Excellent............

Please use this code:

  showModal() {
    history.pushState(null, 'modalOpened');
    this.modal.show();
  }

  hideModal() {

  }

  ngOnInit() {
    this.location.onPopState(() => this.modal.hide());
  }

I added fake history state in 'showModal' method to prevent route change on back button. Hope that helps.

The challenge is to close the modal instead of changing the route, in case a modal is open

I assume that there is a route change when you use back button. In this case you can listen to router events and use hide() method to close the modal.

this.router.events.subscribe((event: Event) => {
    // close your modal here
});