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Tyll Krueger

Publications and source records attributed to Tyll Krueger.

At least 19 recordsLinked to original sources
arXiv2026

Household size can explain 40% of the variance in cumulative COVID-19 incidence across Europe

Household size impacts the spread of respiratory infectious diseases: Larger households tend to boost transmission by acquiring external infections more frequently and subsequently transmitting them back into the community. Furthermore, mandatory interventions primarily modulate contagion between households rather than within them. We developed an approach to quantify the role of household size in epidemics by separating within-household from out-household transmission, and found that household size explains 41% of the variability in cumulative COVID-19 incidence across 34 European countries (95% confidence interval: [15%, 46%]). The contribution of households to the overall dynamics can be quantified by a boost factor that increases with the effective household size, implying that countries with larger households require more stringent interventions to achieve the same levels of containment. This suggests that households constitute a structural (dis-)advantage that must be considered when designing and evaluating mitigation strategies.

q-bio.PE↗
arXiv2025

Coupling opinion dynamics and epidemiology

This research investigates the coupled dynamics of behavior and infectious disease using a mathematical model. We integrate a two-state q-voter opinion process with SIS-type infection dynamics, where transmission rates are influenced by the opinion and an infection-induced switching mechanism represents individuals reassessing their behavior upon infection. Analytically, we derive conditions for the stability of endemic and disease-free equilibria. Numerical simulations reveal complex dynamics: above a certain infectivity threshold, the system can exhibit alternative basins of attraction leading to a balanced endemic fixed point or stable limit cycles. Notably, the dominant asymptotic opinion and resulting epidemiological outcomes show non-monotonic relationships with infectivity, highlighting the potential for adaptive behavior to induce complex system dynamics. These findings underscore the critical role of social interventions; shifts in behavioral norms and trust can permanently alter epidemic outcomes, suggesting that such interventions are as crucial as biomedical controls

physics.soc-ph↗
arXiv2025

Modelling variability of the immunity build-up and waning following RNA-based vaccination

RNA-based vaccination has been broadly applied in the COVID pandemic. A characteristic of the immunization was fast waning immunity. However, the time scale of this process varied considerable for virus subtypes and among individuals. Understanding the origin of this variability is crucial in order to improve future vaccination strategies. Here, we introduce a mathematical model of RNA-based vaccination and the kinetics of the induced immune response. In the model, antigens produced following vaccination rise an immune response leading to germinal center reactions and accordingly B-cell differentiation into memory B-cells and plasma cells. In a negative feedback loop, the antibodies synthesized by newly specified plasma cells shut down the germinal center reaction as well as antigen-induced differentiation of memory B-cell into plasma cells. This limits the build-up of long-lasting immunity and thus is accompanied by fast waning immunity. The detailed data available on infection with and vaccination against SARS-CoV-2 enabled computational simulation of essential processes of the immune response. By simulation, we analyzed to which extent a single or double dose vaccination provides protection against infection. We find that variability of the immune response in individuals, originating e.g. in different immune cell densities, results in a broad log-normal-like distribution of the vaccine-induced protection times that peaks around 100 days. Protection times decrease for virus variants with mutated antibody binding sites or increased replication rates. Independent of these virus specifics, our simulations suggest optimal timing of a second dose about 5 weeks after the first in agreement with clinical trials.

