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Introduction
Additional affiliations
January 2008 - December 2009
September 2007 - April 2011
January 2006 - August 2007
Education
September 2001 - June 2004
Publications
Publications (169)
We provide an in silico study of stochastic viral infection extinction from a pharmacokinetical viewpoint. Our work considers a non-specific antiviral drug that increases the virus clearance rate, and we investigate the effect of this drug on early infection extinction. Infection extinction data are generated by a hybrid multiscale framework that a...
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 infe...
Background
In Hungary, although six types of vaccines were widely available, the percentage of people receiving the primary series of COVID-19 vaccination remained below the EU average. This paper investigates the reasons for Hungary’s lower vaccination coverage by exploring changing attitudes towards vaccination, socio-demographic determinants, an...
Optimizing vaccination impact during an emerging disease becomes crucial when vaccine supply is limited, and robust protection requires multiple doses. Facing this challenge during the early stages of the COVID-19 vaccine deployment, a pivotal policy question arose: whether to administer a single dose to a larger proportion of the population by def...
Predicting viral evolution presents a significant challenge and is a critical public health priority. In response to this challenge, we develop a novel model for viral evolution that considers a trade-off between immunity evasion and transmissibility. The model selects for a new strain with the highest invasion fitness, taking into account this tra...
COVID-19, caused by SARS-CoV-2, manifests with differing severity across distinct patient subgroups, with outcomes influenced by underlying comorbidities such as cancer, which may cause functional and compositional alterations of the immune system during tumor progression. We aimed to investigate the association of SARS-CoV-2 infection and its comp...
We construct and analyse a compartmental model for the spread of COVID-19 considering testing and quarantine with a risk-based evaluation of individuals to be tested, meaning that symptomatic individuals as well as contacts of confirmed cases are tested with higher probability. The model includes the isolation of the positively tested, for a fixed...
Vaccination has proven to be the most effective public health measure in the fight against various infectious diseases. For emerging or re-emerging diseases, a highly efficacious vaccine may not be available at the start of an outbreak. Timelines for availability of a safe and effective vaccine may significantly affect disease dynamics, its burden,...
Vaccination has proven to be the most effective public health measure in the fight against various infectious diseases. For emerging or re-emerging diseases, a highly efficacious vaccine may not be available at the start of an outbreak. Timelines for availability of a safe and effective vaccine may significantly affect disease dynamics, its burden,...
Monitoring the effective reproduction number Rt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_t$$\end{document} of a rapidly unfolding pandemic in real-time is key t...
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 cons...
Motivated by the emergence of new variants during the COVID-19 pandemic, we consider an epidemiological model of disease transmission dynamics, where novel strains appear by mutations of the virus. In the considered scenarios, disease prevalence in the population is modulated by social distancing. We study the various patterns that are generated un...
Motivated by the emergence of new variants during the COVID-19 pandemic, we consider an epidemiological model of disease transmission dynamics, where novel strains appear by mutations of the virus. In the considered scenarios, disease prevalence in the population is modulated by social distancing. We study the various patterns that are generated un...
In this paper, we investigate pattern dynamics in a reaction‐diffusion‐chemotaxis food chain model with predator‐taxis, which extends previous studies of reaction‐diffusion food chain model. By virtue of diffusion semigroup theory, we first prove global classical solvability and boundedness for the considered model over a bounded domain Ω⊂ℝn(n≥1)$$...
Several studies have reported the waning effectiveness of COVID-19 vaccines. This study aims to demonstrate the applicability of the screening method for estimating vaccine effectiveness (VE) in a pandemic. We report VE in Hungary, estimated with the screening method, in 2021, covering a period of Alpha and the Delta variant, including the booster...
Background
Evidence and advice for pregnant women evolved during the COVID-19 pandemic. We studied social contact behaviour and vaccine uptake in pregnant women between March 2020 and September 2021 in 19 European countries.
Methods
In each country, repeated online survey data were collected from a panel of nationally-representative participants....
Összefoglalás: Tanulmányunkban ismertetjük a Magyarországon eddig lezajlott öt járványhullám néhány alapvető járványügyi jellemzőit és a leglényegesebb központi járványkezelési intézkedéseket azzal a céllal, hogy a tanulságok levonása a hazai egészségbiztonság növelését szolgálja. Deskriptív epidemiológiai elemzésünk a 2020. március 4. és 2022. már...
In this paper, we investigate pattern dynamics in a reaction-diffusion-chemotaxis food chain model with predator-taxis, which enriches previous studies about diffusive food chain models. By virtue of diffusion semigroup theory, we first show the global classical solvability and uniform boundedness of the considered model over a bounded domain Ω ⊂ R...
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 implicit...
Many countries have secured larger quantities of COVID-19 vaccines than their population is willing to take. The abundance and the large variety of vaccines created not only an unprecedented intensity of vaccine related public discourse, but also a historical moment to understand vaccine hesitancy better. Yet, the heterogeneity of hesitancy by vacc...
