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

Abstract

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.

An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect

“…A Mahata et al [ 23 ], a fractional order dynamical system of susceptible, exposed, infected, recovered, and vaccinated populations was shown, with a single delay added in the infectious population to account for the time necessary for the said population to recover. They used the Adam–Bashforth–Moulton approach to derive numerical solutions to the model system.…”

Study of a Nonlinear System of Fractional Differential Equations with Deviated Arguments Via Adomian Decomposition Method

“…Many studies have been conducted in the field of mathematics, and it has been shown that differential equations using fractional operators are effective in demonstrating epidemic models linked to many infectious illnesses [7,12]. Two leading implementations of fractional calculus are in epidemiological and biomathematical models [6,18,19]. Ahmad et al [2] performed simulations of a fractional model for CoViD-19 transmission, taking into account various values of the non-integer order derivative and came to the conclusion that the value of = 0.97 best matched the actual data.…”

“…FDEs with deviated arguments have many applications in science and engineering, including fractals theory, chemistry, biology, physics, neural network, weather prediction model, etc. [19,26]. Brauer et al [5] presented logistic equations, which are particularly applicable to epidemic systems.…”

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

“…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.…”