Abstract: Massive increases in the availability of animal tracking data presents rich opportunities for mathematical modeling and statistical analyses. This seminar will provide an overview of how non-Markovian stochastic processes are being used to understand animal movement and space use, especially the structure of individuals’ so-called ‘home ranges.’ I will focus on the area of ‘cognitive movement ecology’ that seeks to build bridges between animal movement and such biologically rich topics as memory and learning. Previous work has addressed the importance of reused pathways for movement in a range of biological systems from ants to elephants. Here I report on results from a study that brought together a global database of almost 1300 GPS movement tracks from range-resident mammalian carnivores to test—for free-ranging animals in the wild—predictions from laboratory experiments investigating aspects of animal cognition. By calculating the location of ‘probability ridges’ within each individual’s 2D home range, we developed a statistical metric that provides a concise summary of internal home range structure, identifying the extent to which travel is concentrated along favored routes. Using these ridges in a comparative analysis, we found strong evidence for a clade-level difference in the carnivores’ reliance on preferred travel routes. On average, home ranges of canids featured ~30% greater ‘ridge density’ than did felids, after fully controlling for effects of body mass, environmental covariates, hunting strategy, home range size, and phylogenetic correlation. Providing the first large-scale, ‘in the wild’ support for experimental predictions concerning evolutionary differences in the nature of spatial memory among carnivores, we found that felids tended to rely on a reduced set of heavily traveled routes for movement whereas canids employed less spatially intensive movement. These differences, which suggest a greater reliance among canids on navigation via higher-level cognitive processes such as path integration and cognitive maps, have critical implications for how predators use space and interact with mobile resource species.
Abstract: Including diffusion in the classical framework of SIR equations in epidemiology leads to reaction-diffusion systems. In epidemiology, diffusion arises under several guises. After reviewing some classical results, Prof. Berestycki will present recent and ongoing work on spatial spreading, social diffusion, and diffusion on graphs motivated by the Covid-19 pandemic.
Abstract: Accurate, reliable, and timely estimates of pathogen variant risk are essential for informing public health responses. Unprecedented rates of genomic sequencing have generated new insights into variant dynamics. However, estimating the fitness advantage of a novel variant shortly after emergence, or its dynamics more generally in data-sparse settings, remains difficult. This challenge is exacerbated in countries where surveillance is limited or intermittent. To stabilize inference in these data-sparse settings, we develop a hierarchical modeling approach to estimate variant fitness advantage and prevalence by pooling data across geographic regions. We demonstrate our method by reconstructing SARS-CoV-2 BA.5 variant emergence, and assess performance using retrospective, out-of-sample validation. We show that stable and robust estimates can be obtained even when sequencing data are sparse. Finally, we discuss how this method can inform risk assessment of novel variants and provide situational awareness on circulating variants for a range of pathogens and use-cases.
Abstract: Many inexperienced long-distant bird, insect and turtle migrants reach remote non-breeding destinations independently, using inherited geomagnetic or celestial compass cues. Inexperienced migrants are also proposed to detour unfavorable regions using inherited geomagnetic signposts to trigger switches in migratory headings (Zugknicks). However, the overall relative feasibility among migratory compass courses and signposts (often termed clock-and-compass migration) remains uncertain, particularly at population levels. To address these unknowns, I developed a compass-based migration model incorporating spatiotemporal geomagnetic data (1900-2023) and an evolutionary algorithm, accounting for trans-generational changes in inherited geomagnetic headings and signposts through population mixing and natal dispersal. Signposted trans-hemispheric songbird migrations remained viable over the 124-year period, including through a highly geomagnetically unstable region (East-arctic North America and Greenland) and across a migratory divide maintained through dominant allelic inheritance. The key role of intrinsic variability in inheritance of headings is also discussed. Finally, I discuss how migratory orientation programs could both mediate and constrain evolution of routes in response to global climate change.
Abstract: In this talk, I will discuss my work on the interplay between human behavior and infectious diseases: how human activity can impact epidemic dynamics and how people respond to outbreaks. First, I will develop a compartmental model to demonstrate how awareness-based behavior with group-level heterogeneity in decision-making and disease risk can produce complicated and counterintuitive epidemic dynamics. Second, I will use a Twitter data set containing over 4.2 million posts about COVID-19 vaccines from April 2021 to characterize an understudied set of potential anti-vaccine influencers: perceived experts (i.e., people who signal expertise in the biomedical sciences).
