Use 18.04 sources.list:
sudo mv /etc/apt/sources.list /home/user/sources.list.bk
sudo vi /etc/apt/sources.list
Paste the repositories to it:
deb http://us.archive.ubuntu.com/ubuntu/ bionic main restricted
deb http://us.archive.ubuntu.com/ubuntu/ bionic-updates main restricted
deb http://us.archive.ubuntu.com/ubuntu/ bionic universe
deb http://us.archive.ubuntu.com/ubuntu/ bionic-updates universe
deb http://us.archive.ubuntu.com/ubuntu/ bionic multiverse
deb http://us.archive.ubuntu.com/ubuntu/ bionic-updates multiverse
deb http://security.ubuntu.com/ubuntu bionic-security main restricted
deb http://security.ubuntu.com/ubuntu bionic-security universe
deb http://security.ubuntu.com/ubuntu bionic-security multiverse
Then update packages and install alpine:
sudo apt update && sudo apt install alpine
Alpine is installed and starts correctly:
$ alpine
Creating subdirectory "/home/spacer/mail" where Alpine will store
its mail folders.
Alpine finished -- Closed empty folder "INBOX"
user@ubuntu18:~$ cat /etc/lsb-release
DISTRIB_ID=Ubuntu
DISTRIB_RELEASE=18.10
DISTRIB_CODENAME=cosmic
DISTRIB_DESCRIPTION="Ubuntu 18.10"
Also, as FedonKadifeli suggested in comment, you could do the next:
If you want to continue using an outdated release then edit
/etc/apt/sources.list
and change archive.ubuntu.com
and
security.ubuntu.com
to old-releases.ubuntu.com
But it as it is actually didn't work for me.