Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation

by Thomas J. Jewell, Andrew L. Krause, Philip K. Maini, Eamonn A. Gaffney

We study how “chase-and-run” dynamics, where one group pursues while another escapes, are influenced by chirality, a left–right bias in movement seen in animals and cells. Using nonlocal (integro-differential) advection-diffusion models, we show that angled, chiral motion can strengthen pattern formation, prevent oscillations, and generate novel behaviours like rotating pulses of chasers and runners. We also show how these dynamics can determine whether populations mix or separate. By comparing linear stability analysis with numerical simulations, we reveal when standard theory holds and when it fails. Overall, our results highlight chirality’s potential broader role in shaping ecological and developmental patterns.

Left, a schematic showing a chiral chase-and-run interaction with a chaser cell, c, pursuing a runner cell, ρ. Their movement has a consistent clockwise or anticlockwise bias parameterised by the angles α. Right, a phase diagram of the model, showing the patterning outcome at different values of the chiral running angle and the ratio of diffusivities. Coloured regions are predicted by linear stability analysis and marked points are from numerical simulations.

…where we talk body clocks, timing your meds and, Ways and Means Subcommittees.

Dr. Olivia Walch is the CEO of Arcascope and an investigator at the University of Michigan, where she studies the mathematics of sleep and circadian rhythms through simulations and wearable devices.

She also has a penchant for boots in the winter.

Find out more about Olivia’s work at Arcascope: https://arcascope.com/

Buy her book Sleep Groove on bookshop.org

And for those of you wanting to learn more about the Geometry of Gerrymandering, check out the 2Scientists podcast episode with Dr. Thomas Weighill: https://2scientists.org/podcast/gerrymander.

Find out more about SMB on: 

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

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On the Improvement of the Sterile Insect Technique by Entomopathogenic Fungi: Impact of Residual Fertility and Re-mating Behaviour

by Yves Dumont

The Sterile Insect Technique (SIT) is a pest/vector control method that releases sterile males to disrupt reproduction. In Réunion, CIRAD's AttracTIS project targets the oriental fruit fly, studying how factors like residual fertility (ε), re-mating, and changes in female mating behavior affect SIT effectiveness. An analysis of our SIT structured model shows SIT works only if εR_S < 1, where R_S is the basic offspring number of sterile-mated females. Typically, the biology of double-sterile-mated females is overlooked. Combining SIT with entomopathogenic fungi, which shorten insect lifespans and reduce R_S, can allow for lower radiation doses, and thus improve sterile male fitness, or reduce the release rates. 

The compartimental diagram related to the SIT structured model with re-mating and residual fertility.

Dynamics and Persistence of a Generalized Multi-strain SIS Model

by Scott Greenhalgh, Tabitha Henriquez, Michael Frutschy, and Rebecah Leonard

Non-autonomous differential equation compartmental models are powerful tools for predicting trajectories of recurrent epidemics. However, using these models can complicate solution analysis compared to their autonomous counterparts, as the criteria for understanding long-term behavior are often only computable numerically. Our work presents a simple, yet general, non-autonomous SIS model with algebraic expressions for the stability and coexistence criteria of multi-strain periodic solutions, as well as a single-strain asymptotically periodic solution in terms of elementary functions. To illustrate our model’s utility, we fit it to US syphilis data, assessing its ability to match past trends and its predictive accuracy for future outbreaks.

A non-autonomous multi-strain SIS model: persistence of periodic solutions, co-existence, and an asymptotically periodic single-strain solution in terms of elementary functions.

Who should be controlled? The Role of Asymptomatic Individuals, Isolation and Switching in the Dominant Transmission Route in Classical and Network Epidemic Models

by Adriana Acosta-Tovar and Fabio Lopes

Understanding how infectious diseases spread is key to designing effective control strategies. We developed mathematical models to study infections with both direct (person-to-person) and indirect (environmental) transmission, using classical and EBCM-based approaches. Incorporating population heterogeneity gave a more realistic view of dynamics. We found that dominant pathways can shift over time—direct contact early on, environmental exposure later—showing the risk of relying only on early data. Our analysis highlights asymptomatic spread and the effectiveness of isolating symptomatic cases. These insights, relevant to diseases like Mpox or cholera, provide stronger tools for timely public health interventions. 

Who Should be Controlled?  An early dominance of direct transmission may shift toward indirect transmission in heterogeneous networks. In such cases, effective control may require a combination of isolation and environmental measures. This switching phenomenon also occurs in the homogeneous model and in Poisson networks.