Abstract: Studying the evolution of dispersal is important for understanding how populations are distributed in space and how species adapt to changing environments spatially. In this talk, I will present some recent work using integrodifference equation models to study the evolution of dispersal. Integrodifference equations (IDEs) are discrete-time dynamical systems that describe the dynamics of a population distributed over continuous space. In an IDE, dispersal from one location to another is modeled by the kernel of an integral operator referred to as the “dispersal kernel”. We begin with a model where the dispersal kernels are fixed over time, and use pairwise invasion analysis to find which kernels correspond to evolutionarily stable strategies (each kernel is considered a dispersal “strategy”) when there is spatial heterogeneity and seasonal variation. We prove that the evolutionarily stable strategies are the ones that can produce an ideal free distribution (a result also shown in previous studies using other model frameworks). We then develop a model where the dispersal kernel evolves over time by incorporating spatial memory and learning. If the environment is temporally static, the model has an equilibrium corresponding to the ideal free distribution. The simulation results indicate some level of convergence towards this equilibrium even when the environment changes over time. Overall, the mechanism proposed in the second model shows a possible way for the dispersal kernel of a population to evolve towards one that is ideal free.
Abstract: The modern medical perspective on neurological diseases has evolved, slowly, since the 20th century but recent breakthroughs in medical imaging have quickly transformed medicine into a quantitative science. Today, mathematical modeling and scientific computing allow us to go farther than observation alone. Bringing together neuroimaging and mesh generation tools together with numerical methods and scientific computing, experimental and data-informed mathematical models are leading to new clinical insights into serious diseases that affect the nervous system.
In this talk, I will discuss some foundations for modeling the brain on both short and long time scales. Topics covered will include an introduction to continuum multi-fluid porous tissue models of the brain, numerical methods for porous multifluid models and the use of high-dimensional network dynamical systems to model neurodegenerative diseases such as Alzheimer's disease. Along the way, we will see how magnetic resonance imaging can be used to extract the computational assets that are essential for patient-specific mathematical brain modeling.
Abstract: There are predator-prey biological systems in which the roles of the prey and the predator changes as a function of time and/or the size of the species. We develop a mathematical model for such predator-prey reversal systems. Our mathematical model is constructed as an age-structured model, which allows us to capture the change in roles as a function of time. We study different modes of transitioning from a young population to adult population. We further study the behavior in the trophic constants of the model which allow us to obtain biological meaningful results. This is a joint work with Professors Bill Fagan, Maria Cameron, and Doron Levy.
Title: Towards a novel behavior-epidemiology modeling framework for pandemics of respiratory pathogens
Abstract: The recent COVID-19 pandemic, caused by SARS-CoV-2, has highlighted the importance of explicitly incorporating human behavior into mathematical models for the transmission dynamics and control of emerging, resurging and re-emerging respiratory pathogens. Models that did not explicitly account for the impacts of human behavior changes during the epidemic often had limited predictive power due to distinctly human phenomena such as masking fatigue. In this lecture, I will present a new mathematical framework for incorporating human behavior changes and social influences (as a driver for positive or negative human behavior changes with respect to adherence to control and mitigation measures or overall attitude towards the pandemic) on the transmission dynamics of a respiratory pathogen of major public health significance. The two models to be presented include one probabilistic network model based on a high school contact dataset and one more classical compartmental model that brings in elements of social influence dynamics. I will discuss the merits and demerits of these various modeling types within this framework, and how they might be combined to potentially enhance the predictive capacity of the modeling framework. This is a joint work with Professors Abba Gumel and Michelle Girvan.
