Correction to: Scientific Reports https://doi.org/10.1038/s41598-018-20008-w, published online 26 January 2018

The Supplementary Material file that accompanies this Article contains an error in equations 3 and 5 and the paragraphs that follow them. Equation 3 and the paragraph below it:

$${\forall }_{c,c}DCD(c)=\frac{1}{{N}_{c}}{\sum }_{i{\epsilon }c}\frac{1}{{D}_{i}}{\sum }_{t=1}^{{D}_{i}}{\sum }_{j\in H(t)}DCD(i,j,t)$$

Where c is the category (eg. HCW, patients, etc.), Nc is the number of individuals i belonging to category c, Di the number of days of presence of individual i in the hospital, H(t) is the ensemble of all individuals present in the hospital on day t, and DCD(i,j,t) the cumulative duration of CPIs on day t between individuals i and j.

should read:

$${\forall }_{c,c}DCD(c)=\frac{1}{{N}_{c}}{\sum }_{i{\epsilon }c}\frac{1}{H}{\sum }_{j{\epsilon }H}\frac{1}{{D}_{i,j}}{\sum }_{t{\epsilon }{D}_{i,j}}DCD(i,j,t)$$

Where c is the category (eg. HCW, patients, etc.), Nc is the number of individuals i belonging to category c, Di,j the number of days of contact between i and j in the hospital, H is the ensemble of all individuals present in the hospital, and DCD(i,j,t) the cumulative duration of CPIs on day t between individuals i and j.

Equation 5 and the paragraph below it:

$$\forall (w,{c}_{1},{c}_{2}),wDCD({c}_{1},{c}_{2})=\frac{1}{{N}_{w,c1}}{\sum }_{i=1}^{{N}_{w,c1}}\frac{1}{{D}_{i}}{\sum }_{t=1}^{{D}_{i}}{\sum }_{j=1}^{{N}_{c2}}DCD(i,j,t)$$

Where c1 and c2 are two categories, w is the ward number, Nw,c1 is the number of individuals s belonging to category c1 (staff categories or patients), an Di is the number of days of presence of individual i in the hospital, Nc2 is the number of individuals from category c2 in the hospital, and DCD(i,j,t) is the daily cumulative duration of CPIs of two individuals i and j on day t.

should read:

$$\forall (w,{c}_{1},{c}_{2}),wDCD({c}_{1},{c}_{2})=\frac{1}{{N}_{w,c1}}{\sum }_{i=1}^{{N}_{w,c1}}\frac{1}{{N}_{c2}}{\sum }_{j=1}^{{N}_{c2}}\frac{1}{{D}_{i,j}}{\sum }_{j=1}^{{D}_{i,j}}DCD(i,j,t)$$

Where c1 and c2 are two categories, w is the ward number, Nw,c1 is the number of individuals s belonging to category c1 (staff categories or patients), and Di,j is the number of days of contact between i and j in the hospital, Nc2 is the number of individuals from category c2 in the hospital, and DCD(i,j,t) is the daily cumulative duration of CPIs of two individuals i and j on day t.