Upgrading Nagios core from source was remove from official documentation, so I leave that here. Change nagios-4.5.11 with the version you want to upgrade to.
sudo systemctl stop nagios.service
cd /tmp/
sudo rm -rf nagioscore*
wget -O nagioscore.tar.gz https://github.com/NagiosEnterprises/nagioscore/archive/nagios-4.5.11.tar.gz
tar xzf nagioscore.tar.gz
ll
cd nagioscore-nagios-4.5.11/
sudo ./configure --with-httpd-conf=/etc/apache2/sites-enabled
sudo make all
sudo make install
sudo make install-daemoninit
sudo systemctl start nagios.service
sudo systemctl status nagios.service