I've used a lot of different organics on myself trying to find something that works for the kids (geranium, eucalyptus, citronella, etc) and all the commercial stuff including organic OLE and the normal repellents like deet, picaridin, & permethrin. OLE works pretty well on mosquitoes, I'd say as well as deet 10%... but you have to reapply it religiously (like sunscreen religiously). Citronella also works pretty well on mosquitoes, although not as well as OLE... of the organics, OLE is the gold standard by far (ooh dat smell, its as bad as deet in a different way.) If you're JUST trying to repel mosquitoes in your back yard, don't stress it, OLE will get the job done... that said... ticks are another story.
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The real problem is... except for deet none of them seem to work well on either our local deer ticks (Ohio) or the lone star ticks that are coming up from down south. My one daughter got bitten by a tick at camp with picaridin on her and got lyme disease (and it caused bells palsy) from it (6mo for full facial movement again, but we initially thought she had a stroke while she was asleep... woke up and half her face didn't work at all... freak out doesn't even begin to describe it.) Since then, even on the kids, if we're going somewhere with ticks, we ALL get deet... and not the kids kind, 98%. We're careful to keep it away from their mouth and eyes. Everywhere else gets covered and clothing we use for going out is sprayed in permethrin.
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Alpha-gal (life long allergy to the protein in red meats), Lyme (can be terminal and can leave life long paralysis issues), and last few years we've seen massive increases in the cases of Powassan (death in 10%-40% of people who get it depending on point they discover what it is) are nothing to be screwed with and that's what you're up against with ticks these days.
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There have been a LOT of health concerns voiced about deet, but most studies show it safe to be used so long as you're not getting it in mucus membranes or ingesting it... there were tests even done in india in the past couple years on pregnant women, women on deet fared better than women off it (less cases of malaria and other mosquito borne diseases), and there was no notable effects on the children born between deet users and the control group provided both didn't contract malaria. There is no evidence it causes cancer (studies that suggest it unreplicable and they had flawed methodology in some cases.) The panic about deet is anti-vax bullshit all over again.
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https://www.popsci.com/article/science/deet-safe-use
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https://www.consumerreports.org/insect-repellent/how-safe-is-deet-insect-repellent-safety/
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We use these two:
https://www.amazon.com/Bens-Mosquito-Insect-Repellent-Ounce/dp/B00HJTH0EE/
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https://www.amazon.com/Sawyer-Products-SP657-Permethrin-Repellent/dp/B001ANQVYU/
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The reality is, nothing is going to change your mind or your wife's mind till you get hit... and then it's too late. I was same way, but I didn't get a warning before it happened... and I'd feel guilty seeing this post and not saying anything. So I've said my peace. Deet is the gold standard. It's safe. It works on a broad range of insects. You will never see me or mine in the woods against without it. Ever. One round with Lyme disease and bells palsy in my daughter was one more time than I ever wanted in my life, it was heart breaking, I'd gladly have taken a 10x worse case over her have to deal with that for months.
Here's Oregon's fact sheet: https://www.oregon.gov/oha/PH/DISEASESCONDITIONS/COMMUNICABLEDISEASE/VETERINARIANS/Documents/DiseaseFactsheets/tickborne.pdf
and they reference the cdc page-- https://www.cdc.gov/ticks/
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Seriously, don't screw around, be safe.
Ben's 100% DEET Mosquito, Tick and Insect Repellent, 3.4 Ounce Pump https://www.amazon.com/dp/B00HJTH0EE/ref=cm_sw_r_cp_api_i_fQXmFb6P7RRQ2
Also cabelas, Rei and others. There is another brand called Repel that also has high DEET.
Coleman 100 Max 100% DEET Insect Repellent Spray - 4 oz Can https://www.amazon.com/dp/B01C2V7URA/ref=cm_sw_r_cp_api_i_nRXmFbTEDQ1BX