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

Abstract

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

A simulation of a COVID-19 epidemic based on a deterministic SEIR model

“…Another equivalent approach is an SEIDR model (e.g., De la Sen et al, 2017;Sameni, 2020), where we have to addḊ…”

Some Formal Results on Positivity, Stability, and Endemic Steady-State Attainability Based on Linear Algebraic Tools for a Class of Epidemic Models with Eventual Incommensurate Delays

“…A particular case of the SEIADR (susceptibleexposed-symptomatic infectious-asymptomatic infectiousinfectious corpses-recovered) proposed in [6,7] follows below for the case when the vaccination and treatment control parameters 0 , , and are constant and there is no impulsive control for the infectious corpses removal control action:̇(…”

“…The frontier between both situations typically occurs when the reproduction number is unity. See, for instance, [6][7][8][9][10][11][12] and 2 Discrete Dynamics in Nature and Society some references therein. In those studies, the first orthant of the space state is an invariant subspace as a result of the nonnegativity properties of the state trajectory solutions which is also an invoked property of other biological problems related to species evolution dynamics.…”

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

“…An SEIADR model is an extended SEIR model proposed in [43]. Apart from the classical subpopulations of "susceptible" (S), "exposed" (E), "symptomatic infectious" (I), and "recovered" (or immune) (R), it has two additional subpopulations, namely, "asymptomatic infectious" (A) and "dead-infective" (D).…”

“…(c) The controls (7)-(9) can be of different types including constant and feedback actions. The nonnegativity and boundedness of the solutions through time, the equilibrium points, their stability, and the existence of eventual limit oscillatory solutions and their stability properties have been investigated in [43]. The study of those properties is common in a wide sampling of other alternative epidemic models discussed in the background literature.…”