arXiv subjects

Gergely Röst

Publications and source records attributed to Gergely Röst.

At least 19 recordsLinked to original sources

arXiv2026

Delayed Pattern Formation in Two-Dimensional Domains

This study investigates how the interaction between gene expression time delay and domain size governs spatio-temporal pattern formation in a reaction-diffusion system. To investigate these phenomena, we utilize a modified version of the Schnakenberg model called the ligand internalisation (LI) model. In a one-dimensional domain, a linear relationship has been observed between the gene expression time delay and the time it takes for patterns to form. We extend the model to the two-dimensional domain and confirm that a similar relationship holds there as well. However, our exploration reveals a non-monotonic correlation between domain size and the time required for pattern emergence. To unravel these dynamics, we consider a range of initial conditions, including random perturbations of the spatially homogeneous steady state and initial conditions from its unstable manifold. We compute a two-parameter chart of patterns with respect to time delay and domain size.

math.DS↗

arXiv2025

Bistability and complex bifurcation diagrams generated by waning and boosting of immunity

We investigate an epidemiological model that incorporates waning of immunity at the individual level and boosting of the immune system upon re-exposure to the pathogen. When immunity is fully restored upon boosting, the system can be expressed as an SIRS-type model with discrete and distributed delays. We conduct a numerical bifurcation analysis varying the boosting force and the maximum period of immunity (in the absence of boosting), while keeping other parameters fixed at values representative of a highly infectious disease like pertussis. The stability switches of the endemic equilibrium, identified numerically, are validated using an established analytical approach, confirming that the equilibrium is unstable in a bounded parameter region, and stable outside this region. Using recently developed continuation methods for models with discrete and distributed delays, we explore periodic solutions and their bifurcations. Our analysis significantly extends previous findings and reveals a rich dynamical landscape, including catastrophic bifurcations of limit cycles, torus bifurcations, and bistability regions where two stable periodic solutions coexist, differing in amplitude and period. These complex bifurcations have critical public health implications: perturbations--such as non-pharmaceutical interventions--can shift the system between attractors, leading to long-term consequences from short-term measures.

math.DS↗

arXiv2025

The Effect of Assortativity on Mpox Spreading with Two Core Groups

The spread of infectious diseases often concentrates within specific subgroups of a broader population. For instance, during recent mpox outbreaks in non-endemic countries, transmission primarily affected men who have sex with men (MSM). However, the internal structure of these subpopulations plays a crucial role in disease dynamics and should be accurately represented in mathematical models. In this study, we highlight the importance of modeling interactions between distinct subgroups and their impact on transmission patterns. We consider a stochastic SEIR-based model with two core groups embedded into the general population, and investigate the outcome of the outbreak with different levels of symmetry between these groups and assortativity in their contacts. Our results indicate that the efficiency of commonly used non-pharmaceutical interventions is greatly influenced by these factors, hence they should be considered in the design of intervention strategies.

q-bio.PE↗

arXiv2025

Simulating cell populations with explicit cell cycle length -- implications to cell cycle dependent tumour therapy

In this study, we present a stochastic simulation model designed to explicitly incorporate cell cycle length, overcoming limitations associated with classical compartmental models. Our approach employs a delay mechanism to represent the cell cycle, allowing the use of arbitrary distributions for cell cycle lengths. We demonstrate the feasibility of our model by fitting it to experimental data from melanoma cell lines previously studied by Vittadello et al. Notably, our model successfully replicates experimentally observed synchronization phenomena that multi-stage models could not adequately explain. By using a gamma distribution to model cell cycle lengths, we achieved excellent agreement between our simulations and empirical data, while significantly reducing computational complexity and parameter estimation challenges inherent in multi-stage approaches. Our results highlight the importance of explicitly incorporating cell cycle lengths in modeling cell populations, with potential implications for optimizing cell cycle-dependent tumor therapies.

q-bio.PE↗

arXiv2024

What you saw is what you got? -- Correcting reported incidence data for testing intensity

