scholarly journals Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission

2021 ◽  
Vol 18 (5) ◽  
pp. 6012-6033
Author(s):  
Lin Zhao ◽  
◽  
Haifeng Huo
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Spatial Propagation

scholarly journals Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
Kai Wang
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Media Coverage ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

Turing pattern selection in a reaction-diffusion epidemic model

2011 ◽  
Vol 20 (7) ◽  
pp. 074702 ◽  
Author(s):  
Wei-Ming Wang ◽  
Hou-Ye Liu ◽  
Yong-Li Cai ◽  
Zhen-Qing Li
Keyword(s):  
Epidemic Model ◽  
Reaction Diffusion ◽  
Pattern Selection ◽  
Turing Pattern

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.

A reaction–diffusion epidemic model with incubation period in almost periodic environments

2020 ◽  
pp. 1-24
Author(s):  
LIZHONG QIANG ◽  
BIN-GUO WANG ◽  
ZHI-CHENG WANG
Keyword(s):  
Time Delay ◽  
Spatial Heterogeneity ◽  
Incubation Period ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Fixed Time ◽  
Reaction Diffusion Equations ◽  
Threshold Dynamics ◽  
Almost Periodic ◽  
Periodic Reaction

In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent $${\lambda ^*}$$ for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of $${\lambda ^*}$$ . It is shown that the disease-free almost periodic solution is globally attractive if $${\lambda ^*} < 0$$ , while the disease is persistent if $${\lambda ^*} < 0$$ . By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation

2020 ◽  
Vol 134 ◽  
pp. 109686 ◽  
Author(s):  
Muhammad Farhan Tabassum ◽  
Muhammad Saeed ◽  
Ali Akgül ◽  
Muhammad Farman ◽  
Nazir Ahmad Chaudhry
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Padé Approximation ◽  
Pade Approximation ◽  
Aids Epidemic ◽  
Hiv Aids

scholarly journals Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

2020 ◽  
Author(s):  
Jorge E. Macías‐Díaz ◽  
Nauman Ahmed ◽  
Muhammad Jawaz ◽  
Muhammad Rafiq ◽  
Muhammad Aziz ur Rehman
Keyword(s):  
Epidemic Model ◽  
Reaction Diffusion ◽  
Delayed Reaction ◽  
Discrete Method
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