On the dynamics and mitigation of SARS-CoV-2 outbreak in India via a fractional modelling with the Liouville–Caputo derivative

Abstract

The dawn of the year 2019 had brought in a dangerous demon called novel coronavirus which wrecked havoc on the entire world. India has observed the very first case of SARS-CoV-2 infection on 30 January, 2020 and till date as of September, 2025, there are 70,47,53,890 total cases out of which 70,10,681 deaths were recorded. Due to this reason there had been an urge of studying the dynamics of this deadly disease and mathematical models are effective way to have an analytical study of the disease outbreak and control. Hence, in this work, an epidemic modelling has been efficiently formulated as a Susceptible(S)-Exposed(E)-Infected(I)-Asymptomatically infected(A)-Quarantined(Q)-Hospitalized(H)-Recovered(R) (S E I A Q H R) model, where the derivative is applied in the Liouville–Caputo (L-C) fractional sense. An analysis has been done regarding the transmission dynamics, causes, control, preventive measures like the effect of quarantine, self-isolation, environmental impacts and other initiatives that has been taken by the Indian government to alleviate the spread of the communicable virus. The data available regarding the infected population of India from 27th July, 2020 to 26th July, 2021 has been taken into consideration (Figure 2) for analysis and, in accordance with that, several parameter values of the fractional model have been fitted. Furthermore, the local stability and global stability analysis have been conducted for the pandemic equilibrium state. In addition to that, based on the sensitivity analysis along with the dynamics of the threshold values like the reproduction ratio R0?2.589, we figure out the efficiency of the preventive strategies, which forecast the outbreaks in future and potential of the control measures of the disease. Apart from that, an effective numerical technique has been employed to simulate the model and the resulting numerical values have been further tabulated and depicted graphically. © 2025 Elsevier Ltd