Global stability analysis of an SIR epidemic model with demographics and time delay on networks

2014 ◽  
Vol 410 ◽  
pp. 268-275 ◽  
Author(s):  
Jianrong Wang ◽  
Jianping Wang ◽  
Maoxing Liu ◽  
Youwen Li
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Global Stability ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Global Stability Analysis ◽  
Sir Epidemic

Global stability of a diffused SIR epidemic model with general incidence rate and time delay

2016 ◽  
Vol 10 ◽  
pp. 807-816
Author(s):  
El Mehdi Lotfi ◽  
Mehdi Maziane ◽  
Marouane Mahrouf ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Time Delay ◽  
Global Stability ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
General Incidence Rate

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 Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Shujing Gao ◽  
Zhidong Teng ◽  
Juan J. Nieto ◽  
Angela Torres
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Epidemic Model ◽  
Discrete Dynamical System ◽  
Vaccination Rate ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Sir Epidemic ◽  
Distributed Time Delay ◽  
Large Pulse

Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.

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