後天免疫缺乏症候群（AIDS）是由人類免疫缺乏病毒（HIV）感染引起。該病毒會逐漸干擾宿主的免疫系統，最終導致其衰竭。儘管高效抗逆轉錄病毒療法能夠抑制宿主體內的病毒，但通常難以徹底清除。因此，專家將永久抑制病毒複製或維持患者的長期緩解狀態視為一種替代治療目標，即「功能性治癒」。 Bonhoffer、Adams 及其合作者提出了一個數學模型來描述功能性治癒現象，隨後 Chen對該模型進行了定性分析。他指出，只有當患者的免疫刺激能力在感染細胞數量低於某一閾值時便開始減弱，才能觀察到功能性治癒現象。然而，在 Chen 的研究中，無論免疫力強弱，只要生物系統具備至少兩個穩定且具有生物學意義的平衡態，即被視為可實現功能性治癒。在一項相關的大規模研究對象研究中，部分參與者因免疫刺激不足導致病毒反彈風險較高而不得不退出研究；這清楚地表明，由感染細胞激發的患者免疫能力在實現功能性治癒的過程中也起著至關重要的作用。
本研究以「精英控制者」（elite controllers）的病毒量作為低病毒量狀態的參考基準。我們推導出了免疫刺激強度的下限與上限：若患者的免疫刺激強度超過該下限，則可望實現低病毒量狀態；反之，若其強度低於該上限，則無法維持低病毒量狀態。從臨床角度來看，這些結果是 Chen 等人研究的補充，有助於判斷哪些患者適合將低病毒量狀態作為治療終點（即實現功能性治癒），哪些則不適合。因此，這些標準對於 HIV 感染的治療具有重要意義。

Acquired immunodeficiency syndrome (AIDS) is caused by the infection of Human immunodeficiency virus (HIV). The viruses may progressively interfere with hosts' immune systems and lead to their failure. Though highly active antiretroviral therapy may suppress the within-host viruses, it is usually difficult to eliminate them completely. Specialists therefore consider to permanently suppress the virus replication or to maintain patients' long-term remission state as an alternative treatment goal, called a functional cure. Bonhoeffer, Adams and their collaborators propose a mathematical model to describe the phenomenon of a functional cure. Chen later provides a qualitative analysis to their model. He shows that the phenomenon of a functional cure can be observed only if the capability of patients' immune stimulation starts to attenuate when the number of infected cells is below a threshold. However, regardless of the strength of immunity, a biological system is viewed to be functional curable in Chen's work when it possesses at least two stable and biological meaningful equilibrium states. In a related large-scale cohort study, some participants have to drop out from the study for greater risk of viral rebound due to insufficient immune stimulation. It clearly indicates that the capability of patients' immunity stimulated by infected cells also plays a crucial role in achieving a functional cure.
In this study, elite controllers' viral load serves as a reference level of low-viral-load status. We derive a lower and a upper bounds on the strength of immune stimulation. If a patient's strength of immune stimulation is greater than the lower bound, a low-viral-load state is achievable. Conversely, if a patient's strength of immune stimulation is less than the upper bound, a sustained low-viral-load state is not possible. From clinical viewpoints, the results provide complementary criteria to Chen's work, which may be used to identify which patients may and may not use the low-viral-load state as a treatment endpoint as a functional cure case. Therefore, the criteria are important in the treatment of HIV infection.

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