ABSTRACT
Turkey reported the first case of COVID-19 on 11 March 2020 since the outbreak of the deadly coronavirus pandemic. COVID-19 spread rapidly in Turkey, where about a total of 3,208,173 cases of infected persons were registered by 29 March 2021 with 2,957,093 cases of recovered persons and 31,076 reported deaths. A new mathematical COVID-19 model containing six classes is presented. Also, the positive invariant region of the solutions, basic reproductive number, disease-free equilibrium, and its stability are highlighted. Afterward, the disease-free equilibrium is locally asymptotically stable when R0 < 1. Moreover, the proposed model was further generalized to the fractional-order derivative in the AtanganaBaleanu (ABC) context for a more successful realization. Besides, the existence and uniqueness of solutions via techniques of Schaefer's and Banach fixed point theorems were established. Based on the publicly recorded number of infected people from 1-31 July 2020 in Turkey and least-squares curve fitting techniques with fminsearch function the fractionalorders model has been validated and can better fit the data compared with the integer-order model. Also, using the Atangana-Toufik scheme, numerical solutions, as well as simulations, are presented for different values of fractional order. © 2022, Thammasat University. All rights reserved.
ABSTRACT
The research work in this paper attempts to describe the outbreak of Coronavirus Disease 2019 (COVID-19) with the help of a mathematical model using both the Ordinary Differential Equation (ODE) and Fractional Differential Equation. The spread of the disease has been on the increase across the globe for some time with no end in sight. The research used the data of COVID-19 cases in Nigeria for the numerical simulation which has been fitted to the model. We brought in the consideration of both asymptomatic and symptomatic infected individuals with the fact that an exposed individual is either sent to quarantine first or move to one of the infected classes with the possibility that susceptible individual can also move to quarantined class directly. It was found that the proposed model has two equilibrium points; the disease-free equilibrium point ( DFE ) and the endemic equilibrium point ( E 1 ) . Stability analysis of the equilibrium points shows ( E 0 ) is locally asymptotically stable whenever the basic reproduction number, R 0 < 1 and ( E 1 ) is globally asymptotically stable whenever R 0 > 1 . Sensitivity analysis of the parameters in the R 0 was conducted and the profile of each state variable was also depicted using the fitted values of the parameters showing the spread of the disease. The most sensitive parameters in the R 0 are the contact rate between susceptible individuals and the rate of transfer of individuals from exposed class to symptomatically infected class. Moreover, the basic reproduction number for the data is calculated as R 0 ≈ 1.7031 . Existence and uniqueness of solution established via the technique of fixed point theorem. Also, using the least square curve fitting method together with the fminsearch function in the MATLAB optimization toolbox, we obtain the best values for some of the unknown biological parameters involved in the proposed model. Furthermore, we solved the fractional model numerically using the Atangana-Toufik numerical scheme and presenting different forms of graphical results that can be useful in minimizing the infection.