Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuanyuan Ma, Yue Cui, Min Wang
Summary: This study proposes a new SIQRS model based on nonlinear incidence, which takes into account the impact of lagging public awareness on propagation characteristics. The stability of the system is proven by calculating the basic reproduction number and constructing suitable Lyapunov functions. Targeted and acquaintance immunization strategies are found to be more effective than uniform immunization. The conclusions of the theoretical research are verified through numerical simulation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
B. M. Almuqati
Summary: In this study, we investigate the mechanism of a multi-group epidemic model with logistic growth and delay time distribution. Despite its importance, the consideration of logistic growth effect in such models is rare. Our findings show that R0 plays a crucial role in the global stability of disease-free and endemic equilibria. We also construct suitable Lyapunov functions to examine the global stability of these equilibria. Numerical simulations of the model are introduced as well.
Article
Mathematics, Applied
Mehmet Turan, Rezan Sevinik Adiguzel, F. Koc
Summary: This paper presents a epidemic model with varying population, a new vaccination strategy, and time delay. It investigates the impact of vaccination in terms of vaccine efficacy and the time required to see the effects. It also explores ways to control the spread of the disease based on the basic reproduction ratio. Numerical simulations are provided to illustrate the theoretical findings.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Materials Science, Multidisciplinary
Salih Djilali, Soufiane Bentout, Tarik Mohammed Touaoula, Abdessamad Tridane, Sunil Kumar
Summary: In this research, the global properties of a heroin epidemic model with time distributed delay and nonlinear incidence function are investigated. The system shows threshold dynamics in terms of R-0, with the drug-free equilibrium being globally asymptotically stable for R-0 < 1. Persistence of heroin consumption is observed for R-0 > 1, and global stability of the endemic equilibrium is demonstrated using a suitable Lyapunov function. Illustrative numerical simulations are used to support the mathematical results.
RESULTS IN PHYSICS
(2021)
Article
Mathematical & Computational Biology
Abdelheq Mezouaghi, Salih Djillali, Anwar Zeb, Kottakkaran Sooppy Nisar
Summary: This research investigates the global dynamics of a delayed epidemic model with partial susceptible protection, aiming to determine the relation between the isolation rate and the basic reproduction number in order to eliminate the infection from the population.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
R. P. Gupta, Arun Kumar
Summary: The current study presents the complex dynamics of an SIR epidemic model with saturated incidence rate and treatment. Rigorous results for the asymptotic stability of equilibrium states are provided, and several bifurcations are discussed. Extensive numerical simulations are conducted to validate these results.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Biology
Xiaogang Liu, Yuming Chen, Xiaomin Li, Jianquan Li
Summary: In this paper, a system of ODEs-PDE is formulated to model diseases with latency-age and differential infectivity. One ODE and two DDE models are derived based on the ways latent individuals leave the latent stage. The global stability of the models is focused on, with each model characterized by a threshold dynamics determined by the basic reproduction number.
JOURNAL OF MATHEMATICAL BIOLOGY
(2023)
Article
Materials Science, Multidisciplinary
Amir Khan, Rukhsar Ikram, Anwarud Din, Usa Wannasingha Humphries, Ali Akgul
Summary: This work investigates an epidemic model for corona-virus (COVID-19) with random perturbations and time delay, analyzing the impact of delay-stochastic approach on disease transmission and establishing conditions for disease extinction. Results indicate that Brownian motion and noise terms have a significant influence on epidemic transmission, with the potential for infection to decrease or vanish with large noise levels. Numerical simulations validate the results for all classes of the problem.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Mechanical
Lihua Dai, Xianning Liu, Yuming Chen
Summary: This paper proposes and analyzes a fractional-order SIS model with a generalized transmission function and media coverage. The existence, uniqueness, and non-negativeness of solutions are obtained. The basic reproduction number R0 is calculated using the next generation matrix method, serving as a threshold parameter. Numerical simulations demonstrate the main theoretical results and reveal the impact of media coverage on disease transmission.
