Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model

Wei, Zhijian; Le, Meitao

doi:10.1155/2015/434537

Cited by 7 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Flow diagram of the control-free model transitions [45,46]. In particular, a discrete epidemic model is investigated in [14], which possesses a unique nonnegative equilibrium to which the solutions converge, and the case of imperfect vaccination under nonlinear incidence rate is investigated in [16]. On the other hand, in [47], general conditions for maintenance of the positivity of a dynamic system under its discretization are given and discussed.…”

Section: The Seiadr Epidemic Modelmentioning

confidence: 99%

“…The positivity of the solution is investigated in a number of works. See, for instance, [10][11][12][13] and [14] and some references therein. In particular, the properties of boundedness, oscillatory behaviors, positivity, and stability together with the injection of some constant, feedback regular, and impulsive control laws are investigated in [10,11] in proposed true-mass epidemic SEIR models with uncertainties and eventual delays.…”

Section: Introductionmentioning

confidence: 99%

“…The online supervisory action decides if the active configuration has to be switched or not at each current tentative testing switching time instant. See, for instance, [14,[31][32][33], references therein, and [34]. In particular, the parametrical estimation is incorporated as well in [35][36][37][38] to identify potentially unknown system parameters.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A switched multicontroller for an SEIADR epidemic model with monitored equilibrium points and supervised transients and vaccination costs

et al. 2018

View full text Add to dashboard Cite

This paper presents a multicontroller structure for an SEIADR (susceptible-exposedsymptomatic infectious-asymptomatic infectious-dead lying bodies recovered by immunity, or immune, subpopulations) epidemic model, which has three different controls involving feedback, namely, the vaccination on the susceptible subpopulation, the antiviral treatment on the symptomatic infectious subpopulation, and the impulsive removal on the infective lying bodies. The incorporation of the asymptomatic infectious and infective dead bodies to SEIR-type models allows a better modeling of diseases where the death bodies are infective as, for instance, the Ebola disease. The proposed supervised multicontroller scheme consists of a parallel disposal of several alternative controller parameterizations together with a switching scheme that chooses the active controller through consecutive time intervals via a supervisory decision scheme. The supervisory scheme decides to switch or not at testing time instants. Switching is performed to a distinct active scheme to the current active if the tentative controller minimizes the value of a loss function compared to the values of the other control schemes available in the parallel controller disposal. The supervisory loss (or cost) function incorporates several additive weighted terms including the infection loss function evolution and the vaccination, antiviral treatment, and bodies removal efforts.

show abstract

Section: The Seiadr Epidemic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A switched multicontroller for an SEIADR epidemic model with monitored equilibrium points and supervised transients and vaccination costs

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Thus, the final stages of the illness under study can be split into live and immune individuals, i.e., recovered (R) subpopulation, and infectious and dead individuals, i.e., dead (D) subpopulation. Given this, it has been widely studied the non negativity of the solutions [14][15][16] and the use of perturbations and nonlinear incidence rates (as seen in [17][18][19] and [19][20][21][22], respectively). Reducing the disease within the population should be main objective of the control measures proposed i.e., vaccination strategies and the medical treatment of the infectious subpopulation through antiviral treatment or care of the symptoms, which we will also include in our equations.…”

Section: Introductionmentioning

confidence: 99%

On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties

et al. 2018

View full text Add to dashboard Cite

A new discrete SEIADR epidemic model is built based on previous continuous models. The model considers two extra subpopulation, namely, asymptomatic and lying corpses on the usual SEIR models. It can be of potential interest for diseases where infected corpses are infectious like, for instance, Ebola. The model includes two types of vaccinations, a constant one and another proportional to the susceptible subpopulation, as well as a treatment control applied to the infected subpopulation. We study the positivity of the controlled model and the stability of the equilibrium points. Simulations are made in order to provide allocation and examples to the different possible conditions. The equilibrium point with no infection and its stability is related, via the reproduction number values, to the reachability of the endemic equilibrium point.

show abstract

“…The positivity of the solution is investigated in a number of works. See, for instance, [6][7][8][9]12] and some references therein. The use of nonlinear incidence rates in the models is also investigated in a number of papers.…”

Section: Introductionmentioning

confidence: 99%

On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease

Sen

Ibeas

Alonso‐Quesada

et al. 2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

This paper studies the nonnegativity and local and global stability properties of the solutions of a newly proposed SEIADR model which incorporates asymptomatic and dead-infective subpopulations into the standard SEIR model and, in parallel, it incorporates feedback vaccination plus a constant term on the susceptible and feedback antiviral treatment controls on the symptomatic infectious subpopulation. A third control action of impulsive type (or "culling") consists of the periodic retirement of all or a fraction of the lying corpses which can become infective in certain diseases, for instance, the Ebola infection. The three controls are allowed to be eventually time varying and contain a total of four design control gains. The local stability analysis around both the disease-free and endemic equilibrium points is performed by the investigation of the eigenvalues of the corresponding Jacobian matrices. The global stability is formally discussed by using tools of qualitative theory of differential equations by using Gauss-Stokes and Bendixson theorems so that neither Lyapunov equation candidates nor the explicit solutions are used. It is proved that stability holds as a parallel property to positivity and that disease-free and the endemic equilibrium states cannot be simultaneously either stable or unstable. The periodic limit solution trajectories and equilibrium points are analyzed in a combined fashion in the sense that the endemic periodic solutions become, in particular, equilibrium points if the control gains converge to constant values and the control gain for culling the infective corpses is asymptotically zeroed.Hindawi

show abstract

Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model

Cited by 7 publications

References 18 publications

A switched multicontroller for an SEIADR epidemic model with monitored equilibrium points and supervised transients and vaccination costs

A switched multicontroller for an SEIADR epidemic model with monitored equilibrium points and supervised transients and vaccination costs

On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties

On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease

Contact Info

Product

Resources

About