Examples:

// Create an instance that spans August 1st, 1980 and is associated
// with a Cartesian position.
const timeInterval = new Cesium.TimeInterval({
    start : Cesium.JulianDate.fromIso8601('1980-08-01T00:00:00Z'),
    stop : Cesium.JulianDate.fromIso8601('1980-08-02T00:00:00Z'),
    isStartIncluded : true,
    isStopIncluded : false,
    data : Cesium.Cartesian3.fromDegrees(39.921037, -75.170082)
});

// Create two instances from ISO 8601 intervals with associated numeric data
// then compute their intersection, summing the data they contain.
const left = Cesium.TimeInterval.fromIso8601({
    iso8601 : '2000/2010',
    data : 2
});

const right = Cesium.TimeInterval.fromIso8601({
    iso8601 : '1995/2005',
    data : 3
});

//The result of the below intersection will be an interval equivalent to
//const intersection = Cesium.TimeInterval.fromIso8601({
//  iso8601 : '2000/2005',
//  data : 5
//});
const intersection = new Cesium.TimeInterval();
Cesium.TimeInterval.intersect(left, right, intersection, function(leftData, rightData) {
    return leftData + rightData;
});

// Check if an interval contains a specific time.
const dateToCheck = Cesium.JulianDate.fromIso8601('1982-09-08T11:30:00Z');
const containsDate = Cesium.TimeInterval.contains(timeInterval, dateToCheck);