One of the main concerns about the fast spreading coronavirus disease 2019 (Covid-19) pandemic is how to intervene. We analysed severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) isolates data using the multifractal approach and found a rich in viral genome diversity, which could be one of the root causes of the fast Covid-19 pandemic and is strongly affected by pressure and health index of the hosts inhabited regions. The calculated mutation rate ( m r) is observed to be maximum at a particular pressure, beyond which mr maintains diversity. Hurst exponent and fractal dimension are found to be optimal at a critical pressure ( P m), whereas, for P > P m and P < P m, we found rich genome diversity relating to complicated genome organisation and virulence of the virus. The values of these complexity measurement parameters are found to be increased linearly with health index values.