Stability analysis of a time delayed SIR epidemic model with nonlinear incidence rate

Naresh, Ram; Tripathi, Agraj; Tchuenche, Jean M.; Sharma, Dileep

doi:10.1016/j.camwa.2009.03.110

Cited by 31 publications

(12 citation statements)

References 21 publications

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“…In this paper, we will consider two different delays , which are important parameters on the dynamic behavior. So, the present study is continuation of the previous work = by Naresh et al [43].…”

Section: Model Formulation and Invariant Regionsupporting

confidence: 74%

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Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate

Pei

et al. 2014

Abstract and Applied Analysis

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A delay SIR epidemic model with difference in immunity and successive vaccination is proposed to understand their effects on the disease spread. From theorems, it is obtained that the basic reproduction number governs the dynamic behavior of the system. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition about the basic reproduction number. By use of new computational techniques for delay differential equations, we prove that the system is permanent. Our results indicate that the recovery rate and the vaccination rate are two factors for the dynamic behavior of the system. Numerical simulations are carried out to investigate the influence of the key parameters on the spread of the disease, to support the analytical conclusion, and to illustrate possible behavioral scenarios of the model.

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Section: Model Formulation and Invariant Regionsupporting

confidence: 74%

“…In this paper, we will consider two different delays which are important parameters on the dynamic behavior. So, the present study is continuation of the previous work by [43]. Furthermore, from biological epidemic point of view, we investigate successive vaccination and difference in immunity in our system.…”

Section: Discussionmentioning

confidence: 65%

Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate

Pei

et al. 2014

Abstract and Applied Analysis

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“…If the basic reproduction number is larger than 1, then the disease-free equilibrium becomes unstable, and there is a unique endemic equilibrium. In most cases, the endemic equilibrium is locally or globally stable for all delays, whereas in some cases it is locally or globally stable only for small delay and Hopf bifurcation of periodic solutions may occur when the delay passes a certain critical value [17,19,20,23,25,29,35]. However, in our model any points (S 1 ,0,R 1 , .…”

Section: Introductionmentioning

confidence: 80%

Multiple epidemic waves in delayed susceptible-infected-recovered models on complex networks

Zou

Chen

2011

Phys. Rev. E

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“…Different observation have been conducted to study the dynamics of HIV/AIDS without time delay [6,8,9,12]. However a few modeling studies have been conducted to describe the effect of time delays [13][14][15]. Mainly HIV transmission in human body has two basic modes, horizontal transmission and vertical transmission.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of a delayed HIV/AIDS Epidemic Model with Saturated Incidence

Biswas¹,

Pal²

2017

IJMTT

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In this paper, we investigate the effect of time delay on an HIV/AIDS epidemic model with saturated incidence rate. We accept that the individuals are being recruited into sexually matured age group at a constant rate and incorporates time delay for one to become infected and the other become fullyblown. We assume that the disease spread only by sexually transmission.The model consists two equilibria, namely, a disease-free equilibrium and an endemic equilibrium. We calculate the basic reproduction number by using the next generation matrix. Mathematical analyses consecrated that the global dynamics of the spread of the HIV/AIDS infectious disease are totally determined by the basic reproduction number 0

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Stability analysis of a time delayed SIR epidemic model with nonlinear incidence rate

Cited by 31 publications

References 21 publications

Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate

Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate

Multiple epidemic waves in delayed susceptible-infected-recovered models on complex networks

Stability Analysis of a delayed HIV/AIDS Epidemic Model with Saturated Incidence

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