The use of generation stochastic models to study an epidemic disease

Chaharborj, Sarkhosh Seddighi; Fudziah, I.; Bakar, Abu; Chaharborj, Reza Seddighi; Majid, Zanariah Abdul; Ahmad, Abd Ghafur

doi:10.1186/1687-1847-2013-7

Cited by 6 publications

(14 citation statements)

References 6 publications

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“…It is worth mentioning that a relevant attention has been paid to the investigation of the stability and nonnegativity and positivity properties of epidemic models in both vaccination-free and vaccination control situations. See, for instance, [14][15][16][17][18][19][20][21][22][23][24][25][26], and also [17,18] in the stochastic framework context. On the other hand, we can point out that the nonnegativity of the solution is commonly required in biological processes to appropriately approach in a coherent fashion their natural evolution.…”

Section: Introductionmentioning

confidence: 99%

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

Sen¹,

Ibeas

2021

Adv Differ Equ

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In this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.

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Section: Introductionmentioning

confidence: 99%

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

Sen¹,

Ibeas

2021

Adv Differ Equ

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“…It has to be mentioned that a relevant attention has been paid to the investigation of the stability and positivity properties of epidemic models in both the vaccination-free and vaccination control situations. See, for instance, [17][18][19][20][21][22][23][24][25][26][27][28][29]. The positivity properties of de solutions and equilibrium points of some epidemic models are studied in detail in [30][31][32][33], while model discretization concerns are discussed in [33,34] and relationships to thermodynamics concepts are discussed in [35].…”

Section: Introductionmentioning

confidence: 99%

On a Controlled Se(Is)(Ih)(Iicu)AR Epidemic Model with Output Controllability Issues to Satisfy Hospital Constraints on Hospitalized Patients

Sen

Ibeas

2020

Algorithms

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An epidemic model, the so-called SE(Is)(Ih)(Iicu)AR epidemic model, is proposed which splits the infectious subpopulation of the classical SEIR (Susceptible-Exposed-Infectious-Recovered) model into four subpopulations, namely asymptomatic infectious and three categories of symptomatic infectious, namely slight infectious, non-intensive care infectious, and intensive care hospitalized infectious. The exposed subpopulation has four different transitions to each one of the four kinds of infectious subpopulations governed under eventually different proportionality parameters. The performed research relies on the problem of satisfying prescribed hospitalization constraints related to the number of patients via control interventions. There are four potential available controls which can be manipulated, namely the vaccination of the susceptible individuals, the treatment of the non-intensive care unit hospitalized patients, the treatment of the hospitalized patients at the intensive care unit, and the transmission rate which can be eventually updated via public interventions such as isolation of the infectious, rules of groups meetings, use of face masks, decrees of partial or total quarantines, and others. The patients staying at the non-intensive care unit and those staying at the intensive care unit are eventually, but not necessarily, managed as two different hospitalized subpopulations. The controls are designed based on output controllability issues in the sense that the levels of hospital admissions are constrained via prescribed maximum levels and the measurable outputs are defined by the hospitalized patients either under a joint consideration of the sum of both subpopulations or separately. In this second case, it is possible to target any of the two hospitalized subpopulations only or both of them considered as two different components of the output. Different algorithms are given to design the controls which guarantee, if possible, that the prescribed hospitalization constraints hold. If this were not possible, because the levels of serious infection are too high according to the hospital availability means, then the constraints are revised and modified accordingly so that the amended ones could be satisfied by a set of controls. The algorithms are tested through numerically worked examples under disease parameterizations of COVID-19.

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“…Also, the potential used in hyperbolic electrodes is as follow, (8) thus, the stochastic potential, , can be written as, (9) where W t is a Wiener procedure and is the noise coefficient determining the size of the stochastic term. 14,15 In this regard, the noise coefficient, , explains the amount of fluctuation potentially. For , the deterministic potential or normal potential can be stated as .…”

Section: Main Properties Of Wiener Processmentioning

confidence: 99%

“…As any Gaussian process, Wiener process is completely described by its expectation and correlation functions 14,15 Main properties of : • • Trajectories of Wiener process are continues functions of (see Figure (1 In can be shown that as , converges in distribution to a stochastic process , termed the Wiener process or Brownian motion. [14][15][16][17] The motions of ion inside quadrupole ion trap with stochastic potential form Fig. (2) shows indicatesa the schematic perspectives of a quadrupole ion trap (QIT).…”

Section: Main Properties Of Wiener Processmentioning

confidence: 99%

See 1 more Smart Citation

Applications of Stochastic Process in the Quadrupole Ion traps

Chaharborj¹,

Kiai²,

Arifina³

et al. 2015

Mass Spectrometry Letters

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: The Brownian motion or Wiener process, as the physical model of the stochastic procedure, is observed as an indexed collection random variables. Stochastic procedure are quite influential on the confinement potential fluctuation in the quadrupole ion trap (QIT). Such effect is investigated for a high fractional mass resolution spectrometry. A stochastic procedure like the Wiener or Brownian processes are potentially used in quadrupole ion traps (QIT). Issue examined are the stability diagrams for noise coefficient, as well as ion trajectories in real time for noise coefficient, . The simulated results have been obtained with a high precision for the resolution of trapped ions. Furthermore, in the lower mass range, the impulse voltage including the stochastic potential can be considered quite suitable for the quadrupole ion trap with a higher mass resolution.

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The use of generation stochastic models to study an epidemic disease

Cited by 6 publications

References 6 publications

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

On a Controlled Se(Is)(Ih)(Iicu)AR Epidemic Model with Output Controllability Issues to Satisfy Hospital Constraints on Hospitalized Patients

Applications of Stochastic Process in the Quadrupole Ion traps

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