Backward bifurcation and stability analysis of a network-based SIS epidemic model with saturated treatment function

2019 ◽  
Vol 527 ◽  
pp. 121407 ◽  
Author(s):  
Yi-Jie Huang ◽  
Chun-Hsien Li
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Backward Bifurcation ◽  
Sis Epidemic Model ◽  
Treatment Function ◽  
Bifurcation And Stability ◽  
Saturated Treatment ◽  
Sis Epidemic

DYNAMICS OF SIS EPIDEMIC MODEL WITH THE STANDARD INCIDENCE RATE AND SATURATED TREATMENT FUNCTION

2012 ◽  
Vol 05 (03) ◽  
pp. 1260003 ◽  
Author(s):  
JINGJING WEI ◽  
JING-AN CUI
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Recruitment Rate ◽  
Globally Asymptotically Stable ◽  
Sis Epidemic Model ◽  
Treatment Function ◽  
Two Factors ◽  
Saturated Treatment ◽  
Disease Free ◽  
Sis Epidemic

An SIS epidemic model with the standard incidence rate and saturated treatment function is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the population are also studied. We find that the effect of the maximum recovery per unit of time and the recruitment rate of the population over some level are two factors which lead to the backward bifurcation, and in some cases, the model may undergo the saddle-node bifurcation or Bogdanov–Takens bifurcation. It is shown that the disease-free equilibrium is globally asymptotically stable under some conditions. Numerical simulations are consistent with our obtained results in theorems, which show that improving the efficiency and capacity of treatment is important for control of disease.

A simple SIS epidemic model with a backward bifurcation

2000 ◽  
Vol 40 (6) ◽  
pp. 525-540 ◽  
Author(s):  
P. van den Driessche ◽  
James Watmough
Keyword(s):  
Epidemic Model ◽  
Backward Bifurcation ◽  
Sis Epidemic Model ◽  
Sis Epidemic

Modelling the role of opportunistic diseases in coinfection

2018 ◽  
Vol 13 (3) ◽  
pp. 28
Author(s):  
Marcos Marvá ◽  
Rafael Bravo de la Parra ◽  
Ezio Venturino
Keyword(s):  
Epidemic Model ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Treatment Rate ◽  
Opportunistic Disease ◽  
Sis Epidemic Model ◽  
Primary Disease ◽  
Sis Epidemic

In this paper, we formulate a model for evaluating the effects of an opportunistic disease affecting only those individuals already infected by a primary disease. The opportunistic disease act on a faster time scale and it is represented by an SIS epidemic model with frequency-dependent transmission. The primary disease is governed by an SIS epidemic model with density-dependent transmission, and we consider two different recovery cases. The first one assumes a constant recovery rate whereas the second one takes into account limited treatment resources by means of a saturating treatment rate. No demographics is included in these models.Our results indicate that misunderstanding the role of the opportunistic disease may lead to wrong estimates of the overall potential amount of infected individuals. In the case of constant recovery rate, an expression measuring this discrepancy is derived, as well as conditions on the opportunistic disease imposing a coinfection endemic state on a primary disease otherwise tending to disappear. The case of saturating treatment rate adds the phenomenon of backward bifurcation, which fosters the presence of endemic coinfection and greater levels of infected individuals. Nevertheless, there are specific situations where increasing the opportunistic disease basic reproduction number helps to eradicate both diseases.

Analysis of a fuzzy epidemic model with saturated treatment and disease transmission

2018 ◽  
Vol 11 (01) ◽  
pp. 1850002 ◽  
Author(s):  
Swapan Kumar Nandi ◽  
Soovoojeet Jana ◽  
Manotosh Manadal ◽  
T. K. Kar
Keyword(s):  
Epidemic Model ◽  
Disease Transmission ◽  
Fuzzy Numbers ◽  
Transmission Rate ◽  
Dynamical Behavior ◽  
Threshold Condition ◽  
Sis Epidemic Model ◽  
Fuzzy Expected Value ◽  
Treatment Function ◽  
Saturated Treatment

In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is customized by considering the disease transmission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investigated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.

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