You are looking at things the wrong way.
define command{
command_name check-host-alive
command_line $USER1$/check_ping -t 10 -H $HOSTADDRESS$ -w 3000.0,80% -c 5000.0,100% -p 5
}
The thing you post is a Nagios command. the '-t 10' is not the interval, but the timeout argument. This means if the check_ping does not get a result in 10 seconds, the command will timeout.
To define the check interval, you need to look at the host (or service) configuration file.
For example:
define host {
host_name bogus-router
alias Bogus Router #1
address 192.168.1.254
parents server-backbone
check_command check-host-alive
check_interval 5
retry_interval 1
max_check_attempts 5
check_period 24x7
process_perf_data 0
retain_nonstatus_information 0
contact_groups router-admins
notification_interval 30
notification_period 24x7
notification_options d,u,r
}
The interval between checks in this example is 5 minutes (check_interval). It is not possible to set intervals of less then one minute with Nagios. If you want to have more granular (free) monitoring, check out InfluxDB, Telegraf and Grafana.