JSFiddle - React, Tailwind, and code Playground

HTML

<div class='selector'></div>

JavaScript

class WidgetBase {

    public element:JQuery;

    constructor() {
        // remove all members, they are only needed at compile time.
        var myPrototype =  (<Function>WidgetBase).prototype;
        $.each(myPrototype, (propertyName, value)=>{
           delete myPrototype[propertyName];
        });
    }

    /**
     * Calles the base implementation of a method when called from a derived method.
     * @private
     */
    public _super(arg1?:any, arg2?:any, arg3?:any, arg4?:any) {

    }

    /**
     * @private
     */
    public _superApply(arguments) {

    }

    /**
     * Gets or sets the value of the widget option associated with the specified optionName.
     */
    public option(optionName:string, value?:any):any {

    }

    // ... further methods from http://api.jqueryui.com/jQuery.widget/
}

class SmartWidget extends WidgetBase {

    constructor(){
        super();
    }

    public _create() {
        var mySmartOption = this.option('smart'); // compiles because of base class
        this.beSmart(mySmartOption);
    }

    public _setOption(key:string, value:any) {
        if (key === 'smart') {
           this.beSmart(value);
        }

        this._super(key, value); // compiles because of base class
    }

    private beSmart(smartOne:any){
        // ...
    }

}

// register
jQuery.widget("myLib.smartWidget", new SmartWidget());

// assuming you are using https://github.com/borisyankov/DefinitelyTyped
declare interface JQuery{
    smartWidget();
    smartWidget(options:any);
    smartWidget(methodName:string, param1?:any, param2?:any, param3?:any, param4?:any);
}


$(".selector").smartWidget({smart:"you"});