MVC with Bootstrap Navbar - Set Selected Item to Active

I'm learning Bootstrap and can't get the selected item into an "active" state. The active state remains on the default item. The newly selected/clicked item changes to active briefly, but reverts back. I've read all the posts and still can't get this code to work. I'm using MVC5 and JQuery 2.1.

EDIT: If I change the li's hrefs to href="#", then the active class gets applied properly. What's happening when a new view gets loaded? I think Sebastian's response is close, but gets messy with Areas.

Markup

<div class="navbar-wrapper">
    <div class="container">
        <div class="navbar navbar-inverse navbar-fixed-top">

            <div class="navbar-header">
                <a class="navbar-toggle" data-toggle="collapse" data-target=".nav-collapse">
                    <span class="icon-bar"></span>
                    <span class="icon-bar"></span>
                    <span class="icon-bar"></span>
                </a>
                <a class="navbar-brand" href="#">Test</a>
            </div>
            <div class="btn-group pull-right">
                <a class="btn dropdown-toggle" data-toggle="dropdown" href="#">
                    <i class="icon-user"></i>Login
          <span class="caret"></span>
                </a>
                <ul class="dropdown-menu">
                    <li><a href="#">Profile</a></li>
                    <li class="divider"></li>
                    <li><a href="#">Sign Out</a></li>
                </ul>
            </div>
            <div class="navbar-collapse collapse">
                <ul class="nav navbar-nav">
                    <li class="active"><a href="~/Home">Home</a></li>
                    <li><a href="~/Home/About">About</a></li>
                    <li><a href="~/Student">Students Sample</a></li>
                    <li class="dropdown">
                        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Dropdown <b class="caret"></b></a>
                        <ul class="dropdown-menu">
                            <li><a href="~/Admin/Home/Index"">Admin</a></li>
                            <li><a href="#">Another action</a></li>
                            <li><a href="#">Something else here</a></li>
                            <li class="divider"></li>
                            <li><a href="#">Separated link</a></li>
                            <li><a href="#">One more separated link</a></li>
                        </ul>
                    </li>
                </ul>
            </div>

        </div>
    </div>
    <!-- /container -->
</div>
<!-- /navbar wrapper -->

Script

<script type="text/javascript">

    $(function () {
        $('.navbar-nav li').click(function () {
            $(this).addClass('active').siblings().removeClass('active');
        });
    });

</script>

You have to check in your controller or view which menu item is active based on the current url:

I have an extension method similar to this:

public static string MakeActiveClass(this UrlHelper urlHelper, string controller)
{
    string result = "active";

    string controllerName = urlHelper.RequestContext.RouteData.Values["controller"].ToString();

    if (!controllerName.Equals(controller, StringComparison.OrdinalIgnoreCase))
    {
        result = null;
    }

    return result;
}

You can use it in your view like this:

<!-- Make the list item active when the current controller is equal to "blog" -->
<li class="@Url.MakeActive("blog")">
   <a href="@Url.Action("index", "blog")">....</a>
</li>