You would need a WebSocket server to make this real-time communication available.

var app = require('express')();
var http = require('http').Server(app);
var io = require('socket.io')(http);

app.get('/', function(req, res){
  res.sendFile(__dirname + '/index.html');
});

io.on('connection', function(socket){
  socket.on('new message', function(msg){
    io.to(msg.username).emit('new message');
  });
socket.on('join', function (room) {
      socket.join(room);
 });
});

http.listen(3000, function(){
  console.log('listening on *:3000');
});

In your backend, you publish a message to a specific channel, probably the channel which the user that has received a message is listening to, with a specific message e.g. "new message".

const io = require('socket.io-client');
const socket = io('localhost');

socket.emit('new message', { username: "john" });

And on the client side, the user who is getting the message is listening to this channel and will be notified.

$(function () {
    var socket = io();
    sio.emit('join', 'john');
    socket.on('new message', function(msg){
      // increment messages count
    });
});