Objects with db connection - php

Question

I have a:
class Person
{
public $data;
public function __construct($name) {
$database = new Database;
$database->prepare('SELECT * FROM persons where name = :name');
$database->bindParam(':name', $name);
$database->execute();
$this->data = $database->fetch();
}
}
and i´m creating persons like this:
$jim = new Person('Jim');
$mike = new Person('Mike');
and this is my database class
class Database
{
private $host = 'localhost';
private $user = 'test';
private $pass = '123';
private $dbname = 'test';
private $dbh;
private $error;
private $stmt;
public function __construct()
{
$dsn = 'mysql:host=' . $this->host . ';dbname=' . $this->dbname;
$options = array(
PDO::ATTR_PERSISTENT => true,
PDO::ATTR_ERRMODE => PDO::ERRMODE_EXCEPTION
);
try{
$this->dbh = new PDO($dsn, $this->user, $this->pass, $options);
}
catch(PDOException $e){
$this->error = $e->getMessage();
echo $this->error;
}
}
public function prepare($query)
{
$this->stmt = $this->dbh->prepare($query);
}
public function bindParam($key, $val)
{
$this->stmt->bindParam($key, $val);
}
public function execute()
{
$this->stmt->execute();
}
public function fetch()
{
return $this->stmt->fetch(PDO::FETCH_ASSOC);
}
}
I´m getting this message very often
Warning: PDO::__construct(): MySQL server has gone away
I want to confirm if this approach is correct. calling the database in the constructor?
How can i know if the created person exists (i mean exist in the database)
should i do something like this?
$jim = new Person('Jim');
if($jim->data) {
echo 'person exists in the db';
}
thank you