Well Twitter has now got your back.
A new tool which is being rolled out by Twitter will enable you set the Twitter app to notify you when there is some activity from the people you follow and not random tweets. The company has also introduced a new notification setting which it has been testing for some time. The quality filter setting option which sieves out low quality tweets by checking on whether they are automated or duplicated and also the account of origin itself. The feature has been designed to improve overtime.
According to Twitter, the features will be introduced gradually so keep checking.