During the COVID-19 pandemic, different types of non-pharmaceutical interventions played an important role in the efforts to control outbreaks and to limit the spread of the SARS-CoV-2 virus. In certain countries, large-scale voluntary testing of non-symptomatic individuals was done, with the aim of identifying asymptomatic and pre-symptomatic infections as well as gauging the prevalence in the general population. In this work, we present a mathematical model, used to investigate the dynamics of both observed and unobserved infections as a function of the rate of voluntary testing. The model indicate that increasing the rate of testing causes the observed prevalence to increase, despite a decrease in the true prevalence. For large testing rates, the observed prevalence also decrease. The non-monotonicity of observed prevalence explains some of the discrepancies seen when comparing uncorrected case-counts between countries. An example of such discrepancy is the COVID-19 epidemics observed in Denmark and Hungary during winter 2020/2021, for which the reported case-counts were comparable but the true prevalence were very different. The model provides a quantitative measure for the ascertainment rate between observed and true incidence, allowing for test-intensity correction of incidence data. By comparing the model to the country-wide epidemic of the Omicron variant (BA.1 and BA.2) in Denmark during the winter 2021/2022, we find a good agreement between the cumulative incidence as estimated by the model and as suggested by serology-studies. While the model does not capture the full complexity of epidemic outbreaks and the effect of different interventions, it provides a simple way to correct raw case-counts for differences in voluntary testing, making comparison across international borders and testing behaviour possible.

q-bio.PE↗

arXiv2023

Bifurcation analysis of waning-boosting epidemiological models with repeat infections and varying immunity periods

We consider the SIRWJS epidemiological model that includes the waning and boosting of immunity via secondary infections. We carry out combined analytical and numerical investigations of the dynamics. The formulae describing the existence and stability of equilibria are derived. Combining this analysis with numerical continuation techniques, we construct global bifurcation diagrams with respect to several epidemiological parameters. The bifurcation analysis reveals a very rich structure of possible global dynamics. We show that backward bifurcation is possible at the critical value of the basic reproduction number, $\mathcal{R}_0 = 1$. Furthermore, we find stability switches and Hopf bifurcations from steady states forming multiple endemic bubbles, and saddle-node bifurcations of periodic orbits. Regions of bistability are also found, where either two stable steady states, or a stable steady state and a stable periodic orbit coexist. This work provides an insight to the rich and complicated infectious disease dynamics that can emerge from the waning and boosting of immunity.

q-bio.PE↗

arXiv2022

Real-time estimation of the effective reproduction number of COVID-19 from behavioral data

Near-real time estimations of the effective reproduction number are among the most important tools to track the progression of a pandemic and to inform policy makers and the general public. However, these estimations rely on reported case numbers, commonly recorded with significant biases. The epidemic outcome is strongly influenced by the dynamics of social contacts, which are neglected in conventional surveillance systems as their real-time observation is challenging. Here, we propose a concept using online and offline behavioral data, recording age-stratified contact matrices at a daily rate. Modeling the epidemic using the reconstructed matrices we dynamically estimate the effective reproduction number during the two first waves of the COVID-19 pandemic in Hungary. Our results demonstrate how behavioral data can be used to build alternative monitoring systems complementing the established public health surveillance. They can identify and provide better signals during periods when official estimates appear unreliable due to observational biases.

physics.soc-ph↗

arXiv2022

In silico evaluation of Paxlovid's pharmacometrics for SARS-CoV-2: a multiscale approach

Paxlovid is a promising, orally bioavailable novel drug for SARS--CoV--2 with excellent safety profiles. Our main goal here is to explore the pharmacometric features of this new antiviral. To provide a detailed assessment of Paxlovid, we propose a hybrid multiscale mathematical approach. We demonstrate that the results of the present \textit{in silico} evaluation match the clinical expectations remarkably well: on the one hand, our computations successfully replicate the outcome of an actual \textit{in vitro} experiment; on the other hand we verify both the sufficiency and the necessity of Paxlovid's two main components (nirmatrelvir and ritonavir) for a simplified \textit{in vivo} case. Moreover, in the simulated context of our computational framework we visualize the importance of early interventions, and identify the time window where a unit--length delay causes the highest level of tissue damage. Finally, the results' sensitivity to the diffusion coefficient of the virus is explored in details.

