Emergence of Bursting and Delay-Induced Spiral Patterns in Eco-Epidemiological Systems

by Namrata Mani Tripathi

Understanding the spatio-temporal dynamics of interacting populations is crucial for ecological systems. We develop an eco-epidemic model with susceptible and infected prey and predators, incorporating carryover $(f_1)$, fear $(f_2)$, and recovery $(\gamma)$. Existence, boundedness, and Hopf bifurcation are established. Without delays, $f_1$ stabilizes while $f_2$ destabilizes dynamics, and recovery affects populations. With delays, chaotic oscillations and bursting arise in unstable regimes, while sufficient recovery suppresses delay effects. Spatial analysis shows Turing patterns, where delays and recovery shape spirals and clusters, influencing ecosystem stability.

Delay-driven eco-epidemic dynamics illustrating how fear, carryover, and recovery generate chaotic oscillations and spiral pattern formation in space.

Final-size solutions for SIRI models with vaccination

by Maria A. Gutierrez and Julia R. Gog

This work extends the deterministic SIR epidemic model to allow reinfections of individuals in the recovered compartment. Hosts with prior immunity, elicited from vaccination or a past infection, are less susceptible to the disease. We interpret partial host immunity as either all-or-none or leaky. For both interpretations, we find final-size solutions for the cumulative number of reinfections and primary infections across a transient epidemic wave. These analytical expressions depend on the vaccination coverage of the host population, the vaccine efficacy on naive hosts, the relative susceptibility to reinfection, and the basic reproduction number (R0). If R0 is above a reinfection threshold, the leaky model has an endemic equilibrium.

Graphical abstract

Observer-Based Source Localization in Tree Infection Networks via Laplace Transforms

by Graham Kesler O’Connor, Julia M. Jess, Devlin Costello, Manuel E. Lladser

Pinpointing "patient zero" in an outbreak, whether a biological disease, a computer virus, or rumor is notoriously difficult. Our paper introduces two new statistical methods based on Laplace transforms to trace the origin of an infection in tree networks when only a subset of nodes report their infection times. This makes our methods suitable for any situation in which a susceptible-infected (SI) infection spreads through a network without loops, with infected nodes infecting susceptible neighbors after random, independent delays, with explicit Laplace transforms. In particular, our methods provide public health, cybersecurity, and intelligence officials with a general tool for tracing and containing outbreaks.

Middle: Formulation of the observers' infection times using Laplace transforms of the edge delays, alongside a proposed source estimator derived from the empirical Laplace transform of the observers. Left: Source localization on a linear network with node 0 as the sole observer, as the infection source shifts from node 1 to node 10. Right: Source localization performance along the Thukela River basin, where the leftmost node is the true source, estimated using the simulated infection times of three downstream observers selected at random.

Join SMB and Springer Nature on June 15, 11:00AM ET for a new virtual workshop designed to provide early career researchers and authors of varying degrees of experience with the guidance necessary to get published and disseminate their research to as broad an audience as possible. Making informed choices about which journals are right for your submissions is key to navigating the complex academic journals landscape. But this is just one step in a multifaceted process that begins with the best ways to present your research topic to an editorial board and ends with the promotion of your published article to your communities for maximum impact. We will also touch upon other trends in the academic literature, including those dubious journals and publishing opportunities that researchers need to be aware of and vigilantly avoid.

Open Science Presentation:
We will also tell you about the ways we are empowering researchers to advance discovery, including Springer Nature's open access strategies and policies and their overarching commitment to an open science future.

Register for this session today! 

Stochastic Analysis of Taxis and Kinesis Properties of Colonial Protozoa

by Yonatan L. Ashenafi & Peter R. Kramer

This study asks whether cells that navigate well alone can still find oxygen or food after joining a colony. Using a choanoflagellate-inspired mathematical model, it shows that colony life can completely change the rules: a steering-based strategy (taxis) that works for single cells can break down collectively, with competing forces even pushing the colony the wrong way. By contrast, a noise-tuning strategy (kinesis) stays remarkably effective, allowing colonies to keep climbing gradients even under adversarial flagellar arrangements. The work shows how reliable collective motion can emerge from noisy, imperfect parts and offers design ideas for simple adaptive microrobotic swarms.

