Increasing stamina with walking includes building quadricep muscles.
This workout helps to build stamina:
6-9 minutes - warm up. Walk at a moderate pace
3 minutes - walk at a fast pace
2 minutes - (1 minute) squats (1 minute) walking lunges
5 minutes - walk at a fast pace, pump your arms it helps with adding speed to your gait
3 minutes - (1 minute) jog in place with high knees (2 minutes) walking lunges
5 minutes - walk at a fast pace, pump your arms
4 minutes - (2 minutes) squats (2 minute) walking lunges
5 minutes - cool down; walk at a moderate to slow pace
You used your quadricep muscles and gluteal muscles...even though this is a quick workout you may experience muscle soreness, this is normal. Lactic acid buildup causes muscle soreness and results in muscles tearing down only to build up again which increase strength and stamina.
Increasing speed in your walking routine includes fast pace walking intermittent with other exercise that keeps your heart rate elevated; elevated heart rate is key.