Math Biology Archives for Fall 2025 to Spring 2026
Role of Mathematical Modeling in Development and Roll Out of Vaccines
When: Tue, August 27, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Elamin Elbasha (Distinguished Scientist at Merck Research Laboratories) - https://scholar.google.com/citations?user=6tEMHAgAAAAJ&hl=en&oi=ao
Abstract: Mathematical modeling plays a major role in providing insights into the development of vaccines and selection of optimal vaccination strategies to control the spread of infectious diseases. For example, mathematical compartmental models provide
answers to pertinent questions relating to R&Amp;D decisions like progression through various phases of development given vaccine properties, vaccine dose-level and regimen, and design of clinical trials. In this talk, I will discuss some of the mathematical modeling approaches used to support these decisions as well as inform vaccine
recommendations once a vaccine is licensed. Examples of a few vaccine-preventable diseases will be used for illustrative purposes.
On The Eco-Evolutionary Dynamics of Inefficient Viral Infections
When: Tue, September 3, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Joshua Weitz (Department of Biology, University of Maryland at College Park) - https://weitzgroup.umd.edu/people/joshua-weitz/
Abstract: Viral infections transform the fate of microbial cells, populations, and ecosystems. The infection and lysis of individual microbes releases new virus particles and redirects carbon and nutrients back through the microbial loop. Yet, there is increasing evidence that the outcome of infections is often nuanced and does not necessarily end in rapid lysis. Instead, viral infections include a spectrum of fates including latency, inefficient infections, and infections that fail inside cells. This talk combines insights from mathematical models, experiments, and field-based evidence to explore how non-lytic outcomes and inefficient infections shape microbial populations and ecosystem functioning.
Microbial spatial dynamics over eco-evolutionary timescales
When: Tue, September 10, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Anshuman Swain (Harvard University, Museum of Comparative Zoology) - https://www.anshumanswain.com
Abstract: Persistently diverse microbial communities are one of biology’s great puzzles. Using an agent-based modeling framework that accommodates high mutation rates and a continuum of species traits, our work looks at microbial communities in which antagonistic interactions occur via the production of, inhibition of, and vulnerability to toxins (e.g., antibiotics). Our study reports that mutation size and mobility enhance microbial diversity and temporal persistence to extraordinarily high levels. These findings—including the discovery that the duration of the transient phase in community assembly provides a guide to equilibrial diversity—highlight the potentially critical role that antagonistic interactions play in promoting the diversity of bacterial systems. Such interactions, together with more frequently studied resource-driven interactions and spatial structure, may drive the enigmatic levels of biodiversity seen in microbial systems.
Two talks: The Distal Regions of Human Acrocentric Short Arms are not Chromosome Specific and Mathematical assessment of the roles of vaccination and Pap screening on the incidence of HPV and related cancers in the Republic of Korea
When: Tue, September 17, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker #1: Valerie Ann Wray (PhD student, UMD Mathematics Department)
Title: The Distal Regions of Human Acrocentric Short Arms are not Chromosome Specific
Abstract: The five human acrocentric chromosomes (13, 14, 15, 21, and 22) are hypothesized to recombine in a non-homologous way resulting in distal regions that are not chromosome specific. Here, we extract segmental duplications from the distal regions of human acrocentric chromosomes, build multiple sequence alignments, and infer phylogenetic trees. The phylogenetic trees show evidence of recombination between heterologous chromosomes. This work began as a summer internship project with Dr. Adam Phillippy at the National Human Genome Research Institute at the NIH.
