scholarly journals Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function

2018 ◽  
Vol 09 (09) ◽  
pp. 1039-1054
Author(s):  
Aboudramane Guiro ◽  
Dramane Ouedraogo ◽  
Harouna Ouedraogo
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence ◽  
Incidence Function ◽  
Sir Epidemic ◽  
Nonlinear Incidence Function

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.

scholarly journals Optimal control of a SIR epidemic model with general incidence function and a time delays

Cubo (Temuco) ◽  
2018 ◽  
Vol 20 (2) ◽  
pp. 53-66 ◽  
Author(s):  
Moussa Barro ◽  
Aboudramane Guiro ◽  
Dramane Ouedraogo
Keyword(s):  
Optimal Control ◽  
Epidemic Model ◽  
Time Delays ◽  
Sir Epidemic Model ◽  
Incidence Function ◽  
Sir Epidemic

scholarly journals Stability Analysis of a Stochastic SIR Epidemic Model with Specific Nonlinear Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Jihad Adnani ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Random Perturbations ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Stochastic Sir ◽  
The Stability

We investigate a stochastic SIR epidemic model with specific nonlinear incidence rate. The stochastic model is derived from the deterministic epidemic model by introducing random perturbations around the endemic equilibrium state. The effect of random perturbations on the stability behavior of endemic equilibrium is discussed. Finally, numerical simulations are presented to illustrate our theoretical results.

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