scholarly journals Stability Analysis of a Complex Dynamics of a SIR Epidemic Model with Bilinear Incidence Rate and Treatment

2020 ◽  
Vol 64 (02) ◽  
pp. 342-351
Author(s):  
Monika Badole ◽  
Sandeep Kumar Tiwari ◽  
Aayush Sharma
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Complex Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic

Stability analysis of a delayed sir epidemic model with diffusion and saturated incidence rate

2020 ◽  
Vol 1 (4) ◽  
Author(s):  
Abdelhadi Abta ◽  
Salahaddine Boutayeb ◽  
Hassan Laarabi ◽  
Mostafa Rachik ◽  
Hamad Talibi Alaoui
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

scholarly journals Stability Analysis of an SIR Epidemic Model with Non-Linear Incidence Rate and Treatment

2015 ◽  
Vol 03 (03) ◽  
pp. 104-110 ◽  
Author(s):  
Olukayode Adebimpe ◽  
Kehinde Adekunle Bashiru ◽  
Taiwo Adetola Ojurongbe
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Non Linear

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.

scholarly journals Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 147 ◽  
Author(s):  
Toshikazu Kuniya
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Transmission Function ◽  
Endemic Equilibrium ◽  
Dimensional System ◽  
Relevant Parameter ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Age Structured

In this paper, we are concerned with the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered (SIR) epidemic model. For a special form of the disease transmission function, we perform the reduction of the model into a four-dimensional system of ordinary differential equations (ODEs). We show that the unique endemic equilibrium of the reduced system exists if the basic reproduction number for the original system is greater than unity. Furthermore, we perform the stability analysis of the endemic equilibrium and obtain a fourth-order characteristic equation. By using the Routh–Hurwitz criterion, we numerically show that the endemic equilibrium is asymptotically stable in some epidemiologically relevant parameter settings.

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