Speaker #2: Soyoung Park (PhD student, UMD Mathematics Department)
Title: Mathematical assessment of the roles of vaccination and Pap screening on the incidence of HPV and related cancers in the Republic of Korea
Abstract: Human Papillomavirus (HPV) is a major sexually-transmitted infection that causes various cancers and genital warts in humans. In addition to accounting for about 99% of cervical cancer cases, it significantly contributes to anal, penile, vaginal, and head and neck cancers. Although HPV is vaccine-preventable (and highly efficacious vaccines exist for preventing infection with some of the most oncogenic HPV subtypes in the targeted population), the disease continues to cause major public health burden globally (largely due to inequity in access to the main control resources (i.e., access to Pap smear and vaccination) and low vaccination coverage in most communities that implement routine HPV vaccination). This talk is based on the use of a new mathematical model (for the natural history of HPV, together with the associated neoplasia) for assessing the combined population-level impacts of Pap cytology screening and vaccination against the spread of HPV in a heterogeneous (heterosexual and homosexual) population. The model, which takes the form of a deterministic system of nonlinear differential equations, will be calibrated and validated using HPV-related cancer data from the Republic of Korea. Theoretical and numerical simulation results will be presented. Conditions for achieving vaccine-derived herd-immunity threshold (for achieving HPV elimination in Korea) will be derived.
Compartmental Models for Epidemiology with Noncompliant Behavior
When: Tue, September 24, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Christian Parkinson (Michigan State University, Department of Mathematics) - https://sites.google.com/math.arizona.edu/chparkin/
Abstract: We formulate and analyze ODE and PDE models for epidemiology which incorporate human behavioral concerns. Specifically, we assume that as a disease spreads and a governing body implements non-pharmaceutical intervention methods, there is a portion of the population that does not comply with these mandates and that this noncompliance has a nontrivial effect on the spread of the disease. Borrowing from social contagion theory, we then allow this noncompliance to spread parallel to the disease. We derive reproductive ratios and large time asymptotics for our models and demonstrate their behavior with simulations.
Multi-scale, host-based network models of immune landscapes
When: Tue, October 1, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. James Watmough (University of New Brunswick, Department of Mathematics and Statistics) - https://watmough.ext.unb.ca
Abstract: The progression and burden of disease outbreaks, and biological invasions more generally, is complicated by heterogeneities in the host population and its environment. There are two sides to this heterogeneity: the risk of infection or transmission, and the cost of disease. For the particular case of SARS-CoV-2 and CoViD, transmission risk is raised or lowered by host behaviour and by host immune history. Familiar aspects of the former being masking and isolation, and of the latter being the time lapsed since vaccination or past infections. Host behaviour and immune history also affect disease risk as does age (through immunosenescence) and various comorbidities. The main objective of this talk is to present preliminary results from simple compartmental and individual-based models designed to predict population-level disease burden and immune landscapes from host behaviour and within-host virus and immune dynamics.
Spatio-Temporal Population Dynamics for Interacting Species
When: Tue, October 8, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Alex Safsten (UMD Math Department) -
Abstract: I will present two PDE models for interacting animal species, both of which have direct application to ecology and/or public health, and both of which posses some surprising behaviors. My first model is for mosquito population control. Mosquitoes top the list of the deadliest animals in the world due to the diseases they carry and transmit to humans, most importantly, malaria. The sterile insect technique (SIT), which entails the periodic mass release of sterilized male mosquitoes into an environment where adult female mosquitoes are abundant, is one of the main promising approaches being proposed to suppress the populations of malaria-spreading mosquitoes. I will use a two-species model of SIT to see how an SIT program can leverage interspecies competition between mosquito species to replace a species of high vectorial capacity with a species of low vectorial capacity. Using this competition, I will show that SIT can locally eradicate malaria-carrying mosquito species at a much lower cost (in terms of the number of sterile males released) than using SIT alone. Second, I will present a PDE model for predator-prey interactions in which the predators' range is a subset of the prey's range. If the predators' range is too large, they may over-hunt the prey whereas if their range is too small, they will not have enough prey available to be able to support a large population. Therefore, I will address the question of, given a range for the prey species, what is the subset of that range for the predator species that maximizes the predator population?
