Multi stability and global bifurcations in epidemic model with distributed delay SIRnS-model

2019 ◽  
Vol 92 (2) ◽  
Author(s):  
Gorm Gruner Jensen ◽  
Florian Uekermann ◽  
Kim Sneppen
Keyword(s):  
Epidemic Model ◽  
Distributed Delay ◽  
Global Bifurcations

scholarly journals Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

2020 ◽  
Vol 133 ◽  
pp. 109643 ◽  
Author(s):  
Tomás Caraballo ◽  
Mohamed El Fatini ◽  
Mohamed El Khalifi ◽  
Richard Gerlach ◽  
Roger Pettersson
Keyword(s):  
Gamma Distribution ◽  
Epidemic Model ◽  
Distributed Delay ◽  
Distribution Kernel

Dynamics of a delayed epidemic model with varying immunity period and nonlinear transmission

2015 ◽  
Vol 08 (02) ◽  
pp. 1550027 ◽  
Author(s):  
Aadil Lahrouz
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Incidence Rates ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
The Basic Reproduction Number

An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.

The long-time behavior of a stochastic SIR epidemic model with distributed delay and multidimensional Lévy jumps

2021 ◽  
Author(s):  
Driss Kiouach ◽  
Yassine Sabbar
Keyword(s):  
Epidemic Model ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Time Behavior ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Long Run ◽  
Long Time ◽  
Lévy Jumps

This paper reports novel theoretical and analytical results for a perturbed version of a SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by Itô–Lévy stochastic differential equations in order to simulate sudden and unexpected external phenomena. By using some new and ameliorated mathematical approaches, we study the long-run characteristics of the perturbed delayed model. Within this scope, we give sufficient conditions for two interesting asymptotic properties: extinction and persistence of the epidemic. One of the most interesting results is that the dynamics of the stochastic model are closely related to the intensities of white noises and Lévy jumps, which can give us a good insight into the evolution of the epidemic in some unexpected situations. Our work complements the results of some previous investigations and provides a new approach to predict and analyze the dynamic behavior of epidemics with distributed delay. For illustrative purposes, numerical examples are presented for checking the theoretical study.

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