NONLINEAR DYNAMICS
(2023)
Article
Mathematical & Computational Biology
Salih Djillai, Soufiane Bentout, Tarik Mohammed Touaoula, Abdessamad Tridane
Summary: This paper investigates a global dynamics of an alcoholism epidemic model with distributed delays, taking into account the social pressure as a factor of drinking. The alcohol addiction is proven to be uniformly persistent in the population, with a globally asymptotically stable equilibrium. The global stability is achieved without a basic reproduction number or threshold condition, and the model's unique equilibrium is shown to be globally attractive using Lyapunov direct method.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Gui Guan, Zhenyuan Guo
Summary: This paper investigates an epidemic model with a saturated treatment rate, analyzing the boundedness, equilibrium points, and stability of the system, as well as observing bifurcation behavior at R-0 = 1. The stability of the disease-spreading equilibrium point is also proved under certain conditions, with numerical simulations validating the theoretical results.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Engineering, Mechanical
Gui Guan, Zhenyuan Guo
Summary: This study proposes a modified SHIR model with time delay and nonlinear incidence rate for two susceptible groups in networks with different topologies. By analyzing the basic reproduction numbers and stability of equilibrium points, the study examines disease spread in homogeneous and heterogeneous networks. Numerical simulations and theoretical analysis are used to study the dynamics of two systems and propose conjectures.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Dandan Sun, Zhidong Teng, Kai Wang, Tailei Zhang
Summary: This paper investigates an age-structured SVIR epidemic model with vaccination and incubation, considering two delays effects. The model is transformed into a non-densely defined abstract Cauchy problem for analysis and the nonnegativity, boundedness, basic reproduction number R0, and existence of equilibria are established. The characteristic equations of linearized systems at equilibria are calculated, and the global stability of disease-free equilibrium and the local stability and existence of Hopf bifurcation at the endemic equilibrium are proven. Numerical examples and simulations verify the theoretical results and demonstrate the existence of stability switch.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Liang Chen, JinRong Wang
Summary: In this paper, we study a delayed adaptive network epidemic model where the rate of demographic change of susceptible and infected individuals is affected by the time-delay effects of local spatial connections. We prove the Hopf bifurcation occurs at the critical value t 0 with delay t as the bifurcation parameter. The criteria for the bifurcation direction and stability are derived using the normal form method and central manifold theory. Numerical simulations are provided to demonstrate the feasibility of the results.
Article
Mathematics, Applied
Eduardo Liz
Summary: The study conducted a thorough bifurcation analysis of the Proportional Threshold Harvesting (PTH) model, providing a comprehensive picture of the 2-parameter bifurcation diagram for the harvesting model. The results explain previous numerical bifurcation diagrams for PTH and reveal new dynamic features with interesting consequences for population management.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
(2022)
Article
Biochemical Research Methods
Istvan Z. Reguly, David Csercsik, Janos Juhasz, Kalman Tornai, Zsofia Bujtar, Gergely Horvath, Bence Keoemley-Horvath, Tamas Kos, Gyoergy Cserey, Kristof Ivan, Sandor Pongor, Gabor Szederkenyi, Gergely Roest, Attila Csikasz-Nagy
Summary: Pandemic management requires reliable and efficient dynamical simulation to predict and control disease spreading. Vaccination strategies prioritising occupational risk groups can minimize infections, while prioritising vulnerable groups can minimize mortality. Intensive vaccination and non-pharmaceutical interventions can significantly suppress the spread of the virus.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Immunology
David W. Dick, Lauren Childs, Zhilan Feng, Jing Li, Gergely Roest, David L. Buckeridge, Nick H. Ogden, Jane M. Heffernan
Summary: COVID-19 seroprevalence in the Canadian population changes over time, and it is estimated that 60-80% of the population will have some immunity to COVID-19 by late Summer 2021. To reduce the spread and severity of COVID-19, it is necessary to increase vaccination uptake in the age group 12-29, and administer booster doses to the age group 50+.
Article
Mathematics, Applied
Eduardo Liz, Elisa Sovrano
Summary: This paper investigates the dynamics of a discrete-time stage-structured population model considering threshold harvesting for juveniles and adults. The study finds all possible equilibria of the system, analyzes their stability, and shows that harvesting does not destabilize globally stable equilibria. The paper also discusses the occurrence of hydra effects and provides a rigorous 2-parameter bifurcation diagram for semelparous populations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Virology
Ferenc A. Bartha, Nora Juhasz, Sadegh Marzban, Renji Han, Gergely Rost
Summary: This study evaluates the pharmacometric features of the orally bioavailable novel drug Paxlovid and proposes a hybrid multiscale mathematical approach. The results match the clinical expectations and confirm the effectiveness and safety of Paxlovid. The study also highlights the importance of early interventions and explores the sensitivity of the results to the diffusion coefficient of the virus.
Article
Infectious Diseases
Lauren Childs, David W. Dick, Zhilan Feng, Jane M. Heffernan, Jing Li, Gergely Rost
Summary: This study developed a model for COVID-19 infection, taking into account the waning and boosting of immunity, changes in virus infectivity, and different vaccination factors. The research found that delaying the second dose of vaccine is appropriate in the Canadian context, and including 15-19 year olds in the vaccine rollout can increase the benefits of vaccination in reducing infections.
