If 3rd party ink can give you a computer virus then the printer isn't built correctly. There's no reason that should happen.

If you’re using an HP printer, such an attack is feasible because of the chips that they use for detecting ink levels, verifying the manufacturer, etc.. As a result, any cartridge could potentially infect your printer (since potentially an attacker could modify a first party ink/toner cartridge and replace its chip with one infected with malware). As such, the only fully “safe” approach is to modify your HP printer such that it doesn’t connect to these chips at all.

I look forward to HP providing firmware that will prevent the printer from communicating with any ink/toner chips (and that will allow printing to continue unabated, relying on the user to notice that ink levels are low and that new ink is required).