scholarly journals Stability and bifurcation analysis of a SIR model with saturated incidence rate and saturated treatment

2016 ◽  
Vol 121 ◽  
pp. 109-132 ◽  
Author(s):  
Erika Rivero-Esquivel ◽  
Eric Avila-Vales ◽  
Gerardo García-Almeida
Keyword(s):  
Incidence Rate ◽  
Bifurcation Analysis ◽  
Sir Model ◽  
Stability And Bifurcation ◽  
Stability And Bifurcation Analysis ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Saturated Treatment

A SATURATED TREATMENT MODEL FOR THE TRANSMISSION DYNAMICS OF RABIES

2019 ◽  
Vol 4 (1) ◽  
pp. 201
Author(s):  
A A Ayoade ◽  
O J Peter ◽  
T A Ayoola ◽  
S Amadiegwu ◽  
A A Victor
Keyword(s):  
Incidence Rate ◽  
Nonlinear Differential Equations ◽  
Viral Disease ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Infectious Agents ◽  
Multiple Control ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Saturated Treatment

Rabies is a viral disease that claims about 59 000 lives globally every year. The ignorance of the fact that man can be a carrier of the disease makes every practical and theoretical approach towards the study of the disease a good development. In this work, a mathematical model is designed to incorporate a saturated incidence rate such that the incidence rate is saturated around the infectious agents. The model is studied qualitatively via stability theory of nonlinear differential equations to assess the effects of general awareness, constant vaccination and the saturated treatment on the transmission dynamics of rabies disease. The effective reproduction number is derived and the numerical simulation is carried out to verify the analytical results. It is discovered that while general awareness plays pivotal roles in averting rabies death, multiple control measures have the tendency of driving rabies to extinction.

scholarly journals Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate

2013 ◽  
Vol 04 (10) ◽  
pp. 60-67 ◽  
Author(s):  
Wanwan Wang ◽  
Maoxing Liu ◽  
Jinqing Zhao
Keyword(s):  
Incidence Rate ◽  
Sir Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

Bifurcation Analysis of an SIV Epidemic Model with the Saturated Incidence Rate

2014 ◽  
Vol 24 (05) ◽  
pp. 1450060 ◽  
Author(s):  
Yakui Xue ◽  
Xiaoming Tang ◽  
Xinpeng Yuan
Keyword(s):  
Population Dynamics ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Vaccination Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

In this paper, an SIV epidemic model with the saturated incidence rate is investigated, considering the factors of population dynamics such as the constant recruitment of population, the natural morality and vaccination strategy. By carrying out the bifurcation analysis of the model, it is shown that numerous kinds of bifurcation occur for the model, such as Hopf bifurcation and Bogdanov–Takens bifurcation. The main results are illustrated by numerical simulations.

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