The Mathematics of Human Population Growth and CO2 Emissions
When: Tue, October 15, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Victor M. Yakovenko (Department of Physics, University of Maryland at College Park) - https://physics.umd.edu/~yakovenk/
Abstract: In a paper published in the Science magazine in 1960, von Foerster et al. argued that human population growth follows a hyperbolic pattern with a singularity in 2026. Using current empirical data from 10,000 BCE to 2023 CE, we re-examine this claim. We find that human population initially grew exponentially as N(t)~exp(t/T) with T~3000 years. This growth then gradually evolved to be super-exponential with a form similar to the Bose function in statistical physics. Population growth further accelerated around 1700, entering the hyperbolic regime N(t)=C/(ts-t) with the projected singularity year ts=2030, which essentially confirms the prediction by von Foerster et al. We attribute the switch from the super-exponential to the hyperbolic regime to the onset of the Industrial Revolution and the transition to massive use of fossil fuels. This claim is supported by a linear relation that we find between population and the increase in CO2 level in the atmosphere from 1700 to 2000. Then, at the end of the 20th century, the inverse population curve 1/N(t) begins to deviate from a straight line and avoids crossing zero, thus escaping a literal singularity. We find that N(t) is well fitted by the square root of the Lorentzian function, with a maximum of slightly more than 8.2 billion people at t=ts. The width 2\tau of the population peak is given by the cutoff time \tau=32 years. We also find that the increase in CO2 level in the atmosphere since 1700 is well fitted by arccot[(ts-t)/\tau_F] with \tau_F=40 years. This fit gives a forecast of the CO2 level in the near future for the 21st century.
The role of behavior in the control of infectious diseases
When: Tue, October 22, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Jacques Bélair (Université de Montréal, Department of Mathematics and Statistics) - https://dms.umontreal.ca/~belair/
Abstract: The recent pandemic has illustrated the usefulness of mathematical modeling in devising strategies for the control of infectious disease propagation. It has also demonstrated the
role played by individual's behaviour in successfully deploying these interventions. I will
present two classes of mathematical models developed around the Covid-19 epidemic.
A first one incorporates the temporary ("Fangcang shelter") hospitals that were deployed in the early stages of epidemic to limit the propagation by isolation of cases; a
second one considers variable levels of compliance with recommended non-pharmaceutical interventions (NPIs), and explore the dynamical consequences of this variability.
Simple models of disease outbreaks
When: Tue, October 29, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. James Yorke (University of Maryland, Institute for Physical Sciences and Math department) - https://yorke.umd.edu
Abstract: Some of the simplest models can have surprising phenomena which will be discussed in this talk. I will describe an infected-mosquito model which exhibits the butterfly effect – huge growth – but without chaos. I will also describe how an SIR can fit a epidemic with a wide range of parameters. Making the model more complex does not help with this problem.
The talk will be based on two papers:
Shayak, B., Jahedi, S., & Yorke, J. A. (2024).
Ambiguity in the use of SIR models to fit epidemic incidence data.
ArXiv. /abs/2404.04181
Yoshitaka Saiki and James A Yorke
Can the flap of a butterfly’s wings shift a tornado into Texas – without chaos?
MDPI Atmosphere
14 (2023), no. 5: 821.
https://doi.org/10.3390/atmos14050821
https://www.mdpi.com/2073-4433/14/5/821
Spatio-temporal clonal evolution of somatic mutations in tissue structures; continuum limit Moran process
When: Tue, November 5, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Kamran Kaveh (Scientific Director at University of Minnesota, Therapy Modeling & Design Center) - https://scholar.google.com/citations?user=4RFJnNIAAAAJ&hl=en
Abstract: Understanding the spatio-temporal evolutionary dynamics of is important to predict evolutionary paths that a mutant subspecies can take. This is particularly important in the context of somatic evolution in epithelial tissue and cancer evolution. Modeling and analyzing natural selection in tissue structures has been a subject of much studies recently. However, the current models lack the ability to predict the spatial patterns and spatio-temporal dynamics of driver mutants in spatial structures. In this talk, I establish a continuum space-time limit of Moran birth-death and death-birth dynamics and derive the PDE that represents the deterministic limit in 1D or 2D lattice, respectively. The Fisher-Kolmogorov-Pitaevskii-Piskunov (FKPP) equation is often used to model spatial evolutionary processes. I show that the Moran process does not recover the FKPP equation in a deterministic limit and calculate the Fisher wave speed (selective waves). If time allows, I will discuss the generalization the model to heterogeneous environments and discuss the isothermal theorem in this context.
