ABSTRACT
In this manuscript, we have studied the dynamical behavior of a deadly COVID‐19 pandemic which has caused frustration in the human community. For this study, a new deterministic SEIHR fractional model is developed for the first time. The purpose is to perform a complete mathematical analysis and the design of an optimal control strategy for the proposed Caputo–Fabrizio fractional model. We have proved the existence and uniqueness of solutions by employing principle of mathematical induction. The positivity and the boundedness of solutions is proved using comprehensive mathematical techniques. Two main equilibrium points of the pandemic model are stated. The basic reproduction number for the model is computed using next generation technique to handle the future dynamics of the pandemic. We develop an optimal control problem to find the best controls for the quarantine and hospitalization strategies employed on exposed and infected humans, respectively. For numerical solution of the fractional model, we implemented the Adams–Bashforth method to prove the importance of order. A general fractional‐order optimal control problem and associated optimality conditions of Pontryagin type are discussed, with the goal to minimize the number of exposed and infected humans. The extremals are obtained numerically. [ FROM AUTHOR]
ABSTRACT
Corona virus disease (Covid-19) which has caused frustration in the human community remains the concern of the globe as every government struggles to defeat the pandemic. To deal with the situation, we have extensively studied a deadly Covid-19 model to provide a deep insight into the disease dynamics. A mathematical analysis of the model utilizing preventive measures is performed with the aim to reduce the disease burden. Some comprehensive mathematical techniques are employed to demonstrate several essential properties of solutions. To start with, we proved the existence and uniqueness of solutions. Equilibrium points are stated both in the absence and presence of the pandemic. Biologically important quantity known as threshold parameter is computed to handle the future disease dynamics and analyzed for its sensitivity. We proved the stability of the proposed model at equilibrium points by employing necessary conditions on threshold parameter. A reliable and competitive numerical analysis is conducted to observe the effectiveness of implemented strategies and to verify obtained analytical results. The most sensitive parameters are determined through sensitivity analysis. An important feature of this study is to employ Non-Standard Finite Difference (NSFD) numerical scheme to solve the system instead of other standard methods like Runge-Kutta method of order 4 (RK4). Finally, several numerical simulations are performed to validate our former theoretical analysis. Numerical results exhibiting dynamical behavior of Covid-19 system under the influence of involved parameters suggest that both the implemented strategies, especially quarantine of exposed individuals, are effective for the substantial reduction in the diseased population and to achieve the herd immunity.