Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function

2019 ◽  
Vol 535 ◽  
pp. 122300 ◽  
Author(s):  
S.P. Rajasekar ◽  
M. Pitchaimani ◽  
Quanxin Zhu
Keyword(s):  
Incidence Rate ◽  
Sir Model ◽  
Dynamic Threshold ◽  
Treatment Function ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
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 an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jinhong Zhang ◽  
Jianwen Jia ◽  
Xinyu Song
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Treatment Function ◽  
Threshold Conditions ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Saturated Treatment

The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings.

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
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