Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate

We formulate a delayed SIR epidemic model by introducing a latent period into susceptible, and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable. Moreover, we prove that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end some numerical simulations are given to compare our model with existing model.

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DYNAMICS OF AN IMPULSIVE STOCHASTIC SIR EPIDEMIC MODEL WITH SATURATED INCIDENCE RATE

Journal of Applied Analysis & Computation ◽

10.11948/20190214 ◽

2020 ◽

Vol 10 (4) ◽

pp. 1396-1415

Author(s):

Wenjie Cao ◽

◽

Tao Pan ◽

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Sir Epidemic Model ◽

Sir Epidemic ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Stochastic Sir

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On the nonstandard numerical discretization of SIR epidemic model with a saturated incidence rate and vaccination

AIMS Mathematics ◽

10.3934/math.2021010 ◽

2021 ◽

Vol 6 (1) ◽

pp. 141-155

Author(s):

Agus Suryanto ◽

◽

Isnani Darti

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Sir Epidemic Model ◽

Sir Epidemic ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Numerical Discretization

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Optimal control of an epidemic model with a saturated incidence rate

Nonlinear Analysis Modelling and Control ◽

10.15388/na.17.4.14050 ◽

2012 ◽

Vol 17 (4) ◽

pp. 448-459 ◽

Cited By ~ 14

Author(s):

Hassan Laarabi ◽

El Houssine Labriji ◽

Mostafa Rachik ◽

Abdelilah Kaddar

Keyword(s):

Optimal Control ◽

Incidence Rate ◽

Epidemic Model ◽

Sir Epidemic Model ◽

Sir Epidemic ◽

Control Framework ◽

Adjoint Variables ◽

Saturated Incidence Rate ◽

Saturated Incidence

In this study we consider a mathematical model of an SIR epidemic model with a saturated incidence rate. We used the optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. The existence result was discussed. A characterization of the optimal control via adjoint variables was established. We obtained an optimality system that we sought to solve numerically by a competitive Gauss–Seidel like implicit difference method.

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Wave propagation of a discrete SIR epidemic model with a saturated incidence rate

International Journal of Biomathematics ◽

10.1142/s1793524519500293 ◽

2019 ◽

Vol 12 (03) ◽

pp. 1950029 ◽

Cited By ~ 1

Author(s):

Qiu Zhang ◽

Shi-Liang Wu

Keyword(s):

Incidence Rate ◽

Traveling Wave ◽

Epidemic Model ◽

Traveling Wave Solutions ◽

Sir Epidemic Model ◽

Sir Epidemic ◽

Wave Solutions ◽

Saturated Incidence Rate ◽

Minimal Wave Speed ◽

Saturated Incidence

This paper is concerned with the traveling wave solutions for a discrete SIR epidemic model with a saturated incidence rate. We show that the existence and non-existence of the traveling wave solutions are determined by the basic reproduction number [Formula: see text] of the corresponding ordinary differential system and the minimal wave speed [Formula: see text]. More specifically, we first prove the existence of the traveling wave solutions for [Formula: see text] and [Formula: see text] via considering a truncated initial value problem and using the Schauder’s fixed point theorem. The existence of the traveling wave solutions with speed [Formula: see text] is then proved by using a limiting argument. The main difficulty is to show that the limit of a decreasing sequence of the traveling wave solutions with super-critical speeds is non-trivial. Finally, the non-existence of the traveling wave solutions for [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] is proved.

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