If you've had a problem not being able to sprint consistently while playing COD, you're not alone. I first ran into the issue on Black Ops 3 and it drove me insane! I looked online and found a plethora of videos created by idiots telling you to blow into joystick, used compressed air, electronic cleaning solutions (Deoxit, etc.), even some that tell you to click your button 30 times pointed in different directions.
NONE OF THAT WORKS! Lmao, I spent the next 3 years trying to figure out what was wrong and finally figured it out. Turns out, this is common with COD players because we sprint constantly. To that end, we create a gap in between the tact button, and the stick that pushes it down (which is needed to engage sprinting).
THE SOLUTION is to wedge a small piece of tape or paper in between those parts to fill that gap. It does involve opening your controller, but it's not that difficult and it saves you from having to buy another controller. Another issue could be the sensor wheel but with so much misinformation about this topic, I doubt anyone will find this from a web search, so I won't go into detail [video link below]. If this saves just 1 COD player from having to buy a new controller, I'd be stoked.
Found a company that makes stickers for this, but this video shows how to install them. They also have good tear down videos for each type of dualshock controller which helps if you haven't taken apart a controller before. Anyways, here are the two solutions that actually work: