Global stability for an SEI model of infectious diseases with immigration and age structure in susceptibility

2019 ◽  
Vol 12 (04) ◽  
pp. 1950042
Author(s):  
Gang Huang ◽  
Chenguang Nie ◽  
Yueping Dong
Keyword(s):  
Infectious Diseases ◽  
Global Stability ◽  
Age Structure ◽  
Lyapunov Functional ◽  
Asymptotically Stable ◽  
Structured Model ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
Age Structured Model ◽  
Sei Model

In this paper, we propose an SEI age-structured model for infectious diseases where the susceptibility depends on the age and with immigration of new individuals into the susceptible, exposed and infectious classes. The existence of a global attractor and the asymptotic smoothness of the solution semi-flow generated by the model are addressed. Using a Lyapunov functional, we show that the unique endemic equilibrium is globally asymptotically stable.

SVIR epidemic model with age structure in susceptibility, vaccination effects and relapse

2017 ◽  
Vol 82 (5) ◽  
pp. 945-970 ◽  
Author(s):  
Jinliang Wang ◽  
Min Guo ◽  
Shengqiang Liu
Keyword(s):  
Age Structure ◽  
Epidemic Model ◽  
Lyapunov Functional ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Combined Effects ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Disease Free

Abstract An SVIR epidemic model with continuous age structure in the susceptibility, vaccination effects and relapse is proposed. The asymptotic smoothness, existence of a global attractor, the stability of equilibria and persistence are addressed. It is shown that if the basic reproductive number $\Re_0<1$, then the disease-free equilibrium is globally asymptotically stable. If $\Re_0>1$, the disease is uniformly persistent, and a Lyapunov functional is used to show that the unique endemic equilibrium is globally asymptotically stable. Combined effects of susceptibility age, vaccination age and relapse age on the basic reproductive number are discussed.

scholarly journals Global stability in a competitive infection-age structured model

2020 ◽  
Vol 15 ◽  
pp. 54
Author(s):  
Quentin Richard
Keyword(s):  
Global Stability ◽  
Basin Of Attraction ◽  
Exclusion Principle ◽  
Globally Asymptotically Stable ◽  
Infection Age ◽  
Age Structured ◽  
The Stability ◽  
Globally Attractive ◽  
Age Structured Model ◽  
Disease Free

We study a competitive infection-age structured SI model between two diseases. The well-posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria are ensured, depending on the basic reproduction number R0x and R0y of each strain. We then exhibit Lyapunov functionals to analyse the global stability and we prove that the disease-free equilibrium is globally asymptotically stable whenever max{R0x, R0y} ≤ 1. With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where R0x ≠ R0y and max{R0x, R0y} > 1, meaning that the strain with the largest R0 persists and eliminates the other strain. In the limit case R0x = Ry0 > 1, an infinite number of endemic equilibria exists and constitute a globally attractive set.

An Age-Structured Model of Fish Population Enhancement

2002 ◽  
pp. 376-394
Author(s):  
Richard Langton ◽  
James Lindholm ◽  
James Wilson ◽  
Sally Sherman
Keyword(s):  
Fish Population ◽  
Structured Model ◽  
Age Structured ◽  
Age Structured Model

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

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