Time delays and synchrony in neural networks
When: Tue, November 12, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Sue Ann Campbell (University of Waterloo-Department of Applied Mathematics) - https://www.math.uwaterloo.ca/~sacampbe/
Abstract: We consider networks of oscillator nodes with time delayed, global circulant coupling. We first study the existence of Hopf bifurcations induced by time delayed coupling, and then apply equivariant Hopf bifurcation theory to determine how these bifurcations lead to different patterns of phase-locked oscillations. We apply the theory to a variety of systems inspired by biological
neural networks to show how Hopf bifurcations can determine the synchronization state of the network. Finally, we discuss how interaction between two Hopf bifurcations corresponding to different oscillation patterns can induce complex torus solutions
in the network.
Persistent Homology: The Birds that Don't Exist
When: Tue, November 26, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Stephanie Chia (Grad Student at University of Maryland, Biology Department) - https://science.umd.edu/biology/faganlab/people/chia.html
Abstract: Persistent homology is a topological data analysis tool that can characterize topological features in point cloud data. A species-trait dataset can be considered as a point cloud, where each species is represented in a multidimensional space defined by its traits. Using persistent homology, we can detect “holes” in this space—regions where certain forms of species are absent. In this talk, I will demonstrate how I use persistent homology to uncover bird forms that don’t exist in nature and discuss the evolutionary mechanisms behind the patterns.
Catastrophes, oscillations, and networks: how simple nonlinear dynamics govern large ecosystems
When: Tue, December 3, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Vadim Karatayev (Department of Biology, University of Maryland at College Park) - https://aqeco-vadim.weebly.com
Abstract: I will discuss how very simple dynamical models largely explain the dynamics of 2,000km kelp forests, Large Marine Ecosystems, sustainability movements, and global climate agreements. A key theme is that novel dynamics emerge from the interplay of (a) saddle node or Hopf bifurcations with (b) stochasticity, transients, or network topology. I will also discuss current and prospective approaches to understanding complex systems in ecology, touching on my planned work on which I'd love to collaborate or advise AMSC students.
Stability and tipping points in noisy environments
When: Tue, December 10, 2024 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Karen Abbott (Case Western Reserve University, Department of Biology) - https://abbottlab480702554.wordpress.com
Abstract: Sudden, persistent changes in ecosystem state or configuration, known in ecology as regime
shifts, are difficult to predict and a cause of great concern. A large, stable prey population may
suddenly collapse to an alternative low-density state in response to a stochastic perturbation,
for example, or stochasticity may trigger outbreaks in pest populations that were previously
stably suppressed. To explain phenomena like these, ecologists have drawn heavily on
deterministic theory that emphasizes the nonlinearities that give rise to bifurcation-induced
tipping points, while marginalizing the complex role of stochasticity in driving transitions
between states. In this talk, I will discuss how different types of tipping points arise, and how
we can use potential functions (including their extensions, such as the quasi-potential) to derive
stronger stability concepts that allow us to move beyond classical deterministic theory. Given
the pervasive influence of large perturbations in nature, this view promises to yield improved
insights into the factors that stabilize or destabilize ecological systems.
CTLNs as a mean field theory for clustered spiking networks
When: Tue, February 4, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Caitlin Lienkaemper (MIT McGovern Institute)-https://lienkaemper.github.io
Abstract: Combinatorial threshold linear networks (CTLNs) model the activity of a network of excitatory neurons against a background of non-specific inhibition. While the simplicity of the CTLN model makes it an ideal setting to study the relationship between a network’s structure and its dynamics, the lack of explicit inhibition makes it difficult to relate CTLNs to more biologically detailed models. To remedy this, we derive the CTLN model as a mean field theory of a clustered spiking network which has an explicit population of inhibitory neurons and a cluster of excitatory neurons corresponding to each neuron in the CTLN. We show that attractors in the CTLN model, such as fixed points, limit cycles, and chaotic attractors, also appear in the clustered spiking network.