Schematic of the taxis and kinesis flagellar-response models for cells within a colony in the presence of an environmental gradient (blue arrows). Left: Colony of taxis-enabled cells. The red arrow indicates the biased flagellar force direction that would generate a torque tending to rotate the cell so that it swims up the environmental gradient. Right: Colony of kinesis-enabled cells. The red wedge indicates the estimated range of motion of the beating flagellum.

From Outbreak to Endemicity or Control: Tracking First Passage Time in Infectious Diseases

by Olusegun M. Otunuga

Understanding when an outbreak will stabilize or resurge is central to infectious disease control. This study introduces a probabilistic framework to predict the timing of epidemic transitions. Rather than focusing only on whether a disease persists, we examine when transmission shifts from growth to endemic stability or control. The approach centers on the effective reproduction number, R(t), which indicates whether spread is expanding or declining. Because transmission changes with behavior, immunity, and policy responses, we incorporate uncertainty into our model. We evaluate when transmission first reaches critical thresholds, whether fixed or time-varying targets reflecting evolving public health conditions and adaptive interventions.

Tracking First Passage Time to Endemicity or Control in Infectious Diseases

…where we talk: biochemical reactions, world famous awards, and rainy days making soup by the beach.

Alicia Dickenstein is Professor Emerita at the University of Buenos Aires. She's President of the National Academy of Exact and Natural Sciences of Argentina and served as Vice President of the IMU. She has received many awards and participated in numerous outreach activities including writing books about mathematics for children.

Learn more about Alicia’s research on her website: http://mate.dm.uba.ar/~alidick

Find out more about the events around: Ada Lovelace day (in Spanish), and the Brazilian Math Olympiad. 

Find out more about SMB on: 

• Twitter: @smb_mathbiology 
• Bluesky: @smbmathbiology.bsky.social 
• Facebook: @smb.org 
• Linkedin: @smb_mathbiology 
• The Bulletin of Mathematical Biology

Apple Link      Spotify Link     Read the full transcript

Mathematical Analysis for a Class of Stochastic Copolymerization Processes

by Lukas Eigentler and Mattia Sensi.

Self-replicating polymers that encode genetic information are central to the origin of biological information. We study a stochastic model of a copolymerization process in which finitely many monomer types attach to or detach from the tip of a polymer, with distinct but fixed binding affinities. We determine a sharp criterion for when the process is recurrent (the polymer length fluctuates around a finite value) or transient (the polymer length diverges to infinity). In the transient case, we characterize both the long-term composition of the polymer and its rate of growth. We place these results on a rigorous probabilistic foundation that provides a precise derivation of predictions from earlier work and enables further generalizations.

Wavelength selection for periodic travelling waves: an unsolved problem

by Lukas Eigentler and Mattia Sensi.

Many models for spatio-temporal patterns admit periodic travelling wave solutions (PTWs) and predict that PTWs can undergo wavelength changes as model parameters are varied; for example leading to ecological theory that dryland vegetation patterns can adaptively change their wavelength to adapt to climate change. While PTW destabilisation is well-understood thanks to Busse balloon theory, we lack understanding of what determines wavelength selection during PTW-to-PTW transitions. In this unsolved problems article, we review the state of the art in predicting PTW destabilisation and knowledge of wavelength selection principles in special cases. We present new numerical data, hoping to stimulate new research into this open problem.

Busse balloon for a model of dryland vegetation patterns showing jumps between wavelength contours.

Time-series models can predict long periods of human temporal EEG responses to randomly alternating visual stimuli

by Richard Foster, Connor Delaney, Dean Krusienski, and Cheng Ly

Brain activity with regularly flickering images has a rhythmic pattern that matches the flicker rate in electroencephalography (EEG) measurements. When the flicker speed changes randomly, the brain’s responses are more complicated. We recorded EEG signals in humans while viewing randomly alternating visual scenes. We tested how well statistical models capture and predict features of EEG. The models ranged from a simple one that used only past EEG values to more complex versions that added extra factors. Although all models considered were able to describe and predict key features of the EEG, the simplest model surprisingly performed as well—and sometimes better—than the more complicated ones. Therefore, simple models are worth considering.

Simpler statistical models can out perform complicated ones for capturing visual cortex EEG.