Increment Notification count

notification_increment.js

$(function() {
  
  var badge_unreadMessages = $("#unread_message_count");
  
  // Script to check for notifications runs
  // If the script comes back with new notifications:
  badge_unreadMessages.text( parseInt( badge_unreadMessages.text() ) + 1 );
  
});

<span id="unread_message_count">0</span>

Then access the current count by

console.log( badge_unreadMessages.text() );