The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes

Wang, Jinliang; Zhang, Ran; Kuniya, Toshikazu

doi:10.1080/17513758.2015.1006696

Cited by 39 publications

(23 citation statements)

References 22 publications

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“…Usually, the introduction of age structure often leads to a system of first-order partial differential equations with appropriate boundary conditions. Such models are called age-structured epidemic models, on which recent works can be found (see other works 1,8,[14][15][16][17][18] and the references therein). Since the latent and removed individuals always become infectious at different rates depending on the time that they have been in their classes, it is interesting to consider models with latent age and relapse age.…”

Section: Introductionmentioning

confidence: 99%

A multigroup SEIR epidemic model with age‐dependent latency and relapse

Liu

Feng

2018

Math Methods in App Sciences

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Different multigroup epidemic models have been proposed, but few models include the latent class that becomes infectious at different rates and the fact that the removed class may relapse into an infectious class at different rates.In this paper, a multigroup SEIR epidemic model is constructed to study the transmission dynamics of infectious diseases with age-dependent latency and relapse. The model is realistic for some infectious diseases, such as TB and herpes virus. The sharp threshold condition, which corresponds to the well-known basic reproduction number ℜ 0 , is derived, and it determines the global stability of each equilibrium. In particular, if ℜ 0 < 1, then the disease-free equilibrium is globally asymptotically stable, whereas if ℜ 0 > 1, the endemic equilibrium exists uniquely and is globally asymptotically stable. We utilize appropriate Lyapunov functionals, graph-theoretical results, and the LaSalle's invariance principle to prove these results. Two specific examples and their corresponding numerical simulations are provided to explain the obtained results. KEYWORDS age-dependent latency, age-dependent relapse, global stability, multigroup epidemic model, threshold condition 6814

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Section: Introductionmentioning

confidence: 99%

A multigroup SEIR epidemic model with age‐dependent latency and relapse

Liu

Feng

2018

Math Methods in App Sciences

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“…In recent years, epidemic models and viral infection models with age-dependent structures have been extensively studied. To name a few, see [13] for a two-group model with infection age, [14] for an SIR model with infection age, [11,16] for SEIR models with infection age, [3] for an SIRS model with infection age, [30] for an SVIER model with infection age, [1,31,33] for models on cholera with infection age, and [2,8,17,18,28,29] for viral infection. Generally, it is not easy to analyse a hybrid system coupled of ODEs and PDEs, especially for the global stability/attractivity of equilibria.…”

Section: Introductionmentioning

confidence: 99%

Global threshold dynamics of an SVIR model with age-dependent infection and relapse

Wang

Lang

Chen

2016

Journal of Biological Dynamics

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A susceptible-vaccinated-infectious-recovered epidemic model with infection age and relapse age has been formulated. We first address the asymptotic smoothness of the solution semiflow, existence of a global attractor, and uniform persistence of the model. Then by constructing suitable Volterra-type Lyapunov functionals, we establish a global threshold dynamics of the model, which is determined by the basic reproduction number. Biologically, it is confirmed that neglecting the possibility of vaccinees getting infected will over-estimate the effect of vaccination strategies. The obtained results generalize some existing ones.

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“…Here, we call the formulas (22) for u * = (u * 1 , u * 2 , u * 3 ) with the characterization of optimal controls. The state variables and the optimal controls variables are found by solving the optimality system, which contain the state system (13), the adjoint system (20), initial conditions and boundary conditions, together with the characterization of the optimal controls (u * 1 , u * 2 , u * 3 ).…”

Section: Theorem 62mentioning

confidence: 99%

“…In the real world phenomena mathematical modelling is one of the powerful tools to describe the dynamical behaviour of different diseases [21,22,24,25]. Mathematicians and biologists used different epidemic models to understand the transition of different infectious diseases in the population.…”

Section: Introductionmentioning

confidence: 99%

The transmission dynamic and optimal control of acute and chronic hepatitis B

Khan

Zaman

Chohan

2016

Journal of Biological Dynamics

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In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number R 0 . We show that if R 0 ≤ 1, then the disease-free equilibrium is both locally as well as globally asymptotically stable. Then, we prove that the model is locally and globally asymptotically stable, if R 0 > 1. To control the spread of this infection, we develop a control strategy by applying three control variables such as isolation of infected and non-infected individuals, treatment and vaccination to minimize the number of acute infected, chronically infected with hepatitis B individuals and maximize the number of susceptible and recovered individuals. Finally, we present numerical simulation to illustrate the feasibility of the control strategy. ARTICLE HISTORY

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The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes

Cited by 39 publications

References 22 publications

A multigroup SEIR epidemic model with age‐dependent latency and relapse

A multigroup SEIR epidemic model with age‐dependent latency and relapse

Global threshold dynamics of an SVIR model with age-dependent infection and relapse

The transmission dynamic and optimal control of acute and chronic hepatitis B

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