Article
Multidisciplinary Sciences
Julia Koltai, Orsolya Vasarhelyi, Gergely Rost, Marton Karsai
Summary: This study records contact matrices through online and phone surveys to understand the changing social mixing patterns. Using census data and representative samples, researchers develop a reconstruction method to obtain more accurate contact matrices and provide crucial data for epidemic models.
SCIENTIFIC REPORTS
(2022)
Article
Multidisciplinary Sciences
Kristof Kutasi, Julia Koltai, Agnes Szabo-Morvai, Gergely Rost, Marton Karsai, Peter Biro, Balazs Lengyel
Summary: Many countries have more COVID-19 vaccines than their population wants to take, leading to a better understanding of vaccine hesitancy. However, the existing literature has neglected the heterogeneity of hesitancy by vaccine types. This study examines the acceptance and evaluation of five vaccine types, finding that hesitancy varies depending on individuals' trusted source of information. Believers of conspiracy theories are more likely to reject mRNA vaccines, while those who follow politicians' advice are more accepting of vector-based or whole-virus vaccines. The study argues that offering a greater selection of vaccines and individual choice can help increase vaccination rates in societies.
SCIENTIFIC REPORTS
(2022)
Article
Ecology
Richmond Opoku-Sarkodie, Ferenc A. Bartha, Monika Polner, Gergely Rost
Summary: This study investigates the transmission dynamics of infectious diseases using SIRS models, taking into account waning immunity. The results highlight the significant impact of the length of the waning immunity period on long-term epidemiological dynamics.
JOURNAL OF BIOLOGICAL DYNAMICS
(2022)
Article
Virology
Eszter Ari, Balint Mark Vasarhelyi, Gabor Kemenesi, Gabor Endre Toth, Brigitta Zana, Balazs Somogyi, Zsofia Lanszki, Gergely Rost, Ferenc Jakab, Balazs Papp, Balint Kintses
Summary: Retrospective evaluation of the SARS-CoV-2 epidemic in Hungary reveals that the first wave was controlled by a national lockdown, while the second wave was mainly driven by a specific transmission lineage.
Article
Mathematics, Applied
Renji Han, Gergely Roest
Summary: In this paper, the pattern dynamics in a reaction-diffusion-chemotaxis food chain model with predator-taxis is investigated. The global classical solvability and boundedness of the model are proved over a bounded domain with smooth boundary using diffusion semigroup theory. The linear stability analysis shows that chemotaxis can induce the losing of stability of the unique positive spatially homogeneous steady state via Turing bifurcation and Turing-spatiotemporal Hopf bifurcation, leading to the formation of stationary Turing pattern and oscillatory pattern. Numerical simulations are performed to illustrate and support the theoretical findings, and interesting non-Turing patterns are found in temporal Hopf parameter space.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Olena Trofymchuk, Eduardo Liz, Sergei Trofimchuk
Summary: In the 1990s, Daniel Kahneman and his colleagues formulated the peak-end evaluation rule, which accurately predicts the remembered utility of pleasant or unpleasant episodes. They proposed a mathematical model for the time evolution of experienced utility based on this rule. They studied the dynamics of the model and showed that it can exhibit chaotic behavior under certain parameters and exogenous stimuli.
Article
Mathematical & Computational Biology
Eduardo Liz, Sergei Trofimchuk
Summary: It is now recognized that personal well-being can be numerically evaluated, with a utility profile indicating the level of happiness at each given moment. The moment-based approach developed by Nobel laureate Daniel Kahneman establishes that experienced utility can be measured in real-time based on the pleasure and pain felt during an episode. A dynamic model of happiness based on this approach incorporates instant and remembered utility, defined by a delay differential equation. Additionally, applying the peak-end rule leads to a class of delay differential equations called differential equations with maxima.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2023)
Article
Mathematics, Applied
Bornali Das, Gergely Rost
Summary: A mathematical model is developed to study the co-infection of Chlamydia trachomatis (C. trachomatis) and herpes simplex virus (HSV) considering the non-cultivable state of C. trachomatis induced by HSV. The dynamics of the sub-systems with single diseases are described in detail. For the co-infection model, the persistence or extinction of HSV solely depends on its basic reproduction number, regardless of C. trachomatis prevalence. However, C. trachomatis may not always invade a HSV-endemic population due to a newly introduced threshold parameter. The model is calibrated and compared with epidemiological observations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematical & Computational Biology
Tamas Tekeli, Attila Denes, Gergely Rost
Summary: The study suggests that mass testing of a high percentage of the population, along with optimized pooling strategies, can effectively reduce disease transmission, with adaptive strategies being more efficient.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)