Abstract
To eradicate most infectious diseases, mathematical modelling of contagious diseases has revealed that a combination of quarantine, vaccination, and cure is frequently required. However, eradicating the disease will remain a difficult task if they aren't provided at the appropriate time and in the right quantity. Control analysis has been shown to be an effective way for discovering the best approaches to preventing the spread of contagious diseases through the development of disease preventive interventions. The method comprises reducing the cost of infection, implementing control measures, or both. In order to gain a better understanding of COVID-19′s future dynamics, this study presents a compartmental mathematical model. The problem is modelled as a highly nonlinear coupled system of classical order ODEs, which is then generalised using the Mittag-Leffler kernel's fractal-fractional derivative. The uniqueness of the fractional model under discussion has also been demonstrated. The boundedness and non-negativity of the considered model are also established. The next generation technique is used to examine basic reproduction, and disease free and endemic equilibrium. We used reported cases from Australia in this investigation due to the high risk of infection. The reported cases are considered between 1st July 2021 and 20th August 2021. On the basis of previous data, the spread of infection is predicted for the next 600 days which is shown through different graphs. The graphical solution of the considered nonlinear model is obtained via numerical scheme by implementing the MATLAB software. Based on the fitted values of parameters, the basic reproduction number ℜ0 is calculated as ℜ0 ≈ 1.58276. Furthermore, the impact of fractional and fractal parameter on the disease spread among different classes is demonstrated. In addition, the impact of quarantine and vaccination on infected people is dramatically depicted. It's been argued that public awareness of the quarantine and effective vaccination can drastically reduce infection rates in the population.