Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment

2009 ◽  
Vol 10 (2) ◽  
pp. 565-575 ◽  
Author(s):  
Xu Zhang ◽  
Xianning Liu
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Backward Bifurcation ◽  
Global Dynamics ◽  
Sis Epidemic Model ◽  
General Incidence Rate ◽  
Sis Epidemic

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.

A SIS Epidemic Model with Eventual Impulsive Effects

2013 ◽  
Vol 393 ◽  
pp. 666-674
Author(s):  
Manuel de La Sen ◽  
A. Ibeas ◽  
S. Alonso-Quesada
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Total Population ◽  
Disease Model ◽  
Impulsive Effects ◽  
Time Varying ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Sis Epidemic

This paper studies a time-varyingSIS(i.e.containing susceptible and infected populations) propagation disease model exhibiting a nonlinear incidence rate and impulsive eventual culling of both populations so that the individuals recover with no immunity to the disease. The nonlinear incidence rate consists of two time-varying additive terms proportional to the susceptible and infected populations normalized to the total population.

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