Fig. 3

When did it start? (A) The value of MSE (Eq. 11) is illustrated versus time (the black curve) for Qom province using a snapshot for the \(12_{th}\) day of the COVID-19 pandemic in Iran. As shown, it has a minimum at (\(t_i^*\)) (Eq. 66). When the third term of the expansion is added to the calculation, \(\Delta _i\) transforms to the gray curve (\(\Delta _i^c\)), with the minimum shifted approximately two days. (B) The estimated origin of time (\(t^*_i\)) versus the date of the snapshot (\(t_e\)) for Iran, considering Qom as the origin node. The points highlighted in green show the used snapshot in panel (A). (C) The value of MSE (Eq. 11) is illustrated versus time (the red curve) for the Washington state using a snapshot for the \(15_{th}\) day of the COVID-19 pandemic in the US. It has a minimum at (\(t_i^*\)) (Eq. 66). When the third term of the expansion is added to the calculation, \(\Delta _i\) transforms to the pink curve (\(\Delta _i^c\)), which approximately lies on the red curve. (D) The estimated origin of time (\(t^*_i\)) versus the date of the snapshot (\(t_e\)) for the US, considering Washington as the origin node. The points highlighted in green show the used snapshot in panel (C). In this analysis, we used the same setup as in Fig. 2; Please refer to the S. M. Section 4 for more details regarding the data.