I am working on one of the previously published dataset and the experiment is like cell line with infected and control in a time course (T1=1hr,T2=4hr,T3=24hr)

         condition timepoint
Mac.T1        ctrl        T1
Mac.T1.1      ctrl        T1
Mac.T1.2      ctrl        T1
Mac.T2        ctrl        T2
Mac.T2.1      ctrl        T2
Mac.T2.2      ctrl        T2
Mac.T3        ctrl        T3
Mac.T3.1      ctrl        T3
Mac.T3.2      ctrl        T3
Inf.T1         Inf        T1
Inf.T1.1       Inf        T1
Inf.T2         Inf        T2
Inf.T2.1       Inf        T2
Inf.T3         Inf        T3
Inf.T3.1       Inf        T3
Inf.T3.2       Inf        T3
Inf.T3.3       Inf        T3

This is the design i used

ds <- DESeqDataSetFromMatrix(countData=counts, colData=samples,design=~ timepoint + condition + timepoint:condition)
dds <- DESeq(dds, test="LRT", reduced = ~ timepoint)

I am interested to look at the differential expression after treatment in T1,T2,T3 time points 

using the function, resultsNames(dds) 

[1] "Intercept"                "timepoint_T2_vs_T1"       "timepoint_T3_vs_T1"       "condition_Inf_vs_ctrl"   
[5] "timepointT2.conditionInf" "timepointT3.conditionInf"

I tried to look for the differential expression in T2 Inf condition results(dds, name="timepointT3.conditionInf", test="wald") and found none have passed the filter of p<0.05 which cannot be true (published data)

Can anybody help me if i am doing something wrong with the design?

Thank you

Take a look at the section in the vignette on interactions, where we introduce what the coefficients mean.

The differences at a time point after the reference level (T1) are the main effect (condition_Inf_vs_ctrl) plus the interaction term.

So for T2 it would be:

results(dds, contrast=list(c("condition_Inf_vs_ctrl", "timepointT2.conditionInf")))

To add together those two coefficients to produce the Inf vs Ctrl difference at T2.