The "Fear" Effect in Competition Systems: Theory and Applications to Avian Invasions
When: Tue, February 11, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Vaibhava Srivastava (Grad Student) (Iowa State University-Department of Mathematics ) - https://vaibhava-srivastava.github.io/Pub.html
Abstract: Non-consumptive effects, such as fear of depredation, can strongly influence predator-prey dynamics. There are several ecological and social motivations for these effects in competitive systems as well. In this work, we consider the classic two species ODE and PDE Lotka-Volterra competition models, where one of the competitors is "fearful" of the other. We find that the presence of fear can have several interesting dynamical effects on the classical competitive scenarios. Notably, we show novel bi-stability dynamics for fear levels in certain regimes. Furthermore, the effects of several spatially heterogeneous fear functions are investigated in the spatially explicit setting. In particular, we show that a weak competition-type situation can change to competitive exclusion under certain integral restrictions on the fear function. Applications of these results to ecological as well as sociopolitical settings are discussed, which connect to the "landscape of fear" (LOF) concept in ecology. Using the test case of northern spotted and barred owl populations in the Pacific Northwest region of the United States, we evaluate if this fear (co-occurrence) model can generate more robust population estimates than previous models. We then evaluate if potential co-occurrence effects among Barred and Northern Spotted Owls are uni- or bi-directional. Lastly, we leverage the best-performing model to evaluate the degree to which a recently proposed barred owl culling program may help recover Northern Spotted Owl populations.
Challenging Conventional Epidemiological Theories: Coexistence and Oscillations in Multi-Strain Epidemics
When: Tue, February 18, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Gavish Nir (Technion – Israel Institute of Technology, Department of Mathematics) - https://ngavish.net.technion.ac.il
Abstract: During the COVID-19 pandemic, variants constantly emerged and interacted with existing ones. Our data-driven research showed that a variant with a basic reproduction number as high as 10 can defy conventional theory. Motivated by this, the talk will present two works on the dynamics of epidemic systems with two strains that provide partial cross-immunity to each other.
In the first part, we challenge the validity of the exclusion principle at a limit in which one strain has a vast competitive advantage over the other strains. We show that when one strain is significantly more transmissible than the other, an epidemic system with partial cross-immunity can reach a stable endemic equilibrium in which both strains coexist with comparable prevalence. Thus, the competitive exclusion principle does not always apply.
The second part explores conditions under which a two-strain epidemic model with partial cross-immunity can lead to self-sustained oscillations. Contrary to previous findings, our results indicate that oscillations can occur even with weak cross-immunity and weak asymmetry. Using asymptotic methods, we reveal that the steady state of coexistence becomes unstable near specific curves in the parameter space, leading to oscillatory solutions for any basic reproduction number greater than one. Numerical simulations support our theoretical findings, highlighting an unexpected oscillatory region.
Stochastic Population Dynamics in Discrete Time
When: Tue, February 25, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Alexandru Hening (Texas A&M University) - https://sites.google.com/tamu.edu/ahening/
Abstract: I will present a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time stochastic difference equations that can include population structure, eco-environmental feedback or other internal or external factors. Using the general theory, I will showcase some interesting examples. I will end my talk by explaining how the population size at equilibrium is influenced by environmental fluctuations.
Mode switching in organisms for solving explore-versus-exploit problems
When: Tue, March 4, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Kathleen Hoffman (Department of Mathematics and statistics, University of Maryland, Baltimore County) - https://userpages.umbc.edu/~khoffman/
Abstract: Fish use active sensing to constantly re-evaluate their position in space. The weakly electric glass knifefish, Eigenmannia virescens, incorporates an electric field as one of its active sensing mechanisms. The motion of the knifefish in a stationary refuge is captured using high-resolution motion tracking and illustrates many small amplitude oscillations inside the refuge coupled with high amplitude “jumps”. We show that this active sensing mechanism is not reflected by a Gaussian distribution of the velocities. Instead, we show that the velocities are more accurately reflected by a mixture of Gaussians because of the number of high amplitude jumps in the tails of the velocity distribution. The experimental position measurements were taken in both the light and the dark showing more frequent bursts of faster movement in the dark, where presumably the fish are relying more on their electric sensor than their vision. Computational models of active state estimation with noise injected into the system based on threshold triggers exhibit velocity distributions that resemble those of the experimental data, more so than with pure noise or zero noise inputs. Similar distributions have been observed in a variety of different senses and species.
