Mathematical modelling of COVID-19 pandemic in Pakistan with optimal control

We propose an innovative mathematical modeling to examine the previous coronavirus disease of 2019 pandemic or (COVID-19). This analysis has been performed qualitatively through differential equation stability theory, as well as the basic reproductive value, which indicates a pandemic index, then calculated from the maximum eigenvalue of the subsequent matrix. We establish the global asymptotic stability criteria for such disease-free state. The actual COVID-19 occurrence documents and data from 01 July, 2021 to 14 August, 2022 in Pakistan are analyzed for estimation methods, leading in fitted values for biological parameters. Sensitivity analyzation is used to identify the much more relevant attributes in the developed framework. This scientific research revealed a deterministic computational formula that assesses the impact of various mitigation measures on the propagation of COVID-19 in a worldwide population. The analysis will concentrate on Pakistan, and relevant data gathered out of that region. If the method were modified for the total number of COVID-19 reported patients as well as the total number of active patients in the Pakistan region, infection rates would be approximated fairly. This research will in some way give government authorities including local hospitals additional knowledge about how to enhance precautionary efforts to minimize infection propagation.