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.

scholarly journals A Bistable Phenomena Induced by a Mean-Field SIS Epidemic Model on Complex Networks: A Geometric Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaoyan Wang ◽  
Junyuan Yang
Keyword(s):  
Complex Networks ◽  
Epidemic Model ◽  
Mean Field ◽  
Geometric Approach ◽  
Backward Bifurcation ◽  
Medical Resources ◽  
Epidemic Curve ◽  
Sis Epidemic Model ◽  
Lag Effect ◽  
Sis Epidemic

In this paper, we propose a degree-based mean-field SIS epidemic model with a saturated function on complex networks. First, we adopt an edge-compartmental approach to lower the dimensions of such a proposed system. Then we give the existence of the feasible equilibria and completely study their stability by a geometric approach. We show that the proposed system exhibits a backward bifurcation, whose stabilities are determined by signs of the tangent slopes of the epidemic curve at the associated equilibria. Our results suggest that increasing the management and the allocation of medical resources effectively mitigate the lag effect of the treatment and then reduce the risk of an outbreak. Moreover, we show that decreasing the average of a network sufficiently eradicates the disease in a region or a country.

Dynamical analysis of the SIS epidemic model in cluster events

2021 ◽  
Author(s):  
Dun Han ◽  
Junjie Wei ◽  
Haidong Xu ◽  
Dandan Li
Keyword(s):  
Epidemic Model ◽  
Dynamical Analysis ◽  
Sis Epidemic Model ◽  
Sis Epidemic

scholarly journals Endemic Behaviour of SIS Epidemics with General Infectious Period Distributions

2014 ◽  
Vol 46 (01) ◽  
pp. 241-255 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Epidemic Model ◽  
Branching Process ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Sis Epidemic Model ◽  
Branching Process With Immigration ◽  
Sis Epidemic ◽  
Sis Epidemics ◽  
Surprising Observation

We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through

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