If you remove everybody except yourself from the Schedule Issues Permission in your permission scheme nobody will be able to add issues to a sprint (active or not).
That might be a solution.
More information about the JIRA Agile permissions can be found here: https://confluence.atlassian.com/display/AGILE/JIRA+Agile+-+JIRA+Configuration#JIRAAgile-JIRAConfiguration-Permissions
Another solution would be to simply monitor your sprint and look at who's adding issues to the sprint and explain to this person why it's a bad idea to add stuff to a sprint.
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