i have another solution for that, we can use Moment-range which is plugin for Moment.js
Just check this moment-rangeMoment Range .
check this Fiddle
var start = new Date(2012, 4, 1);
var end = new Date(2012, 4, 23);
var lol = new Date(2012, 4, 15);
var wat = new Date(2012, 2, 27);
var range = moment().range(start, end);
var range2 = moment().range(lol, wat);
range.contains(lol); // true
range.contains(wat); // false