Global dynamics of a reaction–diffusion malaria model

2021 ◽  
Vol 61 ◽  
pp. 103332
Author(s):  
Ming-Zhen Xin ◽  
Bin-Guo Wang
Keyword(s):  
Reaction Diffusion ◽  
Global Dynamics ◽  
Malaria Model

Dynamics of an infection age-space structured cholera model with Neumann boundary condition

2021 ◽  
pp. 1-30
Author(s):  
WEIWEI LIU ◽  
JINLIANG WANG ◽  
RAN ZHANG
Keyword(s):  
Vibrio Cholerae ◽  
Disease Transmission ◽  
Global Attractivity ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Human Populations ◽  
Global Dynamics ◽  
Infection Age ◽  
Reaction Diffusion Model ◽  
Disease Persistence

This paper investigates global dynamics of an infection age-space structured cholera model. The model describes the vibrio cholerae transmission in human population, where infection-age structure of vibrio cholerae and infectious individuals are incorporated to measure the infectivity during the different stage of disease transmission. The model is described by reaction–diffusion models involving the spatial dispersal of vibrios and the mobility of human populations in the same domain Ω ⊂ ℝ n . We first give the well-posedness of the model by converting the model to a reaction–diffusion model and two Volterra integral equations and obtain two constant equilibria. Our result suggest that the basic reproduction number determines the dichotomy of disease persistence and extinction, which is achieved by studying the local stability of equilibria, disease persistence and global attractivity of equilibria.

scholarly journals Global dynamics of an age-structured malaria model with prevention

2019 ◽  
Vol 16 (3) ◽  
pp. 1625-1653 ◽  
Author(s):  
Zhong-Kai Guo ◽  
◽  
Hai-Feng Huo ◽  
Hong Xiang ◽  
Keyword(s):  
Global Dynamics ◽  
Age Structured ◽  
Malaria Model

scholarly journals Stability Analysis of a Reaction-Diffusion Heroin Epidemic Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Liang Zhang ◽  
Yifan Xing
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Ode Model ◽  
Globally Asymptotically Stable ◽  
D Model ◽  
Drug Free ◽  
The Basic Reproduction Number

A reaction-diffusion (R-D) heroin epidemic model with relapse and permanent immunization is formulated. We use the basic reproduction number R0 to determine the global dynamics of the models. For both the ordinary differential equation (ODE) model and the R-D model, it is shown that the drug-free equilibrium is globally asymptotically stable if R0≤1, and if R0>1, the drug-addiction equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to illustrate our analytical results.

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