q-bio.PE↗
arXiv2025

Block Graph Neural Networks for tumor heterogeneity prediction

Accurate tumor classification is essential for selecting effective treatments, but current methods have limitations. Standard tumor grading, which categorizes tumors based on cell differentiation, is not recommended as a stand-alone procedure, as some well-differentiated tumors can be malignant. Tumor heterogeneity assessment via single-cell sequencing offers profound insights but can be costly and may still require significant manual intervention. Many existing statistical machine learning methods for tumor data still require complex pre-processing of MRI and histopathological data. In this paper, we propose to build on a mathematical model that simulates tumor evolution (O\.{z}a\'{n}ski (2017)) and generate artificial datasets for tumor classification. Tumor heterogeneity is estimated using normalized entropy, with a threshold to classify tumors as having high or low heterogeneity. Our contributions are threefold: (1) the cut and graph generation processes from the artificial data, (2) the design of tumor features, and (3) the construction of Block Graph Neural Networks (BGNN), a Graph Neural Network-based approach to predict tumor heterogeneity. The experimental results reveal that the combination of the proposed features and models yields excellent results on artificially generated data ($89.67\%$ accuracy on the test data). In particular, in alignment with the emerging trends in AI-assisted grading and spatial transcriptomics, our results suggest that enriching traditional grading methods with birth (e.g., Ki-67 proliferation index) and death markers can improve heterogeneity prediction and enhance tumor classification.

cs.CV↗
arXiv2024

Inter-city infections and the role of size heterogeneity in containment strategies

This study examines the effectiveness of regional lockdown strategies in mitigating pathogen spread across regional units, termed cities hereinafter. We develop simplified models to analyze infection spread across cities within a country during an epidemic wave. Isolation of a city is initiated when infection numbers within the city surpass defined thresholds. We compare two strategies: strategy (P) consists in prescribing thresholds proportionally to city sizes, while the same threshold is used for all cities under strategy (U). Given the heavy-tailed distribution of city sizes, strategy (P) may result in more secondary infections from larger cities than strategy (U). Random graph models are constructed to represent infection spread as a percolation process. In particular, we consider a model in which mobility between cities only depends on city sizes. We assess the relative efficiency of the two strategies by comparing the ratios of the number of individuals under isolation to the total number of infections by the end of the epidemic wave under strategy (P) and (U). Additionally, we derive analytical formulas for disease prevalence and basic reproduction numbers. Our models are calibrated using mobility data from France, Poland and Japan, validated through simulation. The findings indicate that mobility between cities in France and Poland is mainly determined by city sizes. However, a poor fit was observed with Japanese data, highlighting the importance to include other factors like e.g. geography for some countries in modeling. Our analysis suggest similar effectiveness for both strategies in France and Japan, while strategy (U) demonstrates distinct merits in Poland.

physics.soc-ph↗
arXiv2023

On the complexity of polygonal billiards

We show that the complexity of the billiard in a typical polygon grows cubically and the number of saddle connections grows quadratically along certain subsequences. It is known that the set of points whose first n-bounces hits the same sequence of sides as the orbit of an aperiodic phase point z converges to z. We establishe a polynomial lower bound estimate on this convergence rate for almost every z. This yields an upper bound on the upper metric complexity and upper slow entropy of polygonal billiards. We also prove significant deviations from the expected convergence behavior. Finally we extend these results to higher dimensions as well as to arbitrary invariant measures.

math.DS↗
arXiv2023

Linear and superlinear spread for continuous-time frog model

Consider a stochastic growth model on $\mathbb{Z} ^d$. Start with some active particle at the origin and sleeping particles elsewhere. The initial number of particles at $x \in \mathbb{Z} ^d$ is $η(x)$, where $η(x)$ are independent random variables distributed according to $μ$. Active particles perform a simple continuous-time random walk while sleeping particles stay put until the first arrival of an active particle to their location. Upon the arrival all sleeping particles at the site activate at once and start moving according to their own simple random walks. The aim of this paper is to give conditions on $μ$ under which the spread of the process is linear or faster than linear. The proofs rely on comparison to various percolation models.

math.PR↗
arXiv2023

SIR-Model for Households

Households play an important role in disease dynamics. Many infections happening there due to the close contact, while mitigation measures mainly target the transmission between households. Therefore, one can see households as boosting the transmission depending on household size. To study the effect of household size and size distribution, we differentiated the within and between household reproduction rate. There are basically no preventive measures, and thus the close contacts can boost the spread. We explicitly incorporated that typically only a fraction of all household members are infected. Thus, viewing the infection of a household of a given size as a splitting process generating a new, small fully infected sub-household and a remaining still susceptible sub-household we derive a compartmental ODE-model for the dynamics of the sub-households. In this setting, the basic reproduction number as well as prevalence and the peak of an infection wave in a population with given households size distribution can be computed analytically. We compare numerical simulation results of this novel household-ODE model with results from an agent--based model using data for realistic household size distributions of different countries. We find good agreement of both models showing the catalytic effect of large households on the overall disease dynamics.