Abstract: Temperate viruses use a variety of strategies to reproduce - ranging from lytic to lysogenic. The basic reproduction number, R0, provides a useful measure of the instantaneous fitness of different viral strategies and their dependence on the factors such as host availability, virus-host ratios and host physiology. However, periodic changes in these factors can create trade-offs between short-term and long-term fitness. In this talk, I will present a computational framework that allows us to examine generalized drivers of viral strategies in periodic environments. We use a compartmental model with a periodic filter to model the eco-evolutionary dynamics of the resource-host-virus system. The filtration step involves differential dilution of susceptible hosts, infected cells and viruses in the system. By choosing appropriate dilution factors, we can create different short-term and long-term selection pressures that may give rise to distinct (and opposing) pressures on viral strategies. In doing so, we also investigate the evolution of viral plasticity, i.e. how the probability of lysogen formation changes in response to cellular multiplicity of infection.
Abstract: Biological systems are traditionally studied as isolated processes (e.g. regulatory pathways, motor protein dynamics, transport of organelles, etc.). Although more recent approaches have been developed to study whole cell dynamics, integrating knowledge across biological levels remains largely unexplored. In experimental processes, we assume that the state of the system is unknown until we sample it. Many scales are necessary to quantify the dynamics of different processes. These may include a magnitude of measurements, multiple detection intensities, or variation in the magnitude of observations. The interconnection between scales, where events happening at one scale are directly influencing events occurring at other scales, can be accomplished using mathematical tools for integration to connect and predict complex biological outcomes. In this work, we focus on building inference methods to study the complexity of the cytoskeleton from one scale to another. We rely on single particle tracking techniques based on stochastic models and explore long-term dynamics of the systems.
Abstract: Antibiotic resistant bacteria are a serious global health threat. As a result, bacteriophage (or 'phage' -- viruses that exclusively infect and lyse bacteria) are increasingly considered as a therapeutic alternative to treat bacterial infections. In this talk I will showcase two examples of how evolutionary processes arising from phage-bacteria interactions pose challenges to phage therapy, but also present opportunities to design successful treatments. The first study examines the efficacy of a phage 'cocktail' composed of two phages that exploit different adsorption routes, via a combination of vitro experiments and nonlinear dynamics models. We analyze a theoretical model of in vivo infection dynamics, where therapeutic phage and the innate immune system can work synergistically to prevent infection, showing if and when the phage cocktail can control the bacterial population. In the second study, I present a model of co-evolving populations of phages and bacteria, given the important role of resistance and counter-resistance in shaping therapeutic outcomes. We aim to address how cross-infection structure and phage and bacterial diversity affect one another in the presence of the immune system. Studying such a model may help us understand how to use evolutionarily aware phage as a means to steer, and potentially control, bacterial evolution in therapeutic settings.
Abstract: Talk 1 (Arani): Mathematically modeling pseudolysogeny in M1 Salinibacter Ruber and EM1 Holosalinivirus Abstract: Bacteriophage are conventionally thought to have two infection strategies: lysis and lysogeny. However alternative infection strategies such as pseudolsyogeny have recently been discovered and require study. Pseudolysogeny occurs when the infecting phage resides intracellularly yet extrachromosomally within its host. This allows the phage genome to passively sustain in the population through asymmetrical division amongst the host’s daughter cells. We attempt to model pseudolysogeny in M1 Salinibacter Ruber and its bacteriophage EM1 Holosalinivirus, to succeed where models that only consider lytic and lysogenic strategies have failed. We build a nonlinear ODE model that accounts for pseudolysogeny, as well as features such as lysis inhibition and multiplicity of infection. We aim to use our model’s success to highlight mechanisms of pseudolysogeny and motivate more study into alternative phage infection strategies.
Talk 2 (Dey): Inferring (higher-order) interactions in complex virus-bacteria communities In complex natural ecosystems multiple species of viruses and their bacterial hosts coexist together. Understanding the ecological life-history traits of virus-host interactions as well as “who interacts with whom” are essential for understanding downstream ecological and evolutionary outcomes. Here we study the in vitro temporal population dynamics of a 5×5 host-virus model community for all the species together as well as when they are in isolated pairs. We find evidence suggesting that the Bayesian inferred virus-host life history traits and mechanistic models from pairwise experiments are inadequate to recapitulate the experimentally observed population dynamics of the community. This inadequacy is addressed by invoking context-dependent shifts in interactions and other emergent higher-order effects, potentially explaining coexistence of multiple virus-host species in a natural ecosystem.
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