The phrase "to stop the spread" means taking actions to prevent something, like a disease or an idea, from spreading and affecting more people. Full definition
I don't have time to correct every ignorant religious poster but I do my part to help stop the spread of lies and misinformation. (religion.blogs.cnn.com)
Not only can you help your cat live a happy, healthy life, but you can also help stop the spread of this deadly disease. (tampabayvets.net)