q-bio.PE↗
arXiv2021

Regional estimates of reproduction numbers with application to COVID-19

In the last year many public health decisions were based on real-time monitoring the spread of the ongoing COVID-19 pandemic. For this one often considers the reproduction number which measures the amount of secondary cases produced by a single infectious individual. While estimates of this quantity are readily available on the national level, subnational estimates, e.g. on the county level, pose more difficulties since only few incidences occur there. However, as countermeasures to the pandemic are usually enforced on the subnational level, such estimates are of great interest to assess the efficacy of the measures taken, and to guide future policy. We present a novel extension of the well established estimator of the country level reproduction number to the county level by applying techniques from small-area estimation. This new estimator yields sensible estimates of reproduction numbers both on the country and county level. It can handle low and highly variable case counts on the county level, and may be used to distinguish local outbreaks from more widespread ones. We demonstrate the capabilities of our novel estimator by a simulation study and by applying the estimator to German case data.

stat.AP↗
arXiv2020

Spatial growth processes with long range dispersion: microscopics, mesoscopics, and discrepancy in spread rate

We consider the speed of propagation of a {continuous-time continuous-space} branching random walk with the additional restriction that the birth rate at any spatial point cannot exceed $1$. The dispersion kernel is taken to have density that decays polynomially as $|x|^{- 2α}$, $x \to \infty$. We show that if $α> 2$, then the system spreads at a linear speed, {while for $α\in (\frac 12 ,2]$ the spread is faster than linear}. We also consider the mesoscopic equation corresponding to the microscopic stochastic system. We show that in contrast to the microscopic process, the solution to the mesoscopic equation spreads exponentially fast for every $α> \frac 12$.

math.PR↗
arXiv2017

Conformity, anticonformity and polarization of opinions: insights from a mathematical model of opinion dynamics

Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper we present a version of the $q$-voter model of opinion dynamics with two types of response to social influence: conformity (like in original $q$-voter model) and anticonformity. We put the model on a social network with the double-clique topology in order to check how the interplay between those responses impacts the opinion dynamics in a population divided into two antagonistic segments. The model is analyzed analytically, numerically and by means of Monte Carlo simulations. Our results show that the systems undergoes two bifurcations as the number of cross-links between cliques changes. Below the first critical point consensus in the entire system is possible. Thus two antagonistic cliques may share the same opinion only if they are loosely connected. Above that point the system ends up in a polarized state.

physics.soc-ph↗
arXiv2013

Universally Typical Sets for Ergodic Sources of Multidimensional Data

We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an $h_0$ with probability one and whose cardinality grows at most at exponential rate $h_0$.

cs.IT↗
arXiv2010

Passive Supporters of Terrorism and Phase Transitions

We discuss some social contagion processes to describe the formation and spread of radical opinions. The dynamics of opinion spread involves local threshold processes as well as mean field effects. We calculate and observe phase transitions in the dynamical variables resulting in a rapidly increasing number of passive supporters. This strongly indicates that military solutions are inappropriate.

physics.soc-ph↗
arXiv2007

Quantisations of piecewise affine maps on the torus and their quantum limits

For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to invariant measures of the classical system, the so called quantum limits, and one would like to understand which invariant measures can occur that way, thereby classifying the semiclassical behaviour of eigenfunctions. We introduce a class of maps on the torus for whose quantisations we can understand the set of quantum limits in great detail. In particular we can construct examples of ergodic maps which have singular ergodic measures as quantum limits, and examples of non-ergodic maps where arbitrary convex combinations of absolutely continuous ergodic measures can occur as quantum limits. The maps we quantise are obtained by cutting and stacking.

math.DS↗