Dynamics analysis and optimal control strategy for a SIRS epidemic model with two discrete time delays

In mid-March 2020, the World Health Organization declared COVID-19, a worldwide public health emergency. This paper presents a study of an SEIRV epidemic model with optimal control in the context of the Caputo fractional derivative of order . The stability analysis of the model is performed. We also present an optimum control scheme for an SEIRV model. The real time data for India COVID-19 cases have been used to determine the parameters of the fractional order SEIRV model. The Adam-Bashforth-Moulton predictor–corrector method is implemented to solve the SEIRV model numerically. For analyzing COVID-19 transmission dynamics, the fractional order of the SEIRV model is found to be better than the integral order. Graphical demonstration and numerical simulations are presented using MATLAB (2018a) software.

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“…Using next generation matrix method [ 39 , 40 ], the reproduction number ( ) can be obtained from the leading eigen value of the matrix where, …”

Section: Model Formulationmentioning

confidence: 99%

Dynamics of Caputo Fractional Order SEIRV Epidemic Model with Optimal Control and Stability Analysis

Mahata¹,

Paul²,

Mukherjee³

et al. 2022

Int. J. Appl. Comput. Math

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“…Using next generation matrix method, 48 , 49

can be determined from the maximum eigen value of

where,

…”

Section: Formulationmentioning

confidence: 99%

Stability analysis and Hopf bifurcation in fractional order SEIRV epidemic model with a time delay in infected individuals

Mahata¹,

Paul

Mukherjee³

et al. 2022

Partial Differential Equations in Applied Mathematics

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Infectious diseases have been a constant cause of disaster in human population. Simultaneously, it provides motivation for math and biology professionals to research and analyze the systems that drive such illnesses in order to predict their long-term spread and management. During the spread of such diseases several kinds of delay come into play, owing to changes in their dynamics. Here, we have studied a fractional order dynamical system of susceptible, exposed, infected, recovered and vaccinated population with a single delay incorporated in the infectious population accounting for the time period required by the said population to recover. We have employed Adam-Bashforth-Moulton technique for deriving numerical solutions to the model system. The stability of all equilibrium points has been analyzed with respect to the delay parameter. Utilizing actual data from India COVID-19 instances, the parameters of the fractional order SEIRV model were calculated. Graphical demonstration and numerical simulations have been done with the help of MATLAB (2018a). Threshold values of the time delay parameter have been found beyond which the system exhibits Hopf bifurcation and the solutions are no longer periodic.

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“…At present times an extensive investigation [10][11][12][13][14][15][16][17][18][19][20][21][22][23] of the spread of the highly contagious Coronavirus disease with alarming fatality rate is being carried out. Different models exist in epidemiology to forecast and explain the complexities of an epidemic.…”

Section: Introductionmentioning

confidence: 99%

Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19

Paul¹,

Mahata²,

Mukherjee³

et al. 2022

Int. J. Appl. Comput. Math

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In this manuscript, a fractional order SEIR model with vaccination has been proposed. The positivity and boundedness of the solutions have been verified. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at diseasefree equilibrium point E 0 when R 0 < 1 and at epidemic equilibrium E 1 when R 0 > 1. It has been found that introduction of the vaccination parameter η reduces the reproduction number R 0 . The parameters are identified using real-time data from COVID-19 cases in India. To numerically solve the SEIR model with vaccination, the Adam-Bashforth-Moulton technique is used. We employed MATLAB Software (Version 2018a) for graphical presentations and numerical simulations.. It has been observed that the SEIR model with fractional order derivatives of the dynamical variables is much more effective in studying the effect of vaccination than the integral model.

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Dynamics analysis and optimal control strategy for a SIRS epidemic model with two discrete time delays

Cited by 31 publications

References 33 publications

Dynamics of Caputo Fractional Order SEIRV Epidemic Model with Optimal Control and Stability Analysis

Dynamics of Caputo Fractional Order SEIRV Epidemic Model with Optimal Control and Stability Analysis

Stability analysis and Hopf bifurcation in fractional order SEIRV epidemic model with a time delay in infected individuals

Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19

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