Analysis on a diffusive two-stage epidemic model with logistic growth and saturated incidence rates

2022 ◽  
Vol 64 ◽  
pp. 103444
Author(s):  
Guodong Liu ◽  
Xiaoyan Zhang
Keyword(s):  
Epidemic Model ◽  
Incidence Rates ◽  
Logistic Growth ◽  
Two Stage ◽  
Saturated Incidence

scholarly journals Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Panpan Wang ◽  
Jianwen Jia
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Incidence Rates ◽  
Saturated Incidence ◽  
Global Positive Solution

Abstract In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.

scholarly journals Stochastic analysis of a SIRI epidemic model with double saturated rates and relapse

2021 ◽  
Author(s):  
Yan Zhang ◽  
Shujing Gao ◽  
Shihua Chen
Keyword(s):  
Epidemic Model ◽  
Sufficient Conditions ◽  
Natural World ◽  
Incidence Rates ◽  
Environmental Fluctuation ◽  
Stochastic Perturbations ◽  
Saturated Incidence ◽  
Global Positive Solution ◽  
Random Fluctuations ◽  
Crucial Part

AbstractInfectious diseases have for centuries been the leading causes of death and disability worldwide and the environmental fluctuation is a crucial part of an ecosystem in the natural world. In this paper, we proposed and discussed a stochastic SIRI epidemic model incorporating double saturated incidence rates and relapse. The dynamical properties of the model were analyzed. The existence and uniqueness of a global positive solution were proven. Sufficient conditions were derived to guarantee the extinction and persistence in mean of the epidemic model. Additionally, ergodic stationary distribution of the stochastic SIRI model was discussed. Our results indicated that the intensity of relapse and stochastic perturbations greatly affected the dynamics of epidemic systems and if the random fluctuations were large enough, the disease could be accelerated to extinction while the stronger relapse rate were detrimental to the control of the disease.

scholarly journals Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

Dynamics of a time-delayed two-strain epidemic model with general incidence rates

2021 ◽  
Vol 153 ◽  
pp. 111527
Author(s):  
El Mehdi Farah ◽  
Saida Amine ◽  
Karam Allali
Keyword(s):  
Epidemic Model ◽  
Incidence Rates

scholarly journals Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

2020 ◽  
pp. 8-19
Author(s):  
Laid Chahrazed
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability ◽  
Disease Free ◽  
Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

Dynamical Analysis of Salmonella Epidemic Model With Saturated Incidence Rate

2021 ◽  
pp. 545-560
Author(s):  
Abiodun Oluwakemi ◽  
Ibrahim Mohammed ◽  
Adebimpe Olukayode ◽  
Oludoun Olajumoke ◽  
Gbadamosi Babatunde ◽  
...  
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Dynamical Analysis ◽  
Saturated Incidence Rate ◽  
Saturated Incidence
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