to limit yourself to only numerics you could do
library(tidyverse)
mydf <- as_tibble(mtcars,rownames="carname")
filter(mydf,
carname=="Merc 230") %>% select_if(is.numeric) %>%
rowSums(na.rm=TRUE)
in this case I'm isolating a relevant row, where the carname is Merc 230, for you its where some variable has the Total Cases label in it... , then select the summable columns, then sum them