Enhancing pedagogical practices with Artificial Neural Networks in the age of AI to engage the next generation in Biomathematics

by Jeremis Morales-Morales, Alonso Ogueda-Oliva, Carmen Caiseda, and Padmanabhan Seshaiyer

We propose leveraging both low-code and high-code programming approaches to facilitate a deeper understanding of Physics-Informed Neural Networks (PINNs) among the general student population, using the widely recognized SIR epidemiological model as a motivating example. 

C-MATH with PINN Framework.

…where we talk conference things in Canada.

The annual SMB meeting is THE international gathering for mathbio nerds, and this year was no exception. 673 conference attendees traveled from 34 countries around the world to meet up in Edmonton, Canada. Join us to learn more from some of these researchers and work on social media in outbreaks, bibliometric analyses and the occasional elk sighting.

• [00:41] Adam MacLean, University of Southern California, USA.

• [05:08] Amy Hurford, Memorial University, Newfoundland and Labrador, Canada.

• [09:45] Francisca Olajide, University of Ottawa, Canada.

• [16:41] Gosia Weh, Moffitt Cancer Center, Florida, USA.

• [22:16] Kira Pugh, Uppsala University, Sweden.

• [25:35] Luis Sordo Vieira, University of Florida, USA.

• [28:22] Mobolaji Williams, Howard University, Washington DC, USA.

• [33:43] Paul Macklin, Indiana University, USA.

• [41:01] Parmvir Bahia, Scientists Inc, Tampa, USA & Artha Science Media, London, UK.

• [47:15] Thomas Woolley, Cardiff University in Wales, UK.

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

Stability of difference equations with interspecific density dependence, competition, and maturation delays

by Geoffrey R. Hosack, Maud El-Hachem and Nicholas J. Beeton

The stability properties of delayed discrete-time model of interspecific competition are examined using directed graphs (figure). For a competitive multi-species model that extends the Beverton-Holt model, return towards the coexistence equilibrium after a local perturbation is guaranteed if intraspecific competition is stronger than interspecific competition. The rate of return depends on the species composition. This property is used to predict an optimised configuration of interspecific competition and rate of return for a system of morphologically indistinguishable species: Although direct observation of the species abundances in the field is not possible, available genotyping methods provide information on species composition. 

Directed graph for three species that connects the nodes of age classes zero (immature recruits) to mature adult stage individuals of age class delta with arcs: survival transitions are shown by red arrows, density dependent recruitment by black arrows, and interspecific interactions by blue arrows. These arcs form cycles that in turn provide sufficient conditions for the stable coexistence of species.

Theoretical Study of Retinoblastioma in the Hereditary and Non-hereditary Processes including the Cancer Growth

by Hiroshi Toki, Yoshiharu Yonekura, Yuichi Tsunoyama, and Masako Bando

Knudson’s two-hit hypothesis distinguished hereditary from sporadic cancers, but real-world incidence
often deviates from its predictions. Our 2P2H (two-period, two-hit) model refines this by incorporating
period-specific mutation rates, particularly after the proliferative phase of retinal cells. We propose that
mutation processes differ fundamentally between proliferative and post-developmental stages. Using
differential equations, we model the temporal evolution of mutation accumulation and cancer onset, while
also accounting for diagnostic time lag—a factor absent in Knudson’s theory. The 2P2H model
accurately reproduces observed incidence curves, resolving prior inconsistencies. We believe it provides
a more precise, biologically grounded framework for understanding cancer initiation.

The 2P2H Model.

Optimal Control of Immune Checkpoint Inhibitor Therapy in a Heart-Tumour Model

by Solveig A. van der Vegt, Ruth E. Baker, and Sarah L. Waters

In modelling the impact of cancer therapy, side effects are almost never explicitly considered, despite the severe risk they can pose to patients. Notably, immune checkpoint inhibitors (ICIs), a commonly used class of drugs, can cause autoimmune myocarditis. This paper presents a framework for optimising the timing of doses of ICIs, where both the effects on the tumour and on the heart are explicitly considered. It demonstrates that it is feasible, in regimes where standard-of-care schedules lead to autoimmune myocarditis, to identify dosing schedules that prevent cardiac side effects while inhibiting tumour growth. This framework represents a significant advancement towards the modelling of safe and effective cancer therapies.

A framework combining optimal control theory and a heart-tumour model which explicitly considers both the effects on the tumour and on the heart, can identify dosing schedules that prevent cardiac side effects while inhibiting tumour growth.