Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2510.19843

Memory Effects in Disease Modelling Through Kernel Estimates with Oscillatory Time History

Adam Mielke·Mads Peter Sørensen·John Wyller
View original source ↗Read source document ↗Export metadata ↓

Abstract

We design a linear chain trick algorithm for dynamical systems for which we have oscillatory time histories in the distributed time delay. We make use of this algorithmic framework to analyse memory effects in disease evolution in a population. The modelling is based on a susceptible-infected-recovered SIR - model and on a susceptible-exposed-infected-recovered SEIR - model through a kernel that dampens the activity based on the recent history of infectious individuals. This corresponds to adaptive behavior in the population or through governmental non-pharmaceutical interventions. We use the linear chain trick to show that such a model may be written in a Markovian way, and we analyze the stability of the system. We find that the adaptive behavior gives rise to either a stable equilibrium point or a stable limit cycle for a close to constant number of susceptibles, i.e.\ locally in time. We also show that the attack rate for this model is lower than it would be without the dampening, although the adaptive behavior disappears as time goes to infinity and the number of infected goes to zero.

Explore related subjects

q-bio.PE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Adam Mielke, Mads Peter Sørensen, John Wyller. 2025-10-19. Memory Effects in Disease Modelling Through Kernel Estimates with Oscillatory Time History. https://doi.org/10.1007/s00285-024-02080-1

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A conceptual predator-prey model with super-long transients

Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute to the coexistence of multiple time scales, adding to the complexity of the system. Typical dynamics in ecosystems, such as the persistence and coexistence of population cycles and chaotic behaviors, the emergence of super-long transients, regime shifts, and the quantifying of resilience, are encapsulated within this single model. The simplicity of our model allows for detailed analysis, reinforcing its potential as a conceptual tool for understanding ecosystems deeply.

q-bio.PE↗
arXiv2026

Mutation Order and Selection Shape Intratumor Heterogeneity in Tumor Evolution

Cancer progression often requires multiple driver mutations, but the same drivers may be acquired in different orders. How these pathways jointly shape tumor clonal structure remains unclear. We develop a multitype branching-process model in which malignant transformation requires two driver mutations, distinguishing malignant cells by mutation order and the independent transformation event that founded their clone. Under a successive exponential approximation, we establish point-process limits for pathway-specific clone sizes and derive a closed-form expression for the limiting expected Simpson's index of the combined malignant population. When both mutation orders yield malignant cells with the same net growth rate, the index decomposes into effective pathway weights, determined by mutation rates and birth-death dynamics at preceding stages, and within-pathway concentration terms, determined by intermediate-to-malignant growth-rate ratios. A driver's effect on heterogeneity thus depends critically on when it is acquired. A strong driver acquired early expands the intermediate lineage and increases the supply of independent malignant founders, whereas the same driver acquired last strengthens the growth and age advantage of early-founded malignant clones. Under additive fitness effects, these opposing mechanisms can produce a non-monotone relationship between selective advantage and clonal concentration. Threshold-like non-additive fitness effects can generate highly concentrated malignant populations, while order-dependent terminal fitness causes the faster-growing pathway to dominate asymptotically. These results show how mutation order, mutational accessibility, selection, and epistasis jointly determine lineage-level intratumor heterogeneity.

q-bio.PE↗
arXiv2026

Phase transitions in microbial lineage trees

Microbial populations exhibit high cell-to-cell variability, which fundamentally shapes population behavior. A striking consequence is the existence of phase transitions, where small genetic or environmental changes trigger abrupt shifts in population dynamics. While biological phase transitions have often been proposed, connecting observed behavior to the underlying physics has remained challenging. We combine population genetics with statistical physics to show how phase transitions arise naturally in microbial populations. We highlight the existence of a first-order transition in a model of bacterial plasmid engineering and find a strict lower bound on the number of plasmids that can be stably maintained in a population.

q-bio.PE↗