I'd suggest looking into limma and edgeR for analysis.
You have to set up the coefficients and contrasts for the linear model. It looks like you have 2 experimental factors and one error term, one being KO status, and the second being time, and the last being known batch groups. You want to correct for batch as it could potentially effect your result. If you don't know the batch status, you can use something like SVA to do a generalized batch correction.
So starting off let's generate the model. I assume you probably have an excel file or csv file with each sample in a row and each column being either KO status, time, and sequencing batch. So read those in and generate a design for a linear model:
factor.table <- read.table("omics.csv", header=TRUE, row.names=1, sep="\t")
ko_status <- as.factor(factor.table$ko_status)
time_status <- factor.table$time_status
batch <- as.factor(factor.table$rnaseq_batch)
design <- model.matrix(~0 + ko_status + time_status + batch + ko_status:time_status)
So that's the basic design, and what it means is that the linear model will generate an intercept for each factor plus any interactions between KO and time status. You then generate contrasts to test for significant differences between defined groups, eg:
cont.matrix <- makeContrasts(KO_true = ko_status1 - ko_status2,
..., levels = design)
You'll have to play around with this a bit to generate the proper contrasts. There are working examples in the limma documentation which will help you figure it out, so do your reading.
Next you filter and normalized the data, then run the linear model:
y <- DGEList(counts = raw_counts)
y <- y[!rowSums(y$counts == 0) == ncol(raw_counts),]
A <- aveLogCPM(y)
y2 <- y[A>1,]
y3 <- calcNormFactors(y2, method = "TMM")
dge <- voomWithQualityWeights(y3, design=design, normalization="quantile", plot=FALSE)
fit <- lmFit(dge, design)
fit2 <- contrasts.fit(fit, cont.matrix)
fit3 <- eBayes(fit2, trend = TRUE, robust = TRUE)
I believe fit2 gives you the main effects, and fit3 will give you the DEG for whichever contrast. I also believe you can use one of the fits to do a repeated measures anova, but I think you can flush out the effect using the interaction term in the design.