Extracellular Geometry Impact in Clustered Cell Migration
When: Tue, March 11, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Brad Peercy (University of Maryland, Baltimore County, Department of Mathematics and Statistics) - https://userpages.umbc.edu/~bpeercy/
Abstract: Cellular migration is impacted by the environment in which cells move. Seductive chemical signals, anchors for climbing, repulsion from neighbors are critical for progression toward an ultimate physiological goal. The space between cells provides the domain for chemoattractant to diffuse, and the geometry of that space can have a significant effect on timing of the trajectory of a cluster of migrating cells. For data of the border cells from the Drosophila melanogaster egg chamber exhibiting this behavior, we present a simplified one-dimensional hybrid agent-based migration model coupled to a reaction-diffusion model of chemoattractant in a canonical geometry. Our results suggest that geometry-induced chemoattractant distribution is sufficient to capture the observed variation in migration trajectories. Predicted counterintuitive slowing of the border cells during overexpression of chemoattractant while maintaining trajectory variation was confirmed. This slowing in overexpression was rescued by mutation.
This work is in collaboration with Naghmeh Akhavan and experimentalists Alex George and Michelle Starz-Gaiano
Mathematics of malaria transmission dynamics: Recent progress and challenges
When: Tue, March 25, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Abba Gumel (University of Maryland, Department of Mathematics) - https://math.umd.edu/~agumel/
Abstract: Since its spillover to humans some 12,000 years ago, malaria, a deadly parasitic disease transmitted between humans via the bite of an infected adult female Anopheles mosquitoes, remains one of the deadliest infectious diseases of mankind. Much progress has been recorded in the battle against malaria over the last decade or two, prompting a renewed quest to significantly reduce its burden (by 90% by 2030) or eradicate it by 2040. Unfortunately, these laudable concerted global efforts are threatened by several challenges, such as widespread resistance to all the currently-available insecticides used in vector control, evolution of drug resistance, climate change, land-use changes, emergence of invasive species, human mobility (rural-urban migration), and quality of public health infrastructure and care. I will discuss some of these advances and challenges, in addition to presenting a mathematical framework for gaining deeper qualitative insight into the transmission dynamics and control of the disease in endemic areas. Some pertinent questions, such as those related to whether climate change will lead to a shift or range expansion of the malaria vector and whether or not the eradication goals can be achieved using existing control resources, will be discussed. Relevant bifurcations, and their implications vis a vis the persistence and/or extinction of the malaria vector and, consequently, the disease, will also be discussed. If time permits, I will discuss the potential utility of some of the DNA-based biocontrol methods (such as the release of transgenic mosquitoes) advanced by entomologists against the malaria vector.
Reaction-diffusion equations with multiple movement modes
When: Tue, April 1, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Chris Cosner (University of Miami) - https://people.miami.edu/profile/ccedbedb58ad79f146714c2dd4b1bdc3
Abstract: Classical reaction-diffusion-advection models assume that all individuals in a species
or subspecies move in the same way and only produce offspring of the same subspecies. There are at least three ways that populations can violate those assumptions. Individuals can change behavior, for example switching between search and resource exploitation. Populations can be stage structured and individuals at different stages can have different movement patterns. Individuals of one subspecies can produce offspring of another subspecies by genetic mutation or recombination. Models for populations whose members can switch between different movement modes can have properties that are different from those for populations where all individuals move in the same way. They may not satisfy the reduction principle, which says that slower dispersal is advantageous, and holds for many types of models with a single movement mode. They typically lead to systems that are cooperative at low densities but competitive at high densities. This talk will describe some models of this type and some of their properties.
Community ecology of infectious disease pathogens
When: Tue, April 8, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Sang Woo Park (University of Chicago, Department of Ecology and Evolution) - https://cobeylab.uchicago.edu/people/daniel-sang-woo-park/
Abstract: The human population presents a richly documented natural laboratories for understanding polymicrobial dynamics of infectious disease pathogens, providing unique opportunities to answer broader questions about diversity and stability of ecological communities. First, inspired by Modern Coexistence Theory, I lay out Pathogen Invasion Theory (PIT) for predicting the outcome of pathogen competition. PIT reveals that mutual invasion of competing strains is near-universal across major human pathogens. Instead, what determines strain co-circulation is the subsequent persistence of competing strains, which depend on the dynamics of the susceptible host populations. Then, using COVID-19 intervention as an example, I examine how pathogen communities respond to perturbations and quantify ecological resilience across major human respiratory pathogens. Resulting estimates provide insights into the susceptible host dynamics and persistence. Finally, I present a case study, illustrating how subtle changes in population-level susceptibility, driven by an expansion of childcare facilities in Japan, translates to complex outbreak dynamics.
