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A Novel Analysis Approach of Uniform Persistence for an epidemic model with Quarantine and Standard Incidence Rate

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 695-707页

作者： Song-bai GUO Yu-ling XUE Xi-liang LI Zuo-huan ZHENG School of Science Beijing University of Civil Engineering and ArchitectureBeijing 102616China School of Mathematics and Statistics Hainan Normal UniversityHaikou 571158China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematics and Information Science Shandong Technology and Business UniversityYantai 264005China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)1.

关键词： uniform persistence epidemic model control reproduction number quarantine standard incidence rate

Construction of a Computational Scheme for the Fuzzy HIV/AIDS epidemic model with a Nonlinear Saturated Incidence Rate

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Computer modeling in Engineering & Sciences 2024年第2期138卷 1405-1425页

作者： Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz Department of Mathematics and Sciences College of Humanities and SciencesPrince Sultan UniversityRiyadh11586Saudi Arabia Department of Mathematics Air UniversityIslamabad44000Pakistan

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

关键词： epidemic model fuzzy rate parameters next generation matrix local stability proposed numerical scheme

Stochastic Bifurcation of an SIS epidemic model with Treatment and Immigration

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Journal of Applied Mathematics and Physics 2024年第6期12卷 2254-2280页

作者： Weipeng Zhang Dan Gu Department of Mathematics Jinan University Guangzhou China School of Mathematics and Statistics Northeast Normal University Changchun China

In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .

关键词： epidemic model Stochastic Averaging Method Singular Boundary Theory Stochastic Bifurcation

Diffusion-induced Spatio-temporal Oscillations in an epidemic model with Two Delays

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 128-153页

作者： Yan-fei DU Ben NIU Jun-jie WEI School of Mathematics Harbin Institute of TechnologyHarbin 150001China School of Mathematics&Data Science Shaanxi University of Science and TechnologyXi'an 710021China Department of Mathematics Harbin Institute of TechnologyWeihai 264209China School of Science Jimei UniversityXiamen 361021China

We investigate a diffusive,stage-structured epidemic model with the maturation delay and freelymoving delay.Choosing delays and diffusive rates as bifurcation parameters,the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation.The normal forms of Hopf bifurcations on the center manifold are calculated,and explicit formulae determining the criticality of bifurcations are derived.There are two different kinds of stable oscillations near the first bifurcation:on one hand,we theoretically prove that when the diffusion rate of infected immature individuals is sufficiently small or sufficiently large,the first branch of Hopf bifurcating solutions is always spatially homogeneous;on the other,fixing this diffusion rate at an appropriate size,stable oscillations with different spatial profiles are observed,and the conditions to guarantee the existence of such solutions are given by calculating the corresponding eigenfunction of the Laplacian at the first Hopf bifurcation point.These bifurcation behaviors indicate that spatial diffusion in the epidemic model may lead to spatially inhomogeneous distribution of individuals.

关键词： epidemic model stage structure delay diffusion Hopf bifurcation spatio-temporal oscillation

Traveling wave solutions for a discrete diffusive epidemic model with asymptomatic carriers

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International Journal of Biomathematics 2023年第2期16卷 221-255页

作者： Ran Zhang Dan Li Hongquan Sun Department of Mathematics College of Science Nanjing University of Aeronautics and Astronautics Nanjing 210016P.R.China School of Mathematical Sciences Anhui University Hefei230601P.R.China School of Mathematics and Physics Jiangsu University of Technology Changzhou 213001P.R.China School of Science Jiujiang University Jiujiang 332005P.R.China

This paper mainly concerns about the traveling wave solution(TwS)for a discrete diffusive epidemic model with asymptomatic carriers.Analysis of the model shows that the minimum wave speed c*exists if a threshold is greater than one.With the help of sub-and super-solutions,we find that the condition for the existence of TWS is R>1 and wave speed c>c^(*).Further,we prove that the TwS connects two different boundary steady states.Through the arguments with Laplace transform,we show there is no TWS for the model if R>1 and o

关键词： epidemic model traveling wave solutions Lattice dynamical system Schauder's fixed point theorem asymptomatic carriers

A regime-switching stochastic SIR epidemic model with a saturated incidence and limited medical resources

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生物数学学报:英文版 2023年第7期16卷 91-110页

作者： Wei Wei Wei Xu Jiankang Liu Department of Applied Mathematics Northwestern Polytechnical University Xi'an 710072 ShaanciP.R.China

The stochastic switching SIR epidemic model with saturated incidence and limited medical treatment is investigated in this paper.By using Lyapunov methods and Ito formula,we first prove that the system has a unique global positive solution with any positive initial value.Then combining inequality technique and the ergodic property of Markov switching,the suficient conditions for extinction and persistence in the mean of the disease are established.The results demonstrate that increasing medical resources and improving supply efficiency can accelerate the transition from the persistent state to the extinct state.Meanwhile,the high incidence rate will slow down the extinction of the disease.Specially,the switching noise can induce the system to toggle between the extinct and persistent states.Finally,some numerical simulations are carried out to confirm the analytical results.

