scholarly journals Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 2993
Author(s):  
Xin Jiang
Keyword(s):  
Theoretical Analysis ◽  
Mathematical Analysis ◽  
Local Stability ◽  
Infection Model ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Infection Rates ◽  
Age Structured ◽  
Rigorous Mathematical Analysis

This paper studies the global dynamics of a cholera model incorporating age structures and general infection rates. First, we explore the existence and point dissipativeness of the orbit and analyze the asymptotical smoothness. Then, we perform rigorous mathematical analysis on the existence and local stability of equilibria. Based on the uniform persistence, we further investigate the global behavior of the cholera infection model. The results of theoretical analysis are well confirmed by numerical simulations. This research generalizes some known results and provides deeper insights into the dynamics of cholera propagation.

Global dynamics of an age-structured viral infection model with general incidence function and absorption

2018 ◽  
Vol 11 (05) ◽  
pp. 1850065 ◽  
Author(s):  
Khalid Hattaf ◽  
Yu Yang
Keyword(s):  
Viral Infection ◽  
Infection Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Incidence Function ◽  
Proposed Model ◽  
Viral Particles ◽  
Age Structured ◽  
Well Posed ◽  
Viral Infection Model

In this paper, we propose an age-structured viral infection model with general incidence function that takes account of the loss of viral particles due to their absorption into susceptible cells. The proposed model is described by partial differential and ordinary differential equations. We first show that the model is mathematically and biologically well-posed. Furthermore, the uniform persistence and the global behavior of the model are investigated. Moreover, the age-structured models and results presented in many previous studies are improved and generalized.

Global stability of an age-structured SVEIR epidemic model with waning immunity, latency and relapse

2017 ◽  
Vol 10 (03) ◽  
pp. 1750038 ◽  
Author(s):  
Lili Liu ◽  
Xianning Liu
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Epidemic Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Sharp Threshold ◽  
Age Dependent ◽  
Waning Immunity ◽  
Age Structured ◽  
Disease Free

The global dynamics of an SVEIR epidemic model with age-dependent waning immunity, latency and relapse are studied. Sharp threshold properties for global asymptotic stability of both disease-free equilibrium and endemic equilibrium are given. The asymptotic smoothness, uniform persistence and the existence of interior global attractor of the semi-flow generated by a family of solutions of the system are also addressed. Furthermore, some related strategies for controlling the spread of diseases are discussed.

scholarly journals Global dynamics for a class of infection-age model with nonlinear incidence

2018 ◽  
Vol 24 (1) ◽  
pp. 47-72 ◽  
Author(s):  
Yuji Li ◽  
Rui Xu ◽  
Jiazhe Lin
Keyword(s):  
Viral Infection ◽  
Reproduction Number ◽  
Infection Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Infection Age ◽  
Age Model ◽  
Viral Infection Model

In this paper, we propose an HBV viral infection model with continuous age structure and nonlinear incidence rate. Asymptotic smoothness of the semi-flow generated by the model is studied. Then we caculate the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on uniform persistence by reformulating the system as a system of Volterra integral equations. The global dynamics of the model is established by using suitable Lyapunov functionals and LaSalle's invariance principle. We further investigate the global behaviors of the HBV viral infection model with saturation incidence through numerical simulations.

scholarly journals Mathematical Analysis of Intraguild Interactions among Hosts, Parasitoids and Predators

2021 ◽  
Vol 52 (1) ◽  
pp. 171-187
Author(s):  
Hongming You ◽  
Kaijen Cheng
Keyword(s):  
Mathematical Model ◽  
Mathematical Analysis ◽  
Local Stability ◽  
Global Dynamics ◽  
Intraguild Interactions ◽  
Positivity Of Solution

In this work, we consider a mathematical model of an omnivorous ecosystem in which intermediate predators are infected by parasites. We first establish the boundeness and positivity of solution with conditions. Then the existence and local stability of all equilibria are clarified in R4. Finally, some global dynamics will be analyzed.  

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