Fighting drug resistance with math
When: Tue, April 15, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Doron Levy (University of Maryland, College Park, Department of Mathematics) - https://www.math.umd.edu/~dlevy/
Abstract: The emergence of drug-resistance is a major challenge in chemotherapy. In this talk we will overview some of our recent mathematical models for describing the dynamics of drug-resistance in solid tumors. These models follow the dynamics of the tumor, assuming that the cancer cell population depends on a phenotype variable that corresponds to the resistance level to a cytotoxic drug. Under certain conditions, our models predict that multiple resistant traits emerge at different locations within the tumor, corresponding to heterogeneous tumors. We show that a higher drug dosage may delay a relapse, yet, when this happens, a more resistant trait emerges. We will show how mathematics can be used to propose an efficient drug schedule aiming at minimizing the growth rate of the most resistant trait, provide extensions to the multi-drug setting, and discuss the competition between cancer cells and healthy cells.
Modeling social complexity in epidemiology: risk perception and adaptive human behavior
When: Tue, April 22, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Baltazar Espinoza (University of Virginia) - https://biocomplexity.virginia.edu/our-team/baltazar-espinoza
Abstract: The recent pandemics have highlighted critical factors that need to be addressed in the modern study of epidemic dynamics, such as the role of human behavior, economics, biosurveillance, and information sharing. The intertwined processes, where individuals make behavioral decisions driven by epidemic dynamics, which in turn reshape the progression of the contagion, make epidemics complex adaptive systems. In this talk, I will show that incorporating adaptive human behavior into epidemiological models can lead to unexpected results. Specifically, I will discuss scenarios in which individuals’ risk perceptions can increase or decrease the final epidemic size, producing a hysteresis-like effect.
A predator-prey model with age-structured role reversal
When: Tue, April 29, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Luis Suarez (University of Maryland College Park, Department of Mathematics) -
Abstract: We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an "ontogenetic niche shift", in which a species' functional role changes as it grows. This structure adds complexity to our model but increases its biological relevance. The time evolution of the age-structured predator population is motivated by the Kermack-McKendrick Renewal Equation (KMRE). Unlike KMRE, the predator population's birth and death rate functions depend on the prey population's size. We establish the existence, uniqueness, and positivity of the solutions to the proposed model's initial value problem. The dynamical properties of the proposed model are investigated via Latin Hypercube Sampling in the 15-dimensional space of its parameters. Our Linear Discriminant Analysis suggests that the most influential parameters are the maturation age of the predator and the rate of consumption of juvenile predators by the prey. We carry out a detailed study of the long-term behavior of the proposed model as a function of these two parameters. In addition, we reduce the proposed age-structured model to ordinary and delayed differential equation (ODE and DDE) models. The comparison of the long-term behavior of the ODE, DDE, and the age-structured models with matching parameter settings shows that the age structure promotes the instability of the Coexistence Equilibrium and the emergence of the Coexistence Periodic Attractor.
Ideas on a traffic light warning system for acute respiratory infections
When: Tue, May 6, 2025 - 12:30pmWhere: Kirwan Hall 3206
Speaker: Dr. Velasco-Hernández (National Autonomous University of Mexico, Institute of Mathematics) - https://www.researchgate.net/profile/Jorge-Velasco-Hernandez
Abstract: We describe two mathematical models developed or inspired by the traffic light system implemented in Mexico to control and mitigate the COVID-19 pandemic. The models are variants of the Kermack MacKendrick models. One proposes a minimal duration restriction strategy for contact rates and mobility, while the other models a traffic light system with different levels of perceived risk, utilizing DALYs to represent the socioeconomic context of the system.