Various measures have been implemented around the world to prevent the spread of SARS-CoV-2. A potential tool to reduce disease transmission is regular mass testing of a high percentage of the population, possibly with pooling (testing a compound of several samples with one single test). We develop a compartmental model to study the applicability o...
Retrospective evaluation of past waves of the SARS-CoV-2 epidemic is key for designing optimal interventions against future waves and novel pandemics. Here we report on analysing genome sequences of SARS-CoV-2 from the first two waves of the epidemic in 2020 in Hungary, mirroring a suppression and a mitigation strategy, respectively. Our analysis r...
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...
We assess the potential consequences of the upcoming SARS-CoV-2 waves caused by the Omicron variant. Our results suggest that even in those regions where the Delta variant is controlled at the moment by a combination of non-pharmaceutical interventions and population immunity, a significant Omicron wave can be expected. We stratify the population a...
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 in silico evalua...
SARS-CoV-2, the causative agent of COVID-19, has caused devastating health and economic impacts around the globe since its appearance in late 2019. The advent of effective vaccines leads to open questions on how best to vaccinate the population. To address such questions, we developed a model of COVID-19 infection by age that includes the waning an...
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 sil...
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 conventio...
Several studies have reported a waning of the effectiveness of COVID-19 vaccines. We report real-life vaccine effectiveness in Hungary, estimated with the screening method, in 2021, i.e., covering the dominance of both the Alpha and the Delta variant, and including the booster roll-out. Hungary is in the unique position to use six different vaccine...
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 implicit...
Pandemic management requires reliable and efficient dynamical simulation to predict and control disease spreading. The COVID-19 (SARS-CoV-2) pandemic is mitigated by several non-pharmaceutical interventions, but it is hard to predict which of these are the most effective for a given population. We developed the computationally effective and scalabl...
In this paper, a predictive-control-based approach is proposed for pandemic mitigation with multiple control inputs. Using previous results on the dynamical modeling of symptom-based testing, the testing intensity is introduced as a new manipulable input to the control system model in addition to the stringency of non-pharmaceutical measures. The c...
COVID-19 seroprevalence changes over time, with infection, vaccination, and waning immunity. Seroprevalence estimates are needed to determine when increased COVID-19 vaccination coverage is needed, and when booster doses should be considered, to reduce the spread and disease severity of COVID-19 infection. We use an age-structured model including i...
We assess the potential consequences of the upcoming SARS-CoV-2 waves caused by the Omicron variant. Our results suggest that even in those regions where the Delta variant is controlled at the moment by a combination of non-pharmaceutical interventions and population immunity, a significant Omicron wave can be expected. We stratify the population a...
We analyze a system of differential equations with state-dependent delay (SD-DDE) from cell biology, in which the delay is implicitly defined as the time when the solution of an ODE, parametrized by the SD-DDE state, meets a threshold. We show that the system is well-posed and that the solutions define a continuous semiflow on a state space of Lips...
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...
We propose a hybrid partial differential equation-agent-based (PDE-ABM) model to describe the spatio-temporal viral dynamics in a cell population. The virus concentration is considered as a continuous variable and virus movement is modelled by diffusion, while changes in the states of cells (i.e. healthy, infected, dead) are represented by a stocha...
We consider three connected populations with strong Allee effect, and give a complete classification of the steady state structure of the system with respect to the Allee threshold and the dispersal rate, describing the bifurcations at each critical point where the number of steady states change. One may expect that by increasing the dispersal rate...
Testing and isolation of cases is an important component of our strategies to fight SARS-CoV-2. In this work, we consider a compartmental model for Covid-19 including a nonlinear term representing symptom-based testing. We analyze how the considered clinical spectrum of symptoms and the testing rate affect the outcome and the severity of the outbre...
There is a threat of COVID-19 resurgence in Fall 2021 in Canada. To understand the probability and severity of this threat, quantification of the level of immunity/protection of the population is required. We use an age-structured model including infection, vaccination and waning immunity to estimate the distribution of immunity to COVID-19 in the...
A Járványmatematikai és Epidemiológiai Projekt egy egyedülálló kezdeményezés Magyarországon, mely jelentős tudást és tapasztalatot halmozott fel a COVID-19 világjárvány során. Jelen tanulmány a pandémia 2. hullámának példáján keresztül áttekinti, hogy miként működött a járványügyi észlelés és monitorozás rendszere, hogyan, milyen eredményekkel vége...
In this note we consider two populations living on identical patches, connected by unidirectional migration, and subject to strong Allee effect. We show that by increasing the migration rate, there are more bifurcation sequences than previous works showed. In particular, the number of steady states can change from 9 (small migration) to 3 (large mi...
Background
Pandemic management includes a variety of control measures, such as social distancing, testing/quarantining and vaccination applied to a population where the virus is circulating. The COVID 19 (SARS-CoV-2) pandemic is mitigated by several non-pharmaceutical interventions, but it is hard to predict which of these regulations are the most...
