Article
Mathematics, Interdisciplinary Applications
Yassine Chakir
Summary: This paper presents a global semi-analytical method based on two-point Pade approximants for solving the SIR epidemic model of childhood diseases. The method provides an explicit analytical solution over the entire time period, including the peak time, which is crucial for understanding disease spread. The efficiency of the method is demonstrated by comparing the results with classical Pade approximations and the numerical Runge-Kutta-Fehlberg method.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematical & Computational Biology
Amine El Koufi, Abdelkrim Bennar, Noura Yousfi
Summary: In this paper, we investigate a stochastic delayed epidemic model with double epidemic hypothesis and vaccination incorporating Levy noise. We show that this model has a unique global positive solution and provide sufficient conditions for extinction and persistence in the mean of the two epidemics. We also prove that the two diseases can coexist under certain conditions.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Sudi Mungkasi
Summary: The study focuses on an SIR epidemic model with constant vaccination strategy and compares the existing variational iteration method with a successive approximation method. It is found that the existing method is inaccurate for large domains, prompting the proposal of an improved version that significantly enhances accuracy.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics
Zai-Yin He, Abderrahmane Abbes, Hadi Jahanshahi, Naif D. Alotaibi, Ye Wang
Summary: This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination and examines its dynamical behavior analytically and numerically. It is verified that the introduced fractional discrete SIR epidemic model with both commensurate and incommensurate fractional orders exhibits chaotic behavior. The discrete fractional model displays more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders.
Article
Engineering, Multidisciplinary
Zhihui Ma, Ting Qi, Xiaohua Li
Summary: In this paper, a generalized stochastic SIR epidemic model with vaccination rules is presented and the threshold behavior of the proposed epidemic model is investigated. The study finds that larger stochastic disturbance can lead to the extinction of infectious diseases, while smaller disturbance heavily relies on the incidence function.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
R. Bobryk
Summary: This paper focuses on an SIR model with random additive perturbations of the transmission rate in the spread of an epidemic. Three models of random perturbation are considered, with two models maintaining the condition of positivity of the transmission rate. An efficient numerical procedure is proposed for stability charts in the presence of bounded noise, and the impact of random perturbations on the stability behavior of disease-free equilibrium is discussed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Multidisciplinary Sciences
F. Sartori, M. Turchetto, M. Bellingeri, F. Scotognella, R. Alfieri, N. -K. -K. Nguyen, T. -T. Le, Q. Nguyen, D. Cassi
Summary: We compared seven node vaccination strategies in twelve real-world complex networks. The best strategies varied between non-adaptive and semi-adaptive approaches, and also depended on the number of available vaccines. Additionally, partial recalculation of node centrality increased the efficacy of the vaccination strategies by up to 80%.
SCIENTIFIC REPORTS
(2022)
Article
Mathematics, Applied
Joao P. S. Mauricio de Carvalho, Alexandre A. A. Rodrigues
Summary: This article examines bifurcations of an SIR model where the susceptible population grows logistically and is subject to constant vaccination. The authors explicitly prove that the endemic equilibrium is a codimension two singularity in the parameter space, and demonstrate various bifurcation curves unfolding the singularity. The study provides useful insights on the proportion of vaccinated individuals required to eliminate the disease and the impact of vaccination on the epidemic outcome.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Engineering, Multidisciplinary
Ibtehal Alazman, Kholoud Saad Albalawi, Pranay Goswami, Kuldeep Malik
Summary: This paper presents a restricted SIR mathematical model to analyze the evolution of a contagious infectious disease outbreak (COVID-19) using available data. The new model focuses on multiple waves of the disease and evaluates the effectiveness of vaccination in eradicating the infection. Stability analysis of the equilibrium points is conducted to examine the stability of the model. The basic reproduction number is calculated, and numerical simulations are performed to evaluate the effects of vaccination.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Applied
Milica Markovic, Marija Krstic
Summary: This paper examines a stochastic susceptible-infectious-recovered (SIR) epidemiological model based on the deterministic SIR model, incorporating general incidence rate, distributed delay, general treatment, and vaccination. The study establishes the existence and uniqueness of the global positive solution for the model, and explores the conditions under which the disease survives in a population by proving the existence of an ergodic stationary distribution. The stability of the disease-free equilibrium in the stochastic model is also investigated. Numerical simulations using real-life data are conducted to illustrate the theoretical findings.
Article
Engineering, Mechanical
Jin Yang, Likun Guan, Zhuo Chen, Yuanshun Tan, Zijian Liu, Robert A. Cheke
Summary: This study proposes a nonlinear pulse SIR model with media coverage to describe the effects of vaccination and isolation measures on the spread of infectious diseases. By selecting suitable strategy parameters, the transmission of the disease can be effectively controlled. Furthermore, the study finds that the model can exhibit complex dynamic behavior under variations in certain key parameters, which has significant biological implications.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Agus Suryanto, Isnani Darti
Summary: In this study, an alternative NSFD scheme is proposed and analyzed to ensure boundedness of solutions, with confirmed dynamic consistency with the corresponding continuous model. Numerical simulations demonstrate the superiority of the proposed NSFD scheme over traditional methods.
Article
Mathematics, Applied
Jiangtao Yang, Zhichun Yang, Yuming Chen
Summary: An SIS epidemic model is developed in this paper for an m-patch environment with pulse vaccination and quarantine at two different fixed moments. The sufficient conditions for disease extinction and persistence are derived, and the threshold value 90 is obtained using persistence theory, impulsive-type Floquet theory, and perturbation techniques. The results show that the infection-free periodic solution is globally asymptotically stable if 90 < 1, and the impulsive system becomes uniformly persistent if 90 > 1. Two special cases are considered to illustrate the joint impact of vaccination, quarantine, and population mobility on disease dynamics when m = 2. Numerical simulations confirm the effectiveness of the theoretical results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Anwarud Din, Yongjin Li, Abdullahi Yusuf
Summary: This study investigates the impact of environmental factors such as humidity and temperature on the dynamics of hepatitis B virus (HBV) transmission through stochastic modeling. It reveals that white noise and transmission coefficient delay play key roles in controlling infection, while delay factor contributes to periodic occurrence and re-infection of the disease. Results suggest that relatively large noise can lead to HBV extinction.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Soufiane Bentout, Salih Djilali, Toshikazu Kuniya, Jinliang Wang
Summary: We study the global dynamics of a susceptible-vaccinated-infected-recovered model that incorporates nonlocal diffusion. By identifying the basic reproduction number Script capital R0 of the model, we obtain threshold-type results that determine the extinction or persistence of the epidemic. Our results show that Script capital R0 is an essential value for determining global epidemic dynamics in our model.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
