Dynamics of a stochastic SIR epidemic model driven by Lévy jumps with saturated incidence rate and saturated treatment function

2021 ◽  
pp. 1-19
Author(s):  
Amine EL Koufi ◽  
Jihad Adnani ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Model Driven ◽  
Sir Epidemic ◽  
Treatment Function ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Stochastic Sir ◽  
Lévy Jumps ◽  
Saturated Treatment

Stability analysis of a delayed sir epidemic model with diffusion and saturated incidence rate

2020 ◽  
Vol 1 (4) ◽  
Author(s):  
Abdelhadi Abta ◽  
Salahaddine Boutayeb ◽  
Hassan Laarabi ◽  
Mostafa Rachik ◽  
Hamad Talibi Alaoui
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

scholarly journals Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jinhong Zhang ◽  
Jianwen Jia ◽  
Xinyu Song
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Treatment Function ◽  
Threshold Conditions ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Saturated Treatment

The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings.

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