def METHOD_NAME(ptask):
    """
    Convert the ``last_update`` and ``last_runs`` timestamps to ISO 8601 strings and return a copy of ``ptask``.
    :param ptask: periodic task dictionary
    :return: a new periodic task dictionary
    """
    ptask = ptask.copy()
    ptask['last_update'] = ptask['last_update'].strftime(AUTH_DATE_FORMAT)
    ptask['last_runs'] = dict((node, timestamp.strftime(AUTH_DATE_FORMAT))
                              for node, timestamp in ptask['last_runs'].items())
    return ptask