking bifurcation solutions. Furthermore, we have proved that the first bifurcation point for the system corresponds to the n=1 mode. Since plaque in reality is unlikely to be strictly radially symmetric, our results could be instrumental in explaining the asymmetric shapes of plaque. (TCPL 201) |
15:55 - 16:15 |
Michele Romanos: Dynamic regulation of motility in structured environments drives spatial organisation of bacterial crowds: insights from experimental data and mathematical modeling ↓ Myxococcus xanthus, a social bacterium, exhibits fascinating collective behaviors such as rippling and swarming, where cells self-organize into complex patterns. This talk presents new biological data on these behaviors, featuring high-resolution analyses of cell movements and reversals. Based on these observations, we derive a kinetic model that identifies a key factor that facilitates the emergence of rippling patterns. Additionally, we introduce a 2D agent-based model that links bacterial reversals to congestion through dynamic motility regulation. This model provides a framework that accurately captures the two patterns observed in the data. The model also highlights the role of background anisotropy in pattern formation.
This work is a collaboration with Vincent Calvez (Laboratoire de Mathématiques de Bretagne Atlantique), Tâm Mignot and Jean-Baptiste Saulnier (Laboratoire de Chimie Bactérienne - Marseille). (TCPL 201) |
16:20 - 16:40 |
Daozhou Gao: Effects of Host Movement on the Prevalence of Vector-borne Diseases ↓ Vector-borne diseases (VBDs) are diseases primarily transmitted to humans and other animals by blood-feeding arthropods, such as mosquitoes, ticks, and bugs. Common VBDs include malaria, dengue fever, Rift Valley fever, Chagas disease, schistosomiasis, and Lyme disease. They constitute a serious threat to global health. For example, malaria alone caused 249 million cases and 608,000 deaths globally in 2022. Human migration and tourism have driven the spread of VBDs wider, faster and longer, as evidenced in recent outbreaks like the 2015-16 Zika virus epidemic. Patch models are widely used to describe the spatial spread of infectious diseases in discrete spaces. Quite a few studies have shown that population dispersal can strengthen or weaken the persistence of VBDs and make disease eradication more challenging. However, it is unclear how human movement affects the host prevalence (proportion of hosts being infected). In this talk, based on a generalized Ross-Macdonald model, we will present some preliminary results on this topic. (Online) |
16:45 - 17:05 |
Nourridine Siewe: Osteoporosis induced by cellular senescence: A mathematical model ↓ Osteoporosis is a disease characterized by a loss of bone mass, which leads to increased fragility and a higher likelihood of fractures. Cellular senescence is the permanent arrest of the normal cell cycle while maintaining cell viability. The number of senescent cells increases with age. Since osteoporosis is an age-related condition, it is natural to consider the extent to which senescent cells contribute to bone density loss and osteoporosis. In this talk, we use a mathematical model to address this question. We also evaluate senolytic drugs, such as fisetin and quercetin, which selectively eliminate senescent cells, and assess their efficacy in reducing bone loss. (TCPL 201) |
17:10 - 17:30 |
Chris Henderson: Control formulation for a road-field population dynamics model ↓ Berestycki, Roquejoffre, and Rossi introduced a reaction-diffusion system for populations that have a distinguished ‘road’ on which they move quickly but do not reproduce. The goal is to understand invasion behavior (fronts). This model has attracted enormous interest in the decade since it was introduced, with a nearly complete picture in the case of a straight road. In this talk, I will discuss a joint work with Adrian Lam in which we provide an optimal control perspective on this problem. This gives a natural interpretation of the front in terms of balancing speed on the road and growth in the field, and it lets us easily deduce that ‘bent’ line case, which was previously not well-understood, is a simple consequence of the straight line case and some elementary geometry. (TCPL 201) |
17:35 - 17:55 |
Kyunghan Choi: Chemotactic Cell Aggregation Viewed as Instability and Phase Separation ↓ In this talk, we focus on the pattern formation of a chemotactic cell aggregation model with a mechanism that density suppresses motility. The model exhibits four types of cell aggregation patterns: single-point peaks, hot spots, cold spots, and stripes, depending on the parameters and mean density. The analysis is performed in two ways. First, traditional instability analysis reveals the existence of two critical densities. This local analysis shows patterns emerge if the initial mean density lies between the two values. Second, a phase separation method using van der Waals’ double well potential reveals that pattern formation is possible in a bigger parameter regime that includes the one identified by the local analysis. This non-local analysis shows that pattern formation occurs beyond the parameter regimes of the classical local instability analysis. (TCPL 201) |
18:00 - 20:00 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building. (Vistas Dining Room) |