Inferring SARS-CoV-2 RNA shedding into wastewater relative to the time of infection – CORRIGENDUM

The authors of the original publication would like to highlight some typographical errors from their article that may potentially cause some problems with interpreting parts of it.

The first error is in table 1: the parameter names are given in upper case, but they should be lower case. For instance, the Greek letters μ, σ, α, β, and θ should all be lower case, as should the r describing the negative binomial size. A corrected version of the table is shown below

Table 1. Summary of parameter. Where the symbol column is empty, there was no symbol used for that parameter

The second error concerns the likelihood equations (the equations immediately following the text “with their likelihood given by”). All of the text here is correct, but the last pieces of text in each equation is in the superscript, and should not be. For the first equation, this is everything including and following the word “if”, and for the second equation this is the word “otherwise,” Both of these should be rendered at the same level as the main part of the equation, and not in the superscript. The equations should appear as they do below.

$$L( {\alpha , \;\beta , \;\theta , \;r\vert C_d( t ) } ) = \displaystyle{{C_d( t ) + r-1} \over {C_d( t ) }}( {1-p} ) ^rp^{C_d( t )} \quad\quad {\rm if}\; C_d( t ) > D_{95}( t ); $$

$$L( {\alpha , \;\beta , \;\theta , \;r\vert C_d( t ) } ) = \mathop \sum \limits_{c = 0}^{D_{95}( t ) } \displaystyle{{c + r-1} \over c}( {1-p} )^rp^{C}\quad \quad\;{\rm otherwise} ,$$