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Qualitative analysis of a reaction-diffusion SIRS epidemic model with nonlinear incidence rate and partial immunity

Infectious Disease Modelling 2023年第3期8卷 881-911页

作者： Jianpeng Wang Zhidong Teng Binxiang Dai School of Mathematics and Statis Central South UniversityChangshaHunan410075People's Republic of China College of Medical Engineering and Technology Xinjiang Medical UniversityUrumqiXinjiang830011People's Republic of China

In this paper,a reaction-diffusion SIRS epidemic model with nonlinear incidence rate and partial immunity in a spatially heterogeneous environment is proposed.The well-posedness of the solution is firstly established.Then the basic reproduction number R0 is defined and a threshold dynamics is obtained.That is,when R_(0)1,the disease is permanent,and there exists at least one positive steady state solution.Finally,the asymptotic profiles of the positive steady state solution as individuals disperse at small and large rates are investigated.Furthermore,as an application of theoretical analysis,a numerical example involving the spread of influenza is discussed.Based on the numerical simulations,we find that the increase of transmission rate and spatial heterogeneity can enhance the risk of influenza propagation,and the increase of diffusion rate,saturation incidence for susceptible and recovery rate can reduce the risk of influenza propagation.Therefore,we propose to reduce the flow of people to lower the effect of spatial hetero-geneity,increase the transfer of infected individuals to hospitals in surrounding areas to increase the diffusion rate,and increase the construction of public medical resources to increase the recovery rate for controlling influenza propagation.

关键词： nonlinear incidence Partial immunity Threshold dynamics Asymptotic profiles Numerical simulations

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Stability and optimal control for delayed rumor-spreading model with nonlinear incidence over heterogeneous networks

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Chinese Physics B 2023年第5期32卷 710-723页

作者：罗续鹏蒋海军陈珊珊李佳容 College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830017China College of Mathematics and Physics Guangxi Minzu UniversityNanning 530006China

On the multilingual online social networks of global information sharing,the wanton spread of rumors has an enormous negative impact on people's lives.Thus,it is essential to explore the rumor-spreading rules in multilingual environment and formulate corresponding control strategies to reduce the harm caused by rumor propagation.In this paper,considering the multilingual environment and intervention mechanism in the rumor-spreading process,an improved ignorants–spreaders-1–spreaders-2–removers(I2SR)rumor-spreading model with time delay and the nonlinear incidence is established in heterogeneous networks.Firstly,based on the mean-field equations corresponding to the model,the basic reproduction number is derived to ensure the existence of rumor-spreading equilibrium.Secondly,by applying Lyapunov stability theory and graph theory,the global stability of rumor-spreading equilibrium is analyzed in detail.In particular,aiming at the lowest control cost,the optimal control scheme is designed to optimize the intervention mechanism,and the optimal control conditions are derived using the Pontryagin's minimum principle.Finally,some illustrative examples are provided to verify the effectiveness of the theoretical results.The results show that optimizing the intervention mechanism can effectively reduce the densities of spreaders-1 and spreaders-2 within the expected time,which provides guiding insights for public opinion managers to control rumors.

关键词： rumor propagation heterogeneous network nonlinear incidence optimal control

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GLOBAL ASYMPTOTICAL PROPERTIES FOR A DIFFUSED HBV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND nonlinear incidence

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Acta Mathematica Scientia 2011年第5期31卷 1959-1967页

作者：王绍利冯新龙何银年 Faculty of Science Xi'an Jiaotong University College of Mathematics and Systems Science Xinjiang University

This article proposes a diffused hepatitis B virus （HBV） model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.

关键词： HBV infection diffusion CTL immune response nonlinear incidence global asymptotical stability

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A nonlinear relapse model with disaggregated contact rates:Analysis of a forward-backward bifurcation

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Infectious Disease Modelling 2023年第3期8卷 769-782页

作者： Jimmy Calvo-Monge Fabio Sanchez Juan Gabriel Calvo Dario Mena Escuela de Matematica Universidad de Costa RicaCiudad Universitaria Rodrigo FacioSan Jose11501Costa Rica Centro de Investigacion en Matematica Pura y Aplicada Universidad de Costa RicaCiudad Universitaria Rodrigo FacioSan Jose11501Costa Rica

Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better.Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation.Therefore,we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses.Our incidence rate function is formulated,taking inspiration from recent adaptive algorithms.It incorporates contact behavior for individuals in each health class.We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios.The relationship between the different contact rates heavily in-fluences these conditions.Numerical examples highlight the effect of temporarily recov-ered individuals and initial conditions on infected population persistence.

关键词： nonlinear relapse nonlinear incidence MaMthematical model Backward bifurcation Adaptive behavior 2000 MSC 37N25 92B05

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A stochastic switched SIRS epidemic model with nonlinear incidence and vaccination:Stationary distribution and extinction

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International Journal of Biomathematics 2020年第3期13卷 137-164页

作者： Xin Zhao Xin He Tao Feng Zhipeng Qiu Department of Mathematics Nanjing University of Science and Technology Nanjing 210094 P.R.China

In this paper,a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases.nonlinear incidence and vaccination strategies are also considered in the proposed model.By using the method of stochastic analysis,we point out the key parameters that determine the persistence and extinction of the diseases.Specifically,if R0^s is greater than 0,the stochastic system has a unique ergodic stationary distribution;while if R ^* is less than 0,the diseases will be extinct at an exponential rate.

关键词： Stochastic SIRS epidemic model nonlinear incidence markov switch sta-tionary distribution extinction

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Analysis of a SIRS model with self- protection

Analysis of a SIRS model with self- protection

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第25届中国控制与决策会议

作者： Yu Cao Yuanwei Jing Feng Yuan Xuting Zheng School of Information Science and Engineering Northeastern University Shenyang Jianzhu University China Medical University

ISBN: (纸本)9781467355339

An improved SIRS model combined with awareness of self-protection based on the existing model with nonlinear incidence according to the fact that the network nodes would take protective measures under virus attack which changed the structure of network was proposed;The asymptotic stability of system under the protective measures was analyzed by Liapunov stability theory;How the protective measures influenced on the spread of virus on uniform network is showed through the compared simulation. By analyzing the improved SIRS models we have obtained that under the non-disease state, self-protection plays less of a role;To the opposite, the self-protection play a big part in epidemic spreading. The final number of infections will be reduced by self-protection under the epidemic state.

关键词： self-protection nonlinear incidence SIRS model asymptotic stability uniform network

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