2 laps of jogging isn't nearly enough. Think about it, that's like 5 minutes, tops. You should increase that to at least ten minutes (maybe more, depending on your fitness, event, etc.). Then you should go into your drills, strides. I've never heard of jumping-rope as a warm-up before, but that doesn't mean it's wrong. If it works for you, stick with it.
As for the stretching, I wouldn't throw it out completely. I'd be willing to bet that those national class athletes all do plenty of stretching, just not as part of their warm-up. Static stretching is usually better after your race/workout. If you want to keep it as part of your warm-up (and it has some value...good quiet time if nothing else), I would recommend doing it well before your event (like 40minutes+), and before your ten minutes running.
Just my 2cents
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