q-bio.QM↗

arXiv2022

Dynamics of an SIRWS model with waning of immunity and varying immune boosting period

SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure may be incorporated. Previous analyses assumed identical waning rates from R to W and from W to S. This implicitly assumes equal length for the period of full immunity and of waned immunity. We relax this restriction, and allow an asymmetric partitioning of the total immune period. Stability switches of the endemic equilibrium are investigated with a combination of analytic and numerical tools. Then, continuation methods are applied to track bifurcations along the equilibrium branch. We find rich dynamics: Hopf bifurcations, endemic double bubbles, and regions of bistability. Our results highlight that the length of the period in which waning immunity can be boosted is a crucial parameter significantly influencing long term epidemiological dynamics.

q-bio.PE↗

arXiv2022

Understanding hesitancy with revealed preferences across COVID-19 vaccine types

Many countries have secured larger quantities of COVID-19 vaccines than their populace is willing to take. This abundance and variety of vaccines created a historical moment to understand vaccine hesitancy better. Never before were more types of vaccines available for an illness and the intensity of vaccine-related public discourse is unprecedented. Yet, the heterogeneity of hesitancy by vaccine types has been neglected so far, even though factual or believed vaccine characteristics and patient attributes are known to influence acceptance. We address this problem by analysing acceptance and assessment of five vaccine types using information collected with a nationally representative survey at the end of the third wave of the COVID-19 pandemic in Hungary, where a unique portfolio of vaccines were available to the public in large quantities. Our special case enables us to quantify revealed preferences across vaccine types since one could evaluate a vaccine unacceptable and even could reject an assigned vaccine to wait for another type. We find that the source of information that respondents trust characterizes their attitudes towards vaccine types differently and leads to divergent vaccine hesitancy. Believers of conspiracy theories were significantly more likely to evaluate the mRNA vaccines (Pfizer and Moderna) unacceptable while those who follow the advice of politicians evaluate vector-based (AstraZeneca and Sputnik) or whole-virus vaccines (Sinopharm) acceptable with higher likelihood. We illustrate that the rejection of non-desired and re-selection of preferred vaccines fragments the population by the mRNA versus other type of vaccines while it generally improves the assessment of the received vaccine. These results highlight that greater variance of available vaccine types and individual free choice are desirable conditions that can widen the acceptance of vaccines in societies.

econ.GN↗

arXiv2021

Monitoring behavioural responses during pandemic via reconstructed contact matrices from online and representative surveys

The unprecedented behavioural responses of societies have been evidently shaping the COVID-19 pandemic, yet it is a significant challenge to accurately monitor the continuously changing social mixing patterns in real-time. Contact matrices, usually stratified by age, summarise interaction motifs efficiently, but their collection relies on conventional representative survey techniques, which are expensive and slow to obtain. Here we report a data collection effort involving over $2.3\%$ of the Hungarian population to simultaneously record contact matrices through a longitudinal online and sequence of representative phone surveys. To correct non-representative biases characterising the online data, by using census data and the representative samples we develop a reconstruction method to provide a scalable, cheap, and flexible way to dynamically obtain closer-to-representative contact matrices. Our results demonstrate the potential of combined online-offline data collections to understand the changing behavioural responses determining the future evolution of the outbreak, and inform epidemic models with crucial data.

physics.soc-ph↗

arXiv2020

Global extinction, dissipativity and persistence for a certain class of differential equations with state-dependent delay

In this paper we study, at different levels of generality, certain systems of delay differential equations (DDE). One focus and motivation is a system with state-dependent delay (SD-DDE) that has been formulated to describe the maturation of stem cells. We refer to this system as the cell SD-DDE. In the cell SD-DDE, the delay is implicitly defined by a threshold condition. The latter is specified by the time at which the (also implicitly defined) solution of an external nonlinear ordinary differential equation (ODE), which is parametrised by a component of the SD-DDE, meets a given threshold value. We focus on the dynamical properties global asymptotic stability (GAS) of the zero equilibrium, persistence and dissipativity/ultimate boundedness.

math.DS↗

arXiv2019

A continuous semiflow on a space of Lipschitz functions for a differential equation with state-dependent delay from cell biology

