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Dear Shan Gao,
There are many legitimate ways to define a design matrix. The best way depends on what questions you want to answer or what hypotheses you want to test.
It looks like you have 35 libraries in total (24 treatment samples and 11 control samples). Is this right? Are all the libraries biologically
I assume that the control samples have received some sort of inactive treatment for the same time period as the active samples.
What is it that you want to test? Do you want to find DE genes between treatment and control at each time? Or do you want to find genes are DE at each time vs 0h, adjusting for control differences?
In any case, you need to create a factors Time and Treatment. There are of length equal to the number of samples (35). Time takes values from 0 up to 48. Treatment takes two values, Treatment or Control, say.
If you can respond to these questions, then I'll give you more help with the design matrix and so on.