Bifurcation of a heroin model with nonlinear incidence rate

2016 ◽  
Vol 88 (1) ◽  
pp. 555-565 ◽  
Author(s):  
Mingju Ma ◽  
Sanyang Liu ◽  
Jun Li
Keyword(s):  
Incidence Rate ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Heroin Model

Dynamical analysis of a reaction–diffusion SEI epidemic model with nonlinear incidence rate

2021 ◽  
pp. 2150041
Author(s):  
Jianpeng Wang ◽  
Binxiang Dai
Keyword(s):  
Steady State ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Dynamical Analysis ◽  
Asymptotically Stable ◽  
Nonlinear Incidence Rate ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Positive Steady State

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] if [Formula: see text], the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if [Formula: see text]. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis.

scholarly journals Some asymptotic properties of SEIRS models with nonlinear incidence and random delays

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Divine Wanduku ◽  
B.O. Oluyede
Keyword(s):  
Differential Equations ◽  
Incidence Rate ◽  
Delay Differential Equations ◽  
Vivax Malaria ◽  
Asymptotic Properties ◽  
Analytical Techniques ◽  
Distributed Delays ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Delay Differential

This paper presents the dynamics of mosquitoes and humans with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN  R0* and  ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given.

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