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Global dynamics of a fractional-order sir epidemic model with memory

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International Journal of Biomathematics 2020年第8期13卷 1-23页

作者： Parvaiz Ahmad Naik School of Mathematics and Statistics Xi’an Jiaotong University Xi’an Shaanxi 710049P.R.China

In this paper,an investigation and analysis of a nonlinear fractional-order sir epidemic model with Crowley-Martin type functional response and Holling type-II treatment rate are established along the *** existence and stability of the equilibrium points are *** sufficient conditions for the persistence of the disease are ***,a threshold value,Ro,is obtained which determines the stability of equilibria,then model equilibria are determined and their stability analysis is considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle invariant *** fractional derivative is taken in Caputo sense and the numerical solution of the model is obtained by LI scheme which involves the memory trace that can capture and integrate all past ***,by using Lyapunov functional approach,the global dynamics of the endemic equilibrium point is ***,some numerical simulations are performed to illustrate the effectiveness of the theoretical results *** outcome of the study reveals that the applied LI scheme is computationally very strong and effective to analyze fractional-order differential equations arising in disease *** results show that order of the fractional derivative has a significant effect on the dynamic ***,from the results,it is obvious that the memory effect is zero for p=*** the fractional-order p is decreased from 1,the memory trace nonlinearly increases from 0,and its dynamics strongly depends on *** memory effect points out the difference between the derivatives of the fractional-order and integer order.

关键词： sir epidemic model Caputo fractional derivative LI scheme memory stability analysis reproduction number Ro

Threshold Dynamics of an sir epidemic model with Nonlinear Incidence Rate and Non-Local Delay Effect

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Wuhan University Journal of Natural Sciences 2018年第6期23卷 503-513页

作者： WANG Shuangming Gansu Finance Collaboration and Innovation Center Lanzhou University of Finance and Economics School of Information Engineering Lanzhou University of Finance and Economics

In this paper, we are concerned with a reaction-diffusion sir epidemic model with nonlinear incidence rate and non-local delay effect in a continuous bounded spatial domain. We introduce the basic reproduction number R_0 of the model by the idea of next generation operator. By means of the theory of dynamical systems and uniform persistence, we investigate the global dynamics of the model in terms of R_0. Finally, we implement numerical simulations to show the feasibility of our results and explore some epidemiological insights.

关键词： sir epidemic model non-local nonlinear incidencerate basic reproduction number persistence

Study on the Dynamics of an sir epidemic model with Saturated Growth Rate

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Journal of Applied Mathematics and Physics 2022年第7期10卷 2164-2174页

作者： Yiting Lu Wenwen Wang Hui Chen Yuming Yan Xiaoliang Zhou School of Mathematics and Statistics Lingnan Normal University Zhanjiang China Zhanjiang Mechanical and Electrical School Zhanjiang China

In this paper, we investigate the dynamic properties of an sir epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.

关键词： sir epidemic model Ito Formula Extinction Persistence in the Mean Sense

Stability Analysis and Bifurcation Control For a Fractional Order sir epidemic model with Delay

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Stability Analysis and Bifurcation Control For a Fractional ...

Dynamic characterization of a stochastic sir infectious disease model with dual perturbation

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作者： Feng Liu Shuxian Huang Shiqi Zheng Hua O Wang School of Automation China University of Geosciences Hubei key Laboratory of Advanced Control and Intelligent Automation for Complex Systems Department of Mechanical Engineering Boston University

In this paper, a delayed fractional sir epidemic model with incommensurate orders is considered. Firstly, the stability is investigated and the conditions of the existence for Hopf bifurcation are attained by analyzing its characteristic equation. When the delay exceeds the critical value, a Hopf bifurcation occurs, the system loses its stability. An fractional PD control method is proposed to control the bifurcation behaviors of the delayed fractional sir epidemic model. Finally, some numerical simulations are given to illustrate the validity of theoretical analysis.

关键词： Fractional order stability bifurcation PD control sir epidemic model

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International Journal of Biomathematics 2021年第4期14卷 1-26页

作者： Driss Kiouach Yassine Sabbar LPAIS Laboratory Faculty of Sciences Dhar El Mahraz Sidi Mohamed Ben Abdellah UniversityFezMorocco

Environmental perturbations are unavoidable in the propagation of infectious *** this paper,we introduce the stochasticity into the susceptible-infected recovered(sir)model via thc^parameter perturbation *** stochastic disturbances associated with the disease transmission coefficient and the mortality rate are presented with two perturbations:Gaussian white noise and Levy jumps,*** idea provides an overview of disease dynamics under different random perturbation *** using new techniques and methods,we study certain interesting asymptotic properties of our perturbed model,namely:persistence in the mean,ergodicity and extinction of the *** illustrative purposes,numerical examples are presented for checking the theoretical study.

