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A SIMPLE DISCRETE-TIME ANALOGUE PRESERVING THE GLOBAL STABILITY OF A CONTINUOUS sirs epidemic model

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International Journal of Biomathematics 2013年第2期6卷 1-17页

作者： YOICHI ENATSU YOSHIAKI MUROYA Graduate School of Fundamental Science and Engineering Waseda University 3-~10hkubo Shinjuku-ku Tokyo 169-8555 Japan Department of Mathematics Waseda University3-4-10hkubo Shinjuku-ku Tokyo 169-8555 Japan

In this paper, we consider the backward Euler discretization derived from a continuous sirs epidemic model, which contains a remaining problem that our discrete model has two solutions for infected population; one is positive and the other is negative. Under an additional positiveness condition on infected population, we show that the backward Euler discretization is one of simple discrete-time analogue which preserves the global asymptotic stability of equilibria of the corresponding continuous model.

关键词： sirs epidemic model backward Euler method global asymptotic stability.

The Effect of State-Dependent Control for an sirs epidemic model with Varying Total Population

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Journal of Applied Mathematics and Physics 2016年第10期4卷 1889-1898页

作者： Fuwei Zhang Linfei Nie College of Mathematics and Systems Science Xinjiang University Urumqi China

Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an sirs epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.

关键词： sirs epidemic model Varying Total Population State-Dependent Pulse Control Periodic Solution Orbital Stability

sirs epidemic modeling using fractional-ordered differential equations:Role of fear effect

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International Journal of Biomathematics 2024年第5期17卷 79-100页

作者： Shiv Mangal O.P.Misra Joydip Dhar School of Mathematics and Allied Sciences Jiwaji University GwaliorMadhya PradeshIndia Department of Mathematics Post Graduate College BinaMadhya PradeshIndia Department of Applied Sciences Atal Bihari Vajpayee-Indian Institute of Information Technology and Management GwaliorMadhya PradeshIndia

In this paper,an sirs epidemic model using Grunwald-Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious *** criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction *** condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation ***,using the Grunwald-Letnikov approximation,the simulation is carried out to confirm the validity of analytic results *** the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021,we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical *** the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases.

关键词： sirs epidemic model fear effect Mittag-Leffler function Hopf bifurcation parameter estimation

GLOBAL STABILITY OF sirs epidemic modelS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

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Acta Mathematica Scientia 2012年第3期32卷 851-865页

作者： Yoichi Enatsu Yukihiko Nakata Yoshiaki Muroya Department of Pure and Applied Mathematics Waseda University3-4-1 OhkuboShinjuku-kuTokyo169-8555Japan Basque Center for Applied Mathematics Mazarredo14 E-48009 BilbaoSpain Department of Mathematics Waseda University 3-4-1 OhkuboShinjuku-kuTokyo 169-8555Japan

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an sirs epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

关键词： sirs epidemic model nonlinear incidence rate global asymptotic stability distributed delays Lyapunov functional

Traveling wave solutions of a nonlocal dispersal sirs model with spatio-temporal delay

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International Journal of Biomathematics 2017年第5期10卷 239-261页

作者： Zhaohai Ma Rong Yuan School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China

This paper is mainly concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal sirs model with nonlocal delayed transmissions. We find that the existence and nonexistence of traveling wave solutions are determined by the critical wave speed c^＊. More specifically, we establish the existence of traveling wave solutions for every wave speed c〉c^＊ and R0 〉 1 by means of upper-lower solutions and Schauder＇s fixed point theorem. Nonexistence of traveling wave solutions is obtained by Laplace transform for any wave speed c ∈ （0, c^＊） and R0 〉 1.

关键词： sirs epidemic model traveling wave solutions nonlocal dispersal nonlocal delay Laplace transform.