Development of resistance to chemotherapy in cancer patients strongly effects the outcome of the treatment. Due to chemotherapeutic agents, resistance can emerge by Darwinian evolution. Besides this, acquired drug resistance may arise via changes in gene expression. A recent discovery in cancer research uncovered a third possibility, indicating tha...
SARS-CoV-2, the causative agent of COVID-19, has caused devastating health and economic impacts around the globe since its appearance in late 2019. The advent of effective vaccines leads to open questions on how best to vaccinate the population. To address such questions, we developed a model of COVID-19 infection by age that includes the waning an...
We propose a hybrid partial differential equation – agent-based (PDE–ABM) model to describe the spatio-temporal viral dynamics in a cell population. The virus concentration is considered as a continuous variable and virus movement is modelled by diffusion, while changes in the states of cells (i.e. healthy, infected, dead) are represented by a stoc...
The COVID-19 pandemic forced authorities worldwide to implement moderate to severe restrictions in order to slow down or suppress the spread of the disease. It has been observed in several countries that a significant number of people fled a city or a region just before strict lockdown measures were implemented. This behavior carries the risk of se...
We prove that all Hopf bifurcations in the Nicholson’s blowfly equation are supercritical as we increase the delay. Earlier results treated only the first bifurcation point, and to determine the criticality of the bifurcation, one needed to substitute the parameters into a lengthy formula of the first Lyapunov coefficient. With our result, there is...
Clarithromycin is a macrolide antibiotic widely used for eradication of Helicobacter pylori infection, and thus resistance to this antibiotic is a major cause of treatment failure. Here, we present the results of a retrospective observational study of clarithromycin resistance (Cla-res) in 4744 H. pylori-infected patients from Central Hungary. We u...
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 conventio...
We consider three connected populations with Allee effect, and give a complete classification of the steady state structure of the system with respect to the Allee threshold and the dispersal rate, describing the bifurcations at each critical point where the number of steady states change. One may expect that by increasing the dispersal rate betwee...
Abstract Vaccines against varicella-zoster virus (VZV) are under introduction in Hungary into the routine vaccination schedule, hence it is important to understand the current transmission dynamics and to estimate the key parameters of the disease. Mathematical models can be greatly useful in advising public health policy decision making by compari...
The management of COVID-19 appears to be a long-term challenge, even in countries that have managed to suppress the epidemic after their initial outbreak. In this paper, we propose a model predictive approach for the constrained control of a nonlinear compartmental model that captures the key dynamical properties of COVID-19. The control design use...
Social interactions represent one of the most important routes of transmission of COVID-19 as they influence the potential patterns of diffusion of infection throughout different segments of the population. Despite their utmost importance, the scientific community is currently lacking data collection methods that record social interactions dynamica...
Testing and isolation of cases is an important component of our strategies to fight SARS-CoV-2. In this work, we consider a compartmental model for COVID-19 including a nonlinear term representing symptom-based testing. We analyze how the considered clinical spectrum of symptoms and the testing rate affect the outcome and the severity of the outbre...
The COVID-19 pandemic forced authorities worldwide to implement moderate to severe restrictions in order to slow down or suppress the spread of the disease. It has been observed in several countries that a significant number of people fled a city or a region just before strict lockdown measures were implemented. This behavior carries the risk of se...
In this paper we consider multistage SIS models of infectious diseases, where infected individuals are passing through infectious stages I 1 , I 2 ,. .. I n and then return to the susceptible compartment. First we calculate the basic reproduction number R 0 , and prove that the disease dies out for R 0 ≤ 1 , while a unique endemic equilibrium exist...
Development of resistance to chemotherapy in patients with cancer strongly affects the patients’ outcome. Due to chemotherapeutic agents, Darwinian selection induces intrinsic resistance. Besides this, another process resulting in drug resistance may take place, when resistance emerges upon changes taking place inside the cells as a result of the t...
First, we consider a spatial dynamic model of seasonal bird migration with stopovers along the migratory routes. Time delays arise from the large distance between stopovers. A whole season is tracked from the departure patch through spring migration, summer breeding, and eventually to the wintering ground, to determine the overall yearly growth of...
COVID-19 epidemic has been suppressed in Hungary due to timely non-pharmaceutical interventions, prompting a considerable reduction in the number of contacts and transmission of the virus. This strategy was effective in preventing epidemic growth and reducing the incidence of COVID-19 to low levels. In this report, we present the first epidemiologi...
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...
Development of resistance to chemotherapy in cancer patients strongly effects the outcome of the treatment. Due to chemotherapeutic agents, resistance can emerge by Darwinian evolution. Besides this, acquired drug resistance may arise via changes in gene expression. A recent discovery in cancer research uncovered a third possibility, indicating tha...
COVID-19 epidemic has been suppressed in Hungary due to timely non-pharmaceutical interventions, prompting a huge reduction in the number of contacts and transmission of the virus. This strategy was effective in preventing epidemic growth and reducing the incidence of COVID-19 to low levels.
In this report, we present the first epidemiological and...