The antiparasitic medication ivermectin has taken the right-ish leaning internet by storm as a cure for COVID-19. In response, the mainstream media has meme-ed it as a horse medication; which is only semi-true. While it is used in veterinary medicine and people are taking the cow/horse/pig versions of the medication, it is also prescribed to humans regularly for things such as river blindness and lice. I am currently looking forward to better data about ivermectin’s usefulness in treating or preventing COVID-19. Until that time, I do not have a firm opinion on people who know what they are getting into and accept the risks of going off label and taking the drug. The problem is that the average ivermectin user has no idea what they are getting into and can not calculate how much they should take.
Take Sean, in the above screenshot. He has a bottle of injectable ivermectin for cows and pigs. He is a mid-40s man who is an office worker at a small firm in the south. It has been over twenty years since he has been in college and close to thirty years since he was in high school, the last time he would have taken a chemistry class and did stoichiometry; he is probably in no state to calculate his own dosage. What is most likely going to happen is that he is going to inject himself with a few milliliters of the solution and call it a day.
If you remember back to college GenChem or high school chemistry, stoichiometry is the math you did to move between units and calculate the results of reactions. It is also the math to calculate how much of the 1% solution one needs to inject to get the intended effect on a certain person.1
WARNING: I am calculating a lethal dose of ivermectin, below. This information is being presented for entertainment purposes only. If you are dumb enough to inject yourself with this much of the drug, it is entirely your fault. Make good choices!
Mass of the drug
Dosages are oftentimes written as the mass of a drug per unit of mass of bodyweight. For example, a known lethal dose of ivermectin is 50 mg/kg in rats. For this, I am going to assume that mice are a good proxy for humans and use that as a starting point. For the bodyweight portion of the math, I am going to use the weight of the average American, 199.8 lb.
Using this information, we can calculate our dose (in milligrams). We first need to convert to kilograms from pounds. Then, we need to multiply by the dosage. Notice how the pounds and kilograms cancel each other out in the equation below. At this point, we know that our dosage is 4530.6 mg.
Volume of the solution
Sean, above, has a 1% solution of ivermectin. From the picture, I can not tell if it is 1% by volume or by mass. However, in the end, we need to get to a volume of the solution to inject. We could do real stoichiometry to convert to moles and use the molar mass to figure out how many micrograms of the drug are in a milliliter of the solution, but that assumes that this solution’s strength was chosen at random instead of to make administration easy. Drugs.com claims that 1 mL of the solution has 10 mg of the drug in it. No idea if this is true, but it seems close enough for this demonstration. Together this is the formula that you need to use.
In total, you need to inject about 453 mL, roughly half a liter, for a lethal dose. The good news is that this is well above the amount that a reasonable person would ever inject into themselves. The bad news is that people experience negative effects from smaller doses. Also, the drug has a number of interactions that can have unknown effects. Remember that the normal ivermectin dosage in humans for parasites is only a few micrograms per kilogram.2
If your heart is set on taking ivermectin, please talk to your doctor. They can calculate your dosage and tell you if one of the recreational drugs, medications, herbal extracts that you take has the possibility of interacting with it. Injecting yourself with a randomly chosen amount of ivermectin is putting your health in danger.
It is arguably dimensional analysis because I shortcut the molar mass section.
For example, 1 mL of the 1% solution, above, is approximately 1 μg per kg for a 220 lb person.