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According to health officials, there are also a further three people that are currently in a critical condition in hospital after seven people in total drank the sanitiser which contained methanol.
The state's Department of Health said the cases were reported to the New Mexico Poison Control Center. The first came in on 7 May and then others in the weeks that followed. They relate to alcoholism, according to health officials.
Some alcoholics have been known to use hand sanitiser to get intoxicated due to the alcohol content in it.
New Mexico Health Secretary Kathy Kunkel said in a statement: "If you think you may have used or consumed hand sanitiser containing methanol, please seek medical care. An antidote to methanol poisoning is available, but the earlier someone gets treated for methanol poisoning the better the chance of recovery."
The tragic announcement came after the US Food and Drug Administration (FDA) warned people to stop using nine hand sanitisers made by Mexican company Eskbiochem SA de CV because of the methanol levels.
The full list can be found here with the FDA stating that the use of these particular products is dangerous due to the presence of methanol (wood alcohol), a substance that can be toxic when absorbed through the skin or ingested.
After testing samples of different sanitisers, the FDA found that one product contained 81 percent methanol and another had 28 percent. It explained: "Methanol is not an acceptable ingredient for hand sanitizers and should not be used due to its toxic effects."
The FDA went on to add: "Consumers who have been exposed to hand sanitizer containing methanol should seek immediate treatment, which is critical for potential reversal of toxic effects of methanol poisoning.
"Substantial methanol exposure can result in nausea, vomiting, headache, blurred vision, permanent blindness, seizures, coma, permanent damage to the nervous system or death.
"Although all persons using these products on their hands are at risk, young children who accidentally ingest these products and adolescents and adults who drink these products as an alcohol (ethanol) substitute, are most at risk for methanol poisoning."
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