关键词： sir epidemic model white noise Levy noise stationary distribution persistence extinction

Time-varying and state-dependent recovery rates in epidemiological models

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Infectious Disease modelling 2017年第4期2卷 419-430页

作者： Scott Greenhalgh Troy Day Department of Mathematics Siena CollegeLoudonvilleNY12211USA Department of Mathematics and Statistics Queen's UniversityJeffery HallKingstonONK7L 3N6Canada

Differential equation models of infectious disease have undergone many theoretical extensions that are invaluable for the evaluation of disease *** instance,while one traditionally uses a bilinear term to describe the incidence rate of infection,physically more realistic generalizations exist to account for effects such as the saturation of ***,such theoretical extensions of recovery rates in differential equation models have only started to be *** is despite the fact that a constant rate often does not provide a good description of the dynamics of recovery and that the recovery rate is arguably as important as the incidence rate in governing the dynamics of a *** provide a first-principles derivation of state-dependent and time-varying recovery rates in differential equation models of infectious *** this derivation,we demonstrate how to obtain time-varying and state-dependent recovery rates based on the family of Pearson distributions and a power-law distribution,*** recovery rates based on the family of Pearson distributions,we show that uncertainty in skewness,in comparison to other statistical moments,is at least two times more impactful on the sensitivity of predicting an epidemic's *** addition,using recovery rates based on a power-law distribution,we provide a procedure to obtain state-dependent recovery *** such state-dependent rates,we derive a natural connection between recovery rate parameters with the mean and standard deviation of a power-law distribution,illustrating the impact that standard deviation has on the shape of an epidemic wave.

关键词： Differential equations Integral equations Infectious disease modeling Waiting time distribution Duration of infectiousness sir epidemic model

Inverse problem for adaptive sir model:Application to COVID-19 in Latin America

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Infectious Disease modelling 2022年第1期7卷 134-148页

作者： Tchavdar T.Marinov Rossitza S.Marinova Department of Natural Sciences Southern University at New OrleansNew OrleansLA70126USA Department of Mathematical and Physical Sciences Concordia University of EdmontonEdmontonABT5B 4E4Canada

This work presents a method for solving an Adaptive Susceptible-Infected-Removed(Asir)epidemic model with time-dependent transmission and removal *** COVID-19 data as of March 2021 are used for identifying the rates from an inverse *** estimated rates are used to solve the adaptive sir system for the spread of the infectious *** method simultaneously solves the problem for the time-dependent rates and the unknown functions of the A-sir *** results show the spread of COVID-19 in the World,Argentina,Brazil,Colombia,Dominican Republic,and *** of the reported affected by the disease individuals from the available real data and the values obtained with the A-sir model demonstrate how well the model simulates the dynamic of the infectious disease.

关键词： Inverse problem sir epidemic model Coefficient identification Time-dependent transmission and removal rates COVID-19

A new epidemic modeling approach:Multi-regions discrete-time model with travel-blocking vicinity optimal control strategy

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Infectious Disease modelling 2017年第3期2卷 304-322页

作者： Omar Zakary Mostafa Rachik Ilias Elmouki Laboratory of Analysis Modeling and Simulation(LAMS)Department of Mathematics and Computer ScienceHassan Ⅱ University of CasablancaBP 7955Sidi OthmanCasablancaMorocco

First,we devise in this paper,a multi-regions discrete-time model which describes the spatial-temporal spread of an epidemic which starts from one region and enters to regions which are connected with their neighbors by any kind of anthropological *** suppose homogeneous Susceptible-Infected-Removed(sir)populations,and we consider in our simulations,a grid of colored cells,which represents the whole domain affected by the epidemic while each cell can represent a sub-domain or ***,in order to minimize the number of infected individuals in one region,we propose an optimal control approach based on a travel-blocking vicinity strategy which aims to control only one cell by restricting movements of infected people coming from all neighboring ***,we show the influence of the optimal control approach on the controlled *** should also note that the cellular modeling approach we propose here,can also describes infection dynamics of regions which are not necessarily attached one to an other,even if no empty space can be viewed between *** theoretical method we follow for the characterization of the travel-locking optimal controls,is based on a discrete version of Pontryagin's maximum principle while the numerical approach applied to the multi-points boundary value problems we obtain here,is based on discrete progressive-regressive iterative *** illustrate our modeling and control approaches by giving an example of 100 regions.

关键词： Multi-regions model sir epidemic model Discrete-time model Optimal control Vicinity Travel-blocking

An Analytic Approximate Solution of the sir model

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Applied Mathematics 2021年第1期12卷 58-73页

作者： I. Lazzizzera Department of Physics University of Trento via Sommarive 14 Povo (Trento) Italy Trento Institute for Fundamental Physics and Applications (INFN) via Sommarive 14 Povo (Trento) Italy

The sir(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure exact (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the exact equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called basic reproduction ratio, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.

关键词： sir epidemic model Kermack-McKendrick model epidemic Dynamics Approximate Analytic Solution