Final answer:
Transdermal (TD) administration is the method that facilitates constant, time-release of medication, whereas oral (A) administration is preferred for home use when treating systemic infections. If a drug isn't well absorbed orally or convenience is secondary, intravenous or intramuscular injections (parenteral, D) are used in healthcare settings.
Step-by-step explanation:
The method of medication administration that allows for a constant, time-release of the medication is transdermal (TD). This delivery system is designed to release a steady amount of medication over a prolonged period, eliminating the need for frequent doses. The medication contained within transdermal patches gets absorbed through the skin and into the bloodstream, providing a controlled release.
Concerning home administration of an antimicrobial to treat a systemic infection, the appropriate and most convenient route would be oral (A) administration. This route is often preferred because it is convenient for patients to take the medication at home, assuming the drug is well absorbed from the gastrointestinal (GI) tract. However, for certain cases where oral administration is not feasible or the drug is not well absorbed, parenteral (D) routes like intravenous or intramuscular injections are preferential, though they usually require administration within a healthcare setting.
In summary, transdermal administration offers the advantage of steady medication release but when it comes to systemic infections and home administration, oral route is typically favored. That said, parenteral routes are better suited for higher plasma levels that are sometimes necessary for treating infections, albeit less convenient for home use.