Search

The deadly coronavirus disease 2019 (COVID‐19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID‐19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human‐to‐human and zoonotic transmissions are considered in the model. The well‐posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state. [ABSTRACT FROM AUTHOR]

The first case of COVID‐19 in India detected on January 30, 2020, after its emergence in Wuhan, China, in December 2019. The lockdown was imposed as anemergency measure by the Indian government to prevent the spread of COVID‐19 but gradually eased out due to its vast economic consequences. Just 15 days after the relaxation of lockdown restrictions, Delhi became India's worst city in terms of COVID‐19 cases. In this paper, we propose a variable‐order fractional SIR (susceptible, infected, removed) model at state‐level scale. We introduce a algorithm that uses the differential evolution algorithm in combination with Adam–Bashforth–Moulton method to learn the parameters in a system of variable‐order fractional SIR model. The model can predict the confirm COVID‐19 cases in India considering the effects of nationwide lockdown and the possible estimate of the number of infliction inactive cases after the removal of lockdown on June 1, 2020. A new parameter p is introduced in the classical SIR model representing the fraction of infected people that get tested and are thereby quarantined. The COVID‐19 trajectory in Delhi, as per our model, predicts the slowing down of the spread between January and February 2021, touching a peak of around 5 lakh confirmed cases. [ABSTRACT FROM AUTHOR]

Novel coronavirus (COVID‐19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID‐19 SEIR epidemic model via Caputo fractional derivatives using a predictor–corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag–Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs. [ABSTRACT FROM AUTHOR]

As the first‐wave COVID‐19 has passed in 2020, people's awareness of self‐protection began to decline gradually. How to prevent and control the second‐wave COVID‐19 has become an important issue in many countries and regions. By analyzing the transmission of the second‐wave COVID‐19 caused by an imported case in Tonghua City, Jilin Province, China, in January 2021, we establish a new mathematical COVID‐19 model to simulate the transmission characteristics of the second‐wave COVID‐19. First, we analyze the basic properties of the model, prove the existence of the equilibrium point, and obtain the expression of the basic reproduction number with important biological significance. Secondly, we use the weighted nonlinear least square estimation method to fit the cases in Tonghua City of Jilin Province in January 2021, and get the estimated value of the parameters. The basic reproduction number of the second‐wave COVID‐19 in Tonghua City is R0=1.0695, which is much smaller than that of the first‐wave COVID‐19 in Wuhan in 2020. Finally, in the optimal control part, we consider two control methods (keeping social distance and nucleic acid detection of all people in the city) to simulate the control of the disease. The results show that the control intensity of the two control methods needs to be dynamically changed and adjusted, so that the cost can be minimized with the least infection. The results of this paper can not only provide suggestions for health management departments, but also provide a reference for the analysis of the second‐wave COVID‐19 in other countries or regions. [ABSTRACT FROM AUTHOR]