The following code should do the trick.
$("#applist").data("kendoMobileListView").refresh()
Check documentation on refresh for further information: http://docs.telerik.com/kendo-ui/api/mobile/listview
Iam not sure why you have used datasource.read(). This function can be used only if you have dynamic data items that are loaded into a template inside the listview and you are deleting items in the source itself and reading rest of the source items after each time you close modal view.Inorder to delete row of a listview and display rest of the rows,just calling refresh function with id of the listview is enough.