It's horrendous, but I think it's important to remember that these terrible incidents are rare. It doesn't seem it because they're in the media, and you can spend all day reading these stories and freaking out, when the fact is that millions upon millions of women make millions and millions of park visits every single day and they're fine. I get scared, too, with all these stories around in the media, but I try not to let it overwhelm me, by remembering that most people go about their business safely, most of the time.
Different but related, in terms of feeling scared, I was getting really freaked out reading about all the young cancers in the DM recently. They're really hammering the topic, which is great for awareness, but I had to stop reading them, and I reminded myself that just over half of people never get cancer. I was beginning to feel that I might have it too, after reading so many stories. After all, it's not like the media runs stories about all the people who lived long lives and never got cancer, is it??
It's important not to let yourself spiral, because that way lies madness. I know it's easier said than done. But I do find that thinking the opposite of where my mind goes helps. To take a really simple example of what I mean, I might think "Hey, this and that person didn't send me Christmas cards" - or I could think about all the people who DID. Counteracting the fears with the positive side, I guess.