Combination Antiretroviral Therapy (cART) consists of a cocktail of drugs administered to HIV-infected patients that can suppress the amount of HIV in the patient's blood plasma to an undetectable level. Our previous work has suggested that some HIV-infected patients, despite being placed on cART, can still have ongoing viral replication occurring in self-sustaining inflamed lymph node follicle sanctuary sites. Spatial models of the putative sites show that inflammation is a necessary condition for ongoing HIV replication. In this study, we model the hypothesis that ongoing HIV replication may provide a sufficiently strong pro-inflammatory signal to maintain inflammation levels consistent with continued HIV replication. A system of ordinary differential equations integrated with a reactive-diffusion system is used to model the HIV dynamics and the diameter of a lymph node follicle as a function of time and external influence. The estimates of the parameters in our model come from prior data when available. The results of our study show that these dynamics have two stable steady-state solutions, one with low inflammation and no ongoing HIV replication in the site, and one with high inflammation and high levels of ongoing HIV replication in the site. We furthermore show that the system can transition between the two outcomes in response to a transient exogenous addition of pro-inflammatory signaling, consistent with the antigenic stimulus of a secondary infection. The spatial isolation of the sites results in a low viral load in the blood plasma for both conditions.