Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility

We propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next-generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number ℛ0 and some assumptions for the incidence rate.

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Threshold Dynamics of an SIR Epidemic Model with Nonlinear Incidence Rate and Non-Local Delay Effect

Wuhan University Journal of Natural Sciences ◽

10.1007/s11859-018-1356-4 ◽

2018 ◽

Vol 23 (6) ◽

pp. 503-513

Author(s):

Shuangming Wang

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Threshold Dynamics ◽

Sir Epidemic Model ◽

Delay Effect ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Sir Epidemic ◽

Non Local

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Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

International Journal of Differential Equations ◽

10.1155/2017/5796958 ◽

2017 ◽

Vol 2017 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Eric Ávila-Vales ◽

Erika Rivero-Esquivel ◽

Gerardo Emilio García-Almeida

Keyword(s):

Numerical Simulations ◽

Incidence Rate ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Global Dynamics ◽

Threshold Parameter ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

General Incidence Rate ◽

The Basic Reproduction Number

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form Sf(I), and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

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A note on an age-of-infection SVIR model with nonlinear incidence

International Journal of Biomathematics ◽

10.1142/s1793524517500644 ◽

2017 ◽

Vol 10 (05) ◽

pp. 1750064 ◽

Cited By ~ 2

Author(s):

Junyuan Yang ◽

Zhen Jin ◽

Lin Wang ◽

Fei Xu

Keyword(s):

Incidence Rate ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Lyapunov Functionals ◽

Threshold Parameter ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Age Of Infection ◽

Number Formula ◽

The Basic Reproduction Number

In this paper, nonlinear incidence rate is incorporated into an age-of-infection SVIR epidemiological model. By the method of Lyapunov functionals, it is shown that the basic reproduction number [Formula: see text] of the model is a threshold parameter in the sense that if [Formula: see text], the disease dies out, while if [Formula: see text], the disease persists.

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Optimal Control for a SIR Epidemic Model with Nonlinear Incidence Rate

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/201611407 ◽

2016 ◽

Vol 11 (4) ◽

pp. 89-104 ◽

Cited By ~ 8

Author(s):

E.V. Grigorieva ◽

E.N. Khailov ◽

A. Korobeinikov

Keyword(s):

Optimal Control ◽

Incidence Rate ◽

Epidemic Model ◽

Sir Epidemic Model ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Sir Epidemic

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Stability Analysis of a Delayed SIR Epidemic Model with Stage Structure and Nonlinear Incidence

Discrete Dynamics in Nature and Society ◽

10.1155/2009/979217 ◽

2009 ◽

Vol 2009 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Xiaohong Tian ◽

Rui Xu

Keyword(s):

Basic Reproduction Number ◽

Epidemic Model ◽

Reproduction Number ◽

Sufficient Conditions ◽

Stage Structure ◽

Sir Epidemic Model ◽

Globally Asymptotically Stable ◽

Sir Epidemic ◽

The Stability ◽

The Basic Reproduction Number

We investigate the stability of an SIR epidemic model with stage structure and time delay. By analyzing the eigenvalues of the corresponding characteristic equation, the local stability of each feasible equilibrium of the model is established. By using comparison arguments, it is proved when the basic reproduction number is less than unity, the disease free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, sufficient conditions are derived for the global stability of an endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.

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

International Journal of Stochastic Analysis ◽

10.1155/2013/431257 ◽

2013 ◽

Vol 2013 ◽

pp. 1-4 ◽

Cited By ~ 6

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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