Final size index-driven strategies for cost-effective epidemic management in metapopulation

by Uvencio José Giménez-Mujica; Jorge Velázquez-Castro; Andrés Anzo-Hernández, and Ignacio Barradas

Designing epidemic control strategies in metapopulations is essential for public health policies. In this article, we propose an efficient resource allocation methodology that considers the epidemic response and the cost of implementing a control strategy in given areas. Using a metapopulation SEIR model, we derive the final epidemic size in each area and propose an index to guide the control strategy. We compare the index with intuitive strategies: allocating all resources to the most affected area and distributing them equitably. We show that an allocation proportional to the index optimizes distribution, avoiding resource concentration in a few areas, keeping local peaks low, and ensuring a balanced epidemic impact across the network.

Right side. Epidemic peak reduction using the proposed index. Left side: Comparison of different control strategies using a network constructed with the ER algorithm.

Modelling Population-Level Hes1 Dynamics: Insights from a Multi-framework Approach

by Gesina Menz and Stefan Engblom

We investigate the behaviour of the Hes1-Delta-Notch signalling pathway governing cell differentiation during neuronal development using both an ordinary differential equation (ODE) model and a related reaction-diffusion master equation (RDME) framework. The ODE model captures transient oscillatory behaviour followed by stable patterning reflecting cell differentiation into neurons and glial cells and is reduced for analytical tractability. The RDME approach, however, allows us to assess the impact of intrinsic noise on pattern formation. Together, the models show that the characteristic dynamics are robust under stochastic fluctuations and that the deterministic stability analysis reflects behaviour in the stochastic setting.

Modelling the Hes1-Notch GRN using both ODE and RDME models allows us to capture behaviour in the deterministic and stochastic settings.

Modeling the effects of a Shock-and-Kill Treatment for HIV: Latency-Reversing Agents and Natural Killer Cells

by Guyue Liu, Suli Liu, Chiyu Zhang, Xu Chen, Wenxuan Li, and Huilai Li

Despite ART's success in suppressing HIV, viral reservoirs persist as barriers to cure. This study leverages a mechanistically grounded mathematical model, calibrated with HIV-1-infected humanized mice data via Bayesian MCMC, to decode how tripartite therapy (ART + LRAs + NK cells) eradicates reservoirs.
Key findings:

(1) NK cells are pivotal modulators - their infusion frequency and dosage critically determine cure likelihood.

(2) The tripartite therapy offers superior viral suppression and accelerated therapeutic effects, with a specific parameter region for achieving a cure of HIV.

Graphical Abstract.

Nutrient-Driven Adaptive Evolution of Foraging Traits Impacts Producer-Grazer Dynamics

by Oluwagbemisola Oladepo, and Angela Peace

Grazers like Daphnia adjust feeding to cope with changes in food quality and availability, while producers like algae vary in abundance and nutrient content. This study uses models to compare fixed and adaptive foraging strategies in grazers. Results show that adaptive foraging can support survival in nutrient-poor environments, acting as evolutionary rescue. However, rapid adaptation may lead to population fluctuations and increase extinction risk. These findings highlight when adaptive foraging aids grazer persistence and when it may destabilize ecosystems, informing our understanding of ecological resilience. 

Nutrient-Driven Adaptive Evolution of Foraging Traits Impacts Producer-Grazer Dynamics: A Graphical Abstract.

Understanding Immune Dynamics in Liver Transplant Through Mathematical Modeling

by Julia Bruner, Kyle Adams, Skylar Grey, Mahya Aghaee, Sergio Duarte, Ali Zarrinpar, and Helen Moore

Liver transplantation is a life-saving procedure for the treatment of end-stage liver disease. However, transplant recipients must take immunosuppressive medications for the rest of their lives, in order to prevent their immune system from attacking and causing damage to the donor liver (known as “rejection”). Although immunosuppressive therapies are necessary to prevent rejection, extended or excessive immunosuppression can lead to life-threatening infections or cancer. We built and analyzed a mechanistic mathematical model to study the immune dynamics involved in the balance between immunosuppression and rejection. Our model identified dynamics between the following quantities as most critical to this immune balance: a type of immune cell called cytotoxic T cells; the inflammation-modulating protein interleukin-2 and the transplanted liver itself. 

Graphical abstract of the study.

The pathogenesis of papilledema: review of the literature and a new hypothesis

by David N. Levine and Ari I. Rapalino

Papilledema, or swelling of the head of the optic nerve, occurs when intracranial pressure exceeds intraocular pressure to an abnormal degree. We conducted a biomechanical analysis of the effect of such excess pressure on the optic nerve. The stresses created in the nerve are: 1) a gradient of tissue pressure and 2) an axially oriented shear stress. Both are sharply localized to the region where the optic nerve exits the eye, and the excessive external pressure on the nerve begins. The gradient of tissue pressure liquifies the axoplasmic gel inside some of the axons – particularly those of large diameter located peripherally in the nerve cross-section - and displaces it towards the cell body, causing swelling of the optic nerve head. 

High intracranial pressure displaces axoplasm from the extraocular portion of the optic nerve into the intraocular portion, causing swelling of the head of the optic nerve.

Impacts of Tempo and Mode of Environmental Fluctuations on Population Growth: Slow- and Fast-Limit Approximations of Lyapunov Exponents for Periodic and Random Environments

by Pierre Monmarché, Sebastian J. Schreiber and Édouard Strickler

This work derives analytical approximations for how environmental fluctuation frequency affects population growth in structured populations experiencing periodic or random switching between environmental states. Key findings: (1) In slow-switching limits, periodic and random fluctuations have equivalent effects on growth rates, but differ significantly in fast-switching limits. (2) Applications to metapopulation models show that slower environmental switching promotes persistence, with random environments allowing higher switching frequencies for persistence than periodic ones. The results demonstrate that both tempo (frequency) and mode of environmental fluctuations critically influence population dynamics. 

Population growth rates in a fluctuating two-patch environment. Both tempo (slow vs. fast) and mode (random vs. periodic) can determine persistence.

… where we talk: Random openings in neurons, Gumbatine, and conferences in Canada.

Jay Newby graduated from the University of Utah Math Biology program in 2010. He was supervised by Paul Bressloff. His expertise includes applied stochastic processes, mathematical modeling, and machine learning tools for bio-image analysis systems.

Learn more about Jay’s work on his webpage: https://sites.ualberta.ca/~jnewby/
Find the weather app we talked about here: earth.nullschool.net
And you can find out about SMB’s annual meeting here: https://2025.smb.org/.

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• Twitter: @smb_mathbiology 
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• The Bulletin of Mathematical Biology

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Matching Habitat Choice and the Evolution of a Species' Range

by Farshad Shirani and Judith R Miller

It is reasonable to think that when individuals of a species detect habitat favorable for their characteristics, they move towards it—a phenomenon called matching habitat choice (MHC). However, this behavior is relatively rare in nature, and a major goal of the present research is to understand why this is so. By developing a model of a species’ range evolution using PDEs and numerically solving the equations, we found that MHC is likely to be prevalent only in environments whose conditions change dramatically over a short distance relative to the movement ability of the organism. Further, when MHC does occur, it increases the spread rate of an invasive species and enhances the species’ chance of survival in rapidly changing environments. 

Matching Habitat Choice and the Evolution of a Species' Range: A Graphical Abstract.