Reffering to your "Gradual reduction is possible by switching over to a different brand of cigarette which has less nicotine. Then the number of cigarettes can be reduced. Another method of nicotine tapering is by sticking to the same brand and reducing the number of cigarettes smoked per day."
Initially your suggestion may work but once the person is habitual and is having more than 20 cigarettes per day then this gradual reduction is not possible. Either by reducing number of cigarettes smoked per day or by using a different brand. Also people even tried using different brand to stop smoking gradually but this does not work out, you need to either strictly not to have any cigarettes or you cannot leave this habit.