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The COVID-19 pandemic hit globally in December 2019 when a certain virus strain from Wuhan, China started proliferating throughout the world. By the end of March 2020, lockdowns and curfews were imposed all over the world halting trade, commerce, education, and various other essential activities. It has been nearly a year since the WHO declared a pandemic but there is still a consistent rise of the cases even with the administration of various types of vaccines and preventive measure. One of the main struggles that the healthcare workers face is to find out the how the virus is spreading amongst a community. The knowledge of this can be used to stop the spread of virus. This is a very important step towards getting things back into momentum to restore activities globally. Many attempts have been made under epidemiology to study the spread of COVID and many mathematical models have emerged as a result that can help with this. A popular model that is used for estimating the effective reproduction number (Rt) has the shortcoming that it cannot simultaneously forecast the future number of cases. This work explores an extension of another model, the SIR-model, in which the model parameters are fitted to recorded data. This makes the model adaptive, opening up the possibilities for estimating the Rt daily and making predictions of future number of confirmed cases. The paper use this adaptive SIR-model (aSIR) to estimate the Rt and create forecasts of new cases in India. The paper purpose is to determine how precise aSIR-models are at estimating the Rt (when compared with FHM’s model). It will also analyze how accurate aSIR-models are at simultaneously forecasting the future spread of Covid-19 in India. The coronavirus spread can be mathematically modelled using factors such as the number of susceptible people, exposed people, infected people, asymptotic people and the number of recovered people. The Khan-Atangana system is an integer-order coronavirus model that uses the above-mentioned factors. Since the coronavirus model depends on the initial conditions, the Khan-Atangana model uses the Atangana-Baleanu operate as it has a non-variant and non-local kernel. Instead, we replace the equations with fractional-order derivatives using the Grünwald-Letnikov derivative. The fractional order derivatives need to be fed with initial conditions and are useful to determine the spread due to their non-local nature. This project proposes to solve these fractional-order derivatives using numerical methods and analyse the stability of this epidemiological model.
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