How can I make a valid design for this data in DESeq2?

[aprice67]

So I have a problem with a dataset I'm working on. Here is information about the samples.

Three viruses at three timepoints:
Virus1_day1, Virus1_day3, Virus1_day8.
Virus2_day1, Virus2_day3, Virus2_day8.
Virus3_day1, Virus3_day3, Virus3_day8.

And mock samples at a single timepoint:
Mock_day6

Here is a link to the actual sample information

Essentially, using DESeq2 I want to compare each virus at each time point to the mock condition. I can't do this because the design model isn't full rank though. I have only a single set of mocks, from day 6, and the viruses from days 1,3, and 8. I want to compare each virus at each time point to the mock set.

Specifically:
Virus1_day1 vs Mock
Virus1_day3 vs Mock
Virus1_day8 vs Mock
Virus2_day1 vs Mock
Virus2_day3 vs Mock
Virus2_day8 vs Mock
Virus3_day1 vs Mock
Virus3_day3 vs Mock
Virus3_day8 vs Mock

What I've done so far is to just separate the input based on timepoint, and then do my design matrix as ~ Virus. I really want to be able to process all of the data in a single set, however, and extract DE data for each comparison with something like,

 
results(dds, contrast=c("Virus","mock","ACali09"),alpha=signif_cutoff)

Can anyone help me figure out how to make the design matrix correctly specify the contrasts I'm trying to do? Thanks very much in advance.