Antivirals like acyclovir and similar nucleoside analogues act only on the cellular machinery within viruses, but not the cellular machinery in human cells. You are right that both viruses and human cells replicate DNA, but they do it in a different way. Some antivirals work on viral DNA polymerase, some work on viral reverse transcriptase, and some probably do something else that I don't know about.
I was reading this tweet thread from Dr. Monica Gandhi about molnupiravirhttps://twitter.com/MonicaGandhi9/status/1415093950000422912Molnupiravir was not developed for SARS-CoV-2- originally thought of as a broad-spectrum antiviral because it is a "nucleoside analogs". We use those a lot in HIV but they basically inhibit the virus from replicating because this compound interrupts the process of copyingwhich led me to this article in Business Insiderhttps://www.bloomberg.com/news/features/2021-03-25/merck-mrk-molnupiravir-pill-could-change-the-fight-against-covidThe first antiviral approved in the U.S. was idoxuridine, a herpes treatment regulators green-lit in 1963, generations after the discovery of antibiotics. Its among a widely used class of drugs called nucleoside analoguessynthetic versions of nucleosides, critical building blocks of DNA and its counterpart, RNA, the messenger molecule that delivers instructions to a cells protein-making factories. Nucleoside analogues prevent viruses from replicating, or from replicating effectively, inside cells.When they do invest, they have much more incentive to focus on chronic diseases than acute ones, which entail inherently shorter treatmentand revenuewindows. If you look at what drugs have been developed against viruses, you have HIV, you have hep C, you have herpes. Those are all chronic infections. That means longer-term therapy,And so here I am, my High School Biology in mind, wondering how if day to day my cells are dividing and so need to replicate DNA, how providing a drug that inhibits replication is safe, especially for chronic diseases where the drug is taken on a daily basis for well, the long term.For the care and feeding of the automod:I am a 60 year old male, non-smoking, and this question has recurred off and on for a few years now, mostly in by frontal lobe I believe, though friends insist that that is located in my rectum