Conditional search in relations

$search = 'Ford'

$set = CarModel::with(
  'brand_info',
  'country_info',
  'color_info',
  'engine_info',
  'cuser',
  'muser'
)
    ->whereHas('color_info', function ($q) {
         $q->where('color', '=', 'red'); // only red cars
    })
    ->where('active', '=', 1);

if ($search !== false && $search !== '') {

    $set->where(function ($query) use ($search) {
       // where on the parent model
       $query->where('name', 'LIKE', "%{$search}%");

       // other columns to be searched in the parent model
       $columns = ['description', 'notes'];

       foreach ($columns as $column) {
          $query->orWhere($column, 'LIKE', "%{$search}%");
       }

       // also include the search in the country info
       $query->orWhereHas('country_info', function ($q) use ($search) {
           $q->where(function ($q) use ($search) {
               $q->where('name', 'LIKE', "%{$search}%");
           });
       });

       // and also in the engine_info relation engine_parts (one level deeper)
       $query->orWhereHas('engine_info.engine_parts_info', function ($q) use ($search) {
           $q->where(function ($q) use ($search) {
               // part_no is in the engine_parts relation within the engine model.
               $q->where('part_no', 'LIKE', "%{$search}%");
           });
      });
  });
}

// total of all finds (no start, limit yet)
$this->total = $set->count();

// here we get the records we need (with start, limit)
$this->results = $set->orderby('number')
     ->limit($limit)
     ->offset($start)
     ->get();

// count of the records in this set
$this->count = $set->count();