关键词： epidemic model extinction persistence Markov switching saturated incidence

Turing pattern selection in a reaction-diffusion epidemic model

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Chinese Physics B 2011年第7期20卷 286-297页

作者：王玮明刘厚业蔡永丽李镇清 College of Mathematics and Information Science Wenzhou University State Key Laboratory of Vegetation and Environmental Change Institute of BotanyChinese Academy of Sciences

We present Turing pattern selection in a reaction-diffusion epidemic model under zero-flux boundary conditions. The value of this study is twofold. First, it establishes the amplitude equations for the excited modes, which determines the stability of amplitudes towards uniform and inhomogeneous perturbations. Second, it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication： on increasing the control parameter v, the sequence ＂H0 hexagons → H0-hexagon-stripe mixtures →stripes → Hπ-hexagon-stripe mixtures → Hπ hexagons＂ is observed. This may enrich the pattern dynamics in a diffusive epidemic model.

关键词： epidemic model pattern selection amplitude equations T^ring instability

Structure-Preserving Dynamics of Stochastic epidemic model with the Saturated Incidence Rate

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Computers, Materials & Continua 2020年第8期64卷 797-811页

作者： Wasfi Shatanawi Muhammad Shoaib Arif Ali Raza Muhammad Rafiq Mairaj Bibi Javeria Nawaz Abbasi Department of Mathematics and General Sciences Prince Sultan UniversityRiyadhSaudi Arabia Department of Medical Research China Medical University HospitalChina Medical UniversityTaichung40402Taiwan Department of M-Commerce and Multimedia Applications Asia UniversityTaichung41354Taiwan Stochastic Analysis&Optimization Research Group Department of MathematicsAir UniversityPAF Complex E-9Islamabad44000Pakistan Faculty of Engineering University of Central PunjabLahorePakistan Department of Mathematics Comsats UniversityIslamabadPakistan

The structure-preserving features of the nonlinear stochastic models are positivity,dynamical consistency and boundedness.These features have a significant role in different fields of computational biology and many more.Unfortunately,the existing stochastic approaches in literature do not restore aforesaid structure-preserving features,particularly for the stochastic models.Therefore,these gaps should be occupied up in literature,by constructing the structure-preserving features preserving numerical approach.This writing aims to describe the structure-preserving dynamics of the stochastic model.We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling.The usual explicit stochastic numerical approaches are time-dependent.We have developed the implicitly driven explicit approach for the stochastic epidemic model.We have proved that the newly developed approach is preserving the structural,dynamical properties as positivity,boundedness and dynamical consistency.Finally,convergence analysis of a newly developed approach and graphically illustration is also presented.

关键词： epidemic model stochastic numerical approaches convergence analysis

Spatial propagation in an epidemic model with nonlocal diffusion:The influences of initial data and dispersals

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Science China Mathematics 2020年第11期63卷 2177-2206页

作者： Wen-Bing Xu Wan-Tong Li Shigui Ruan Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematics and Statistics Lanzhou UniversityLanzhou 730000China Department of Mathematics University of MiamiCoral GablesFL 33146USA

This paper studies an epidemic model with nonlocal dispersals.We focus on the influences of initial data and nonlocal dispersals on its spatial propagation.Here,initial data stand for the spatial concentrations of the infectious agent and the infectious human population when the epidemic breaks out and the nonlocal dispersals mean their diffusion strategies.Two types of initial data decaying to zero exponentially or faster are considered.For the first type,we show that spreading speeds are two constants whose signs change with the number of elements in some set.Moreover,we find an interesting phenomenon:the asymmetry of nonlocal dispersals can influence the propagating directions of the solutions and the stability of steady states.For the second type,we show that the spreading speed is decreasing with respect to the exponentially decaying rate of initial data,and further,its minimum value coincides with the spreading speed for the first type.In addition,we give some results about the nonexistence of traveling wave solutions and the monotone property of the solutions.Finally,some applications are presented to illustrate the theoretical results.

关键词： nonlocal dispersal epidemic model spreading speed initial data dispersal kernel