You can change the visible week using startDate property:
<select id="week">
  <option value="2016-04-04">Week 14</option>
  <option value="2016-04-11">Week 15</option>
</select>
<div id="dp"></div>
<script>
var dp = new DayPilot.Calendar("dp");
dp.viewType = "Week";
dp.init();
$(document).ready(function() {
  $("#week").change(function() {
      dp.startDate = $(this).val();
      // load events for the new week
      // ...
      dp.update();
  });
});
</script>