Dynamics of SEIR epidemic model by optimal auxiliary functions method

Marinca, Bogdan; Marinca, Vasile; Bogdan, Ciprian

doi:10.1016/j.chaos.2021.110949

Cited by 18 publications

(10 citation statements)

References 30 publications

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“…For a general nonlinear differential equation [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ]

with the initial conditions

where L is a linear operator, N is a nonlinear operator, D is the domain of interest, B is a boundary operator, we propose that the approximate solution

to be of the form

where C i are n parameters unknown at this moment and n is an arbitrary positive integer number. The initial approximation Q 0 (τ) can be determined from the linear differential equation

with the initial conditions

…”

Section: Basics Of the Optimal Auxiliary Functions Methodsmentioning

confidence: 99%

Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation

Herişanu

Marinca

2022

Materials

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This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler–Pasternak foundation near the primary resonance. Two Euler–Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mechanical impact are considered. By means of Hamilton’s principle, Eringen’s nonlocal elastic theory, and taking into account the moving nanoparticles, the Galerkin–Bubnov method is applied and accordingly, governing partial differential equations are reduced to two differential equations with variable coefficients. The nonlinear damped and forced vibration is studied using the optimal auxiliary functions method (OAFM). An explicit and very accurate analytical solution is obtained by means of OAFM without considering simplifying hypotheses. An accurate analysis is for the first time reported considering the cumulated effects of nonlinearities simultaneously induced by the Winkler–Pasternak foundation, the curvature of beams and van der Waals force, and also the effect of discontinuities marked by the presence of the Dirac function. Finally, a stability analysis of the considered model is developed by means of the homotopy perturbation method (HPM) using the condition of existence of the two frequencies. It was shown that an increasing of some constitutive parameters substantially reduces the area of stability, all these being of much help in guiding the design of advanced nanoelectromechanical devices, in which nanotubes act as basic elements.

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“…For a general nonlinear differential equation [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ]

with the initial conditions

where L is a linear operator, N is a nonlinear operator, D is the domain of interest, B is a boundary operator, we propose that the approximate solution

to be of the form

where C i are n parameters unknown at this moment and n is an arbitrary positive integer number. The initial approximation Q 0 (τ) can be determined from the linear differential equation

with the initial conditions

…”

Section: Basics Of the Optimal Auxiliary Functions Methodsmentioning

confidence: 99%

Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation

Herişanu

Marinca

2022

Materials

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“…The nonlinear differential Equations ( 10) and ( 11) can be written in a general form as [22][23][24][25][26][27]:…”

Section: Basics Of the Oafmmentioning

confidence: 99%

Approximate Analytical Solutions to Nonlinear Oscillations of Horizontally Supported Jeffcott Rotor

Marinca

Herişanu

2022

Energies

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The present paper focuses on nonlinear oscillations of a horizontally supported Jeffcott rotor. An approximate solution to the system of governing equations having quadratic and cubic nonlinearities is obtained in two cases of practical interest: simultaneous and internal resonance. The Optimal Auxiliary Functions Method is employed in this study, and each governing differential equation is reduced to two linear differential equations using the so-called auxiliary functions involving a moderate number of convergence-control parameters. Explicit analytical solutions are obtained for the first time in the literature for the considered practical cases. Numerical validations proved the high accuracy of the proposed analytical solutions, which may be used further in the study of stability and in the design process of some highly performant devices.

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“…For the SIR model, the infected individuals are capable of infecting the susceptible individuals through the recovery period. Concerning the latent period, the SEIR model, which is an extended model of the SIR, has been used for the simulation of COVID-19 [14][15][16][17][18][19][20][21]. It consists of four compartments of 'Susceptible', 'Exposed who is infected but not infectious during the latent period', 'Infectious who is infectious after the latent period until the recovery period is ended' and 'Recovered'.…”

Section: Calculation For the Case Of Infection During The Latent Peri...mentioning

confidence: 99%

A flexible compartment model for simulation specific to COVID-19

Ohmori

2022

Preprint

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The dynamic relation among ‘Susceptible’, ‘Infected’, ‘Removed (Recovered)’, ‘Death’ and others for COVID-19 disease is a kind of multibody problem. It has been simulated mainly by the compartment models, of which the representative is the SIR model. For the SIR model, ‘Infected’ infects ‘Susceptible’ through the recovery period, and ‘Infected’ is removed as ‘Removed’ not only from the disease but also from the community after the recovery period is ended. For COVID-19, however, the infected individuals should be isolated from the community when they become symptomatic after the latent period is ended. Thus, the infected individuals do not infect susceptible individuals in the community after the latent period, even during the recovery period. Additionally, the infection has occurred in the community even during the latent period before the infected individuals are isolated due to being symptomatic. These two facts for COVID-19 suggest that the simulation by the SIR model would be less accurate in calculating the number of infected individuals and that the results might mislead political and medical interventions. For the model proposed here, the infected individuals are isolated from the community when they become symptomatic after the latent period is ended, but the recovered individuals who have medically recovered and have immunity return to the community, and the infection occurs even during the latent period. The model shows remarkably different results from those simulated by the SIR model. The model also provides the processes evaluating the political and social countermeasures against COVID-19.

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Dynamics of SEIR epidemic model by optimal auxiliary functions method

Cited by 18 publications

References 30 publications

Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation

Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation

Approximate Analytical Solutions to Nonlinear Oscillations of Horizontally Supported Jeffcott Rotor

A flexible compartment model for simulation specific to COVID-19

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