I obviously can't give an opinion on how the following would apply to any specific case, but there are sources which talk about the need to provide medicine to patients, even against their own wishes. Magen Avraham and Kaf Hachaim both cite the Radbaz when saying that one can force a patient to take medicine even if the patient doesn't want to. These opinions are independent of the patient being a rodef - they are all based simply on the patient's own well being. The Rambam likewise says that one is not allowed to risk one's own life unnecessarily.
Magen Avraham 328:6
אם לא רצה החולה לקבל התרופה כופין אותו, חולה אומר צריך אני לתרופה פלונית ורופא אומר א"צ שומעין לחולה ואם הרופא אומר שאותו תרופה יזיקהו שומעין לרופא [רדב"ז ח"א ס"ו כ"ה]:
If the patient does not want the medicine, we force the patient to take it. If the patient says he requires a certain medicine, and the doctor says the patient does not need it, we listen to the patient. If the doctor says that that medicine will harm [the patient], we listen to the doctor.
Kaf HaChaim 328:45
שם. כל חולי שהרופאים אומרים וכו' ואם לא רצה החולה לאכול או לעשות תרופה משום מדת חסידות כופין אותו לעשות. הרדב"ז ח"א סי' ס"ו, כנה"ג בהגה"ט. מ"א סק"ו. ר"ז או' י"א. ח"א כלל ס"ח או' ח'.
If the patient does not want to eat or receive medicine because of a matter of piety, [the patient] is forced to do so.
Regarding parents, the same basic principle applies. The Radbaz has a relevant teshuva. A baby was 2 years old and was still very weak. The baby would be potential danger if it was weaned. It would not nurse from anyone other than it's mother, so a wet nurse wasn't a viable option. The Radbaz suggests a number of options, but ultimately concludes that even if the woman wants to stop nursing, she can be forced to continue nursing because it is important to the babies health. (Teshuvot HaRadbaz 1:349 - I believe this is the one the acharonim above are referring to and either their citation system is something unfamiliar to me or the numbers of the Teshuvot are printed differently in their edition compared to the probably more modern edition digitized by Sefaria).
Although the above answers your question without needing to resort to calling someone a rodef, it is an interesting question. I haven't seen anyone who explicitly says this, however, Rav Aviner comes fairly close. He does say that there is an obligation to vaccinate and dismisses the notion that one has the freedom to chose not to vaccinate. He also says that a non-vaccinator can be considered a rodef.
ש: האם חייבים להתחסן?
ת: כן. ונשמרתם מאוד לנפשותיכם. "הרבה דברים אסרו חכמים מפני שיש בהם
סכנת נפשות. וכל העובר עליהן ואומר: הריני מסכן בעצמי ומה לאחרים עלי בכך
או איני מקפיד בכך, מכין אותו מכת מרדות" (רמב"ם, הלכות רוצח ושמירת נפש
יא ה).
ש: במדינות מודרניות יש חירות הפרט לעשות כרצונו אם לחסן.
ת: א. החירות האמיתית היא לשמור תורה ומצוות. ב. אין לו חרות לסכן ילדיו
שיחלו בגלל שלא חיסן אותם. ג. הוא גם מסכן אחרים שעלולים להידבק ממנו,
ויש בזה משום דין רודף.
Q: Is one obligated to vaccinate?
A: Yes. 'For your own sake be careful' (Devarim 4:15). Many things
were forbidden by the sages since they caused mortal danger. Anyone
who violates this and says 'I am putting myself in danger, what do
other care?' or 'I will be careful' We give him [rabbinic] lashes (Rambam).
Q: In modern countries, we have some freedom to do as we wish with
vaccinations.
A: 1) Real freedom is to guard the Torah and mitzvot. 2) One has no
freedom to endanger one's children that they should become ill because he did not vaccinate them. 3)
he is also endangering others that may be infected by him, and there is in this
the law of rodef (the pursuer).
Would the patient have the status of a rodef (pursuer) whom one is obligated to prevent from committing a murder, by inflicting an injury upon the pursuer?
You ask for an ill person who is carrier of the virus? The Shut clearly does not address a problem of Rodef. But an ill contagious person can be considered as Rodef. e.g one is AIDS carrier an has intercourse with can be viewed as attempting to kill it and may be Rodef.