ABSTRACT
In this paper, we investigate the dynamics of novel coronavirus infection (COVID-19) using a fractional mathematical model in Caputo sense. Based on the spread of COVID-19 virus observed in Algeria, we formulate the model by dividing the infected population into two sub-classes namely the reported and unreported infective individuals. The existence and uniqueness of the model solution are given by using the well-known Picard-Lindelöf approach. The basic reproduction number R 0 is obtained and its value is estimated from the actual cases reported in Algeria. The model equilibriums and their stability analysis are analyzed. The impact of various constant control parameters is depicted for integer and fractional values of α . Further, we perform the sensitivity analysis showing the most sensitive parameters of the model versus R 0 to predict the incidence of the infection in the population. Further, based on the sensitivity analysis, the Caputo model with constant controls is extended to time-dependent variable controls in order obtain a fractional optimal control problem. The associated four time-dependent control variables are considered for the prevention, treatment, testing and vaccination. The fractional optimality condition for the control COVID-19 transmission model is presented. The existence of the Caputo optimal control model is studied and necessary condition for optimality in the Caputo case is derived from Pontryagin's Maximum Principle. Finally, the effectiveness of the proposed control strategies are demonstrated through numerical simulations. The graphical results revealed that the implantation of time-dependent controls significantly reduces the number of infective cases and are useful in mitigating the infection.
ABSTRACT
In this paper, we investigate the dynamics of novel coronavirus infection (COVID-19) using a fractional mathematical model in Caputo sense. Based on the spread of COVID-19 virus observed in Algeria, we formulate the model by dividing the infected population into two sub-classes namely the reported and unreported infective individuals. The existence and uniqueness of the model solution are given by using the well-known Picard-Lindelöf approach. The basic reproduction number
ABSTRACT
The novel coronavirus infectious disease (or COVID-19) almost spread widely around the world and causes a huge panic in the human population. To explore the complex dynamics of this novel infection, several mathematical epidemic models have been adopted and simulated using the statistical data of COVID-19 in various regions. In this paper, we present a new nonlinear fractional order model in the Caputo sense to analyze and simulate the dynamics of this viral disease with a case study of Algeria. Initially, after the model formulation, we utilize the well-known least square approach to estimate the model parameters from the reported COVID-19 cases in Algeria for a selected period of time. We perform the existence and uniqueness of the model solution which are proved via the Picard-Lindelöf method. We further compute the basic reproduction numbers and equilibrium points, then we explore the local and global stability of both the disease-free equilibrium point and the endemic equilibrium point. Finally, numerical results and graphical simulation are given to demonstrate the impact of various model parameters and fractional order on the disease dynamics and control.
ABSTRACT
In this paper, we investigate an epidemic model of the novel coronavirus disease or COVID-19 using the Caputo-Fabrizio derivative. We discuss the existence and uniqueness of solution for the model under consideration, by using the the Picard-Lindelöf theorem. Further, using an efficient numerical approach we present an iterative scheme for the solutions of proposed fractional model. Finally, many numerical simulations are presented for various values of the fractional order to demonstrate the impact of some effective and commonly used interventions to mitigate this novel infection. From the simulation results we conclude that the fractional order epidemic model provides more insights about the disease dynamics.