DeSeq2 time series data

Hi. I am working with a mutant library. It is not RNAseq but the idea is more or less the same. I exposed the mutant library to an antimicrobial compound and I collect samples at different times. After that I extracted the DNA, tagged the pools and I sequenced the samples: treated, untreated at three different times. The thing is that I am not so sure the model I should apply.
My input data is a count matrix (I used Salmon)
My col_data is:

id Tiempo Replica Condition

Sample_1 t1 R1 Untreated

Sample_2 t1 R2 Untreated

Sample_3 t1 R3 Untreated

Sample_4 t2 R2 Untreated

Sample_5 t2 R3 Untreated

Sample_6 t3 R1 Untreated

Sample_7 t3 R2 Untreated

Sample_8 t3 R3 Untreated

Sample_9 t1 R1 Treated

Sample_10 t1 R2 Treated

Sample_11 t1 R3 Treated

Sample_12 t2 R2 Treated

Sample_14 t3 R1 Treated

Sample_15 t3 R2 Treated

Sample_16 t3 R3 Treated

After reading some tutorials my final idea is to use this design formula

ddsFullCountTable <- DESeqDataSetFromMatrix(
countData = countdata,
colData = coldata,
design = ~ Condition + Tiempo + Condition:Tiempo)

because I found in a tutorial the following comment
“The following chunk of code performs a likelihood ratio test, where we remove the strain-specific differences over time. Genes with small p values from this test are those which at one or more time points after time 0 showed a strain-specific effect. Note therefore that this will not give small p values to genes that moved up or down over time in the same way in both strains.”

master.bioconductor.org/packages/release/workflows/vignettes/rnaseqGene/inst/doc/rnaseqGene.html#time-course-experiments

The idea of this analysis is to see witch mutants are enriched or reduced over the time and I am not interested in mutants that are increased at time 1, decreased at time 2 and increased at time 3. I need those mutants that are increasing or decreasing the number trough the time (linear dependency). The idea is that the important mutants are those that have a higher number at the end of the experiment and the mutants that are very decreased after the experiment.

Is it OK to use this design formula or is it better to use another?

Thanks!

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