We establish variants of existing results on existence, uniqueness and continuous dependence for a class of delay differential equations (DDE). We apply these to continue the analysis of a differential equation from cell biology with state-dependent delay, implicitly defined as the time when the solution of a nonlinear ODE, that depends on the state of the DDE, reaches a threshold. For this application, previous results are restricted to initial histories belonging to the so-called solution manifold. We here generalize the results to a set of nonnegative Lipschitz initial histories which is much larger than the solution manifold and moreover convex. Additionally, we show that the solutions define a semiflow that is continuous in the state-component in the $C([-h,0],\R^2)$ topology, which is a variant of established differentiability of the semiflow in $C^1([-h,0],\R^2)$. For an associated system we show invariance of convex and compact sets under the semiflow for finite time.

math.DS↗

arXiv2019

Convergence of solutions in a mean-field model of go-or-grow type with reservation of sites for proliferation and cell cycle delay

We consider the mean-field approximation of an individual-based model describing cell motility and proliferation, which incorporates the volume exclusion principle, the go-or-grow hypothesis and an explicit cell cycle delay. To utilise the framework of on-lattice agent-based models, we make the assumption that cells enter mitosis only if they can secure an additional site for the daughter cell, in which case they occupy two lattice sites until the completion of mitosis. The mean-field model is expressed by a system of delay differential equations and includes variables such as the number of motile cells, proliferating cells, reserved sites and empty sites. We prove the convergence of biologically feasible solutions: eventually all available space will be filled by mobile cells, after an initial phase when the proliferating cell population is increasing then diminishing. By comparing the behaviour of the mean-field model for different parameter values and initial cell distributions, we illustrate that the total cell population may follow a logistic-type growth curve, or may grow in a step-function-like fashion.

q-bio.CB↗

arXiv2019

Global dynamics of a novel delayed logistic equation arising from cell biology

The delayed logistic equation (also known as Hutchinson's equation or Wright's equation) was originally introduced to explain oscillatory phenomena in ecological dynamics. While it motivated the development of a large number of mathematical tools in the study of nonlinear delay differential equations, it also received criticism from modellers because of the lack of a mechanistic biological derivation and interpretation. Here we propose a new delayed logistic equation, which has clear biological underpinning coming from cell population modelling. This nonlinear differential equation includes terms with discrete and distributed delays. The global dynamics is completely described, and it is proven that all feasible nontrivial solutions converge to the positive equilibrium. The main tools of the proof rely on persistence theory, comparison principles and an $L^2$-perturbation technique. Using local invariant manifolds, a unique heteroclinic orbit is constructed that connects the unstable zero and the stable positive equilibrium, and we show that these three complete orbits constitute the global attractor of the system. Despite global attractivity, the dynamics is not trivial as we can observe long-lasting transient oscillatory patterns of various shapes. We also discuss the biological implications of these findings and their relations to other logistic type models of growth with delays.

math.DS↗

arXiv2018

A monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling

For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number, and consequently to a larger epidemic outbreak, when the mean infectious period is fixed. We discuss how this result is related to various stochastic orderings of the distributions of infectious periods. The results are illustrated by a number of explicit stochastic simulations, suggesting that their validity goes beyond regular networks.

q-bio.PE↗

arXiv2018

Global stability of a multistrain SIS model with superinfection and patch structure

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006 7:235-247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters. Finally, we return to the special case of one patch examined in [Math Biosci Eng. 2017 14:421-35] and give a correction to the proof of Theorem 2.2 of that paper.

math.DS↗

arXiv2018

Hopf bifurcation and period functions for Wright type delay differential equations

We present the simplest criterion that determines the direction of the Hopf bifurcations of the delay differential equation $x'(t)=-μf(x(t-1))$, as the parameter $μ$ passes through the critical values $μ_k$. We give a complete classification of the possible bifurcation sequences. Using this information and the Cooke-transformation, we obtain local estimates and monotonicity properties of the periods of the bifurcating limit cycles along the Hopf-branches. Further, we show how our results relate to the often required property that the nonlinearity has negative Schwarzian derivative.

math.DS↗