If you have to use this expression, I would say "in the times to come", but I wouldn't use any of these expressions as they all sound strange to me. I would just say almost every time: "in the future". There are many other ways of saying this, none of which, to me, are preferable to "in the future." as time goes by as the future becomes the present as the clock goes "tick tock" the older we get the closer we get to the 22nd century and so on. By the way, you used "would", a conditional tense, but you have no condition in your sentence. So the better verb, since covid-19 cases are not going to stop anytime soon, would be "will". Hence: There will be more covid-19 cases in the future. I hope that helps.