scholarly journals Phase portraits of SIR epidemic models with vertical transmissions and linear treatment

2021 ◽  
Author(s):  
Marvin Hoti
Keyword(s):  
Epidemic Models ◽  
Phase Portraits ◽  
Sir Epidemic ◽  
Sir Epidemic Models ◽  
Epidemic Diseases

Susceptible-infective-removed epidemic models with horizontal and vertical transmissions and linear treatment rates are investigated. All the ranges of the parameters involved in the models for the infection-free equilibrium and the epidemic equilibrium to be positive are found. Like the previous results on the models without vertical transmissions or the linear treatments, we study stability of these equilibria. The novelty is that we justify that these positive equilibria are stable focuses or stable nodes under suitable conditions on the parameters. These results provide more detailed descriptions of behaviours of the epidemic diseases near the equilibria. Our results will exhibit the effect of the vertical transmissions and the linear treatment rates on the epidemic models. Some simulations results are provided to understand the phase portraits near the equilibria.

scholarly journals Phase portraits of SIR epidemic models with vertical transmissions and linear treatment

2021 ◽  
Author(s):  
Marvin Hoti
Keyword(s):  
Epidemic Models ◽  
Phase Portraits ◽  
Sir Epidemic ◽  
Sir Epidemic Models ◽  
Epidemic Diseases

Susceptible-infective-removed epidemic models with horizontal and vertical transmissions and linear treatment rates are investigated. All the ranges of the parameters involved in the models for the infection-free equilibrium and the epidemic equilibrium to be positive are found. Like the previous results on the models without vertical transmissions or the linear treatments, we study stability of these equilibria. The novelty is that we justify that these positive equilibria are stable focuses or stable nodes under suitable conditions on the parameters. These results provide more detailed descriptions of behaviours of the epidemic diseases near the equilibria. Our results will exhibit the effect of the vertical transmissions and the linear treatment rates on the epidemic models. Some simulations results are provided to understand the phase portraits near the equilibria.

Abel-Gontcharoff pseudopolynomials and the exact final outcome of SIR epidemic models (III)

1999 ◽  
Vol 31 (2) ◽  
pp. 532-550 ◽  
Author(s):  
Claude Lefèvre ◽  
Philippe Picard
Keyword(s):  
Algebraic Structure ◽  
Preceding Paper ◽  
Epidemic Models ◽  
Unified Approach ◽  
Finite Populations ◽  
Final State ◽  
Collective Models ◽  
Markovian Models ◽  
Sir Epidemic ◽  
Sir Epidemic Models

The paper is concerned with the final state and severity of a number of SIR epidemic models in finite populations. Two different classes of models are considered, namely the classical SIR Markovian models and the collective models introduced recently by the authors. First, by applying a simple martingale argument, it is shown that in both cases, there exists a common algebraic structure underlying the exact law of the final state and severity. Then, a unified approach to these statistics is developed by exploiting the theory of Abel-Gontcharoff pseudopolynomials (presented in a preceding paper).

scholarly journals Bifurcation analysis of an SIR epidemic model with saturated treatment function

2021 ◽  
Author(s):  
Phuc Ngo
Keyword(s):  
Epidemic Models ◽  
Stable Node ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic ◽  
Treatment Function ◽  
Sir Epidemic Models ◽  
Saturated Treatment ◽  
Disease Free

In this thesis we investigate the dynamics and bifurcation of SIR epidemic models with horizontal and vertical transmissions and saturated treatment rate. It is proved that such SIR epidemic models always have positive disease free equilibria and also have three positive epidemic equilibria. The ranges of the parameters related in the model were found under which the equilibria of the models are positive. By applying the qualitative theory of planar systems, it is shown the disease free equilibria is a saddle, stable node and globally asymptotically stable. Furthermore, it is also shown that the interior equilibria are saddle, saddle node or saddle point.

scholarly journals Coupling of Two SIR Epidemic Models with Variable Susceptibilities and Infectivities

2007 ◽  
Vol 44 (01) ◽  
pp. 41-57 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Size Distribution ◽  
Random Graph ◽  
Epidemic Model ◽  
Epidemic Models ◽  
Final Size ◽  
Sir Epidemic ◽  
Novel Approach ◽  
Stochastic Epidemic ◽  
Sir Epidemic Models ◽  
Variable Susceptibility

The variable generalised stochastic epidemic model, which allows for variability in both the susceptibilities and infectivities of individuals, is analysed. A very different epidemic model which exhibits variable susceptibility and infectivity is the random-graph epidemic model. A suitable coupling of the two epidemic models is derived which enables us to show that, whilst the epidemics are very different in appearance, they have the same asymptotic final size distribution. The coupling provides a novel approach to studying random-graph epidemic models.

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