Global stability of an age-structured epidemic model with general Lyapunov functional

We formulate an age structured SEIRS model with general screen function and contact rate. A condition is obtained, and under which the endemic equilibrium is locally stable. By constructing suitable Lyapunov function, the global stability of the endemic equilibrium is discussed.

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Global asymptotic stability for a SEI reaction–diffusion model of infectious diseases with immigration

International Journal of Biomathematics ◽

10.1142/s1793524518500444 ◽

2018 ◽

Vol 11 (03) ◽

pp. 1850044

Author(s):

Salem Abdelmalek ◽

Samir Bendoukha

Keyword(s):

Steady State ◽

Asymptotic Stability ◽

Global Stability ◽

Global Asymptotic Stability ◽

Epidemic Model ◽

Lyapunov Functional ◽

Reaction Diffusion ◽

Stability Of Solutions ◽

Reaction Diffusion Model ◽

Globally Stable

This paper studies the local and global stability of solutions for a spatially spread SEI epidemic model with immigration of individuals using a Lyapunov functional. It is shown that in the presence of diffusion, the unique steady state remains globally stable. Numerical results obtained through Matlab simulations are presented to confirm the findings of this study.

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Global stability of an age-structured sir epidemic model with pulse vaccination strategy

Journal of Systems Science and Complexity ◽

10.1007/s11424-011-9177-y ◽

2011 ◽

Vol 25 (3) ◽

pp. 417-429 ◽

Cited By ~ 4

Author(s):

Helong Liu ◽

Jingyuan Yu ◽

Guangtian Zhu

Keyword(s):

Global Stability ◽

Epidemic Model ◽

Vaccination Strategy ◽

Sir Epidemic Model ◽

Pulse Vaccination ◽

Sir Epidemic ◽

Age Structured

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Global stability for a delayed multi-group SIRS epidemic model with cure rate and incomplete recovery rate

International Journal of Biomathematics ◽

10.1142/s1793524515500485 ◽

2015 ◽

Vol 08 (04) ◽

pp. 1550048 ◽

Cited By ~ 3

Author(s):

Yoshiaki Muroya ◽

Toshikazu Kuniya

Keyword(s):

Global Stability ◽

Epidemic Model ◽

Recovery Rate ◽

Lyapunov Functional ◽

Global Analysis ◽

Endemic Equilibrium ◽

Group Model ◽

Cure Rate ◽

Sirs Epidemic Model ◽

Number Formula

In this paper, by applying Lyapunov functional approach, we establish a sufficient condition on the global stability of a "delayed" multi-group SIRS epidemic model with cure rate and incomplete recovery rate which does not depend on the delays and is an extension of the "light drug model" studied in the recent paper [Muroya, Li and Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl. 410 (2014) 719–732] to a multi-group model. Applying a Lyapunov functional on total population of each compartment, we offer new techniques for the delayed system, how to prove the permanence, the existence of the endemic equilibrium and the global stability of disease-free equilibrium for the reproduction number [Formula: see text] and endemic equilibrium for [Formula: see text].

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

International Journal of Biomathematics ◽

10.1142/s1793524519500426 ◽

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.

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