scholarly journals Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

2020 ◽  
Vol 7 ◽  
Author(s):  
Nauman Ahmed ◽  
Mehreen Fatima ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Epidemic Model ◽  
Reaction Diffusion

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 NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

2010 ◽  
Vol 20 (05) ◽  
pp. 731-756 ◽  
Author(s):  
VERÓNICA ANAYA ◽  
MOSTAFA BENDAHMANE ◽  
MAURICIO SEPÚLVEDA
Keyword(s):  
Weak Solution ◽  
Numerical Analysis ◽  
Numerical Scheme ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence Of Weak Solutions ◽  
Early Tumor ◽  
Volume Method

We consider a reaction–diffusion system of 2 × 2 equations modeling the spread of early tumor cells. The existence of weak solutions is ensured by a classical argument of Faedo–Galerkin method. Then, we present a numerical scheme for this model based on a finite volume method. We establish the existence of discrete solutions to this scheme, and we show that it converges to a weak solution. Finally, some numerical simulations are reported with pattern formation examples.

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.

Numerical analysis of diffusive susceptible-infected-recovered epidemic model in three space dimension

2020 ◽  
Vol 132 ◽  
pp. 109535 ◽  
Author(s):  
Nauman Ahmed ◽  
Mubasher Ali ◽  
Dumitru Baleanu ◽  
Muhammad Rafiq ◽  
Muhammad Aziz ur Rehman
Keyword(s):  
Numerical Analysis ◽  
Epidemic Model ◽  
Space Dimension ◽  
Three Space

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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