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One of the most difficult challenges in cancer therapy is the emergence of drug resistance within tumors. Sometimes drug resistance can emerge as the result of mutations and Darwinian selection. However, recently another phenomenon has been discovered, in which tumor cells switch back and forth between drug-sensitive and pre-resistant states. Upon exposure to the drug, sensitive cells die off, and pre-resistant cells become locked in to a state of permanent drug resistance. In this paper, we explore the implications of this transient state switching for therapy scheduling. We propose a model to describe the phenomenon and estimate parameters from experimental melanoma data. We then compare the performance of continuous and alternating drug schedules, and use sensitivity analysis to explore how different conditions affect the efficacy of each schedule. We find that for our estimated parameters, a continuous therapy schedule is optimal. However we also find that an alternating schedule can be optimal for other, hypothetical parameter sets, depending on the difference in growth rate between pre- drug and post-drug cells, the delay between exposure to the drug and emergence of resistance, and the rate at which pre-resistant cells become resistant relative to the rate at which they switch back to the sensitive state.

Lymph nodes (LNs) may serve as a sanctuary site for HIV viruses due to the heterogeneous distribution of the antiretrovirals (ARVs) inside the LNs. There is an ongoing debate whether this represents ongoing cycles of viral replication in the LNs or merely residual virus production by latently infected cells. Previous work has claimed that the measured levels of genetic variation in proviruses sampled from the blood were inconsistent with ongoing replication. However, it is not clear what rate of variation is consistent with ongoing replication in small sanctuary sites. In this study, we used a spherically symmetric compartmental ODE model to track the HIV viral dynamics in the LN and predict the contribution of ongoing replication within the LN to the whole-body proviral pool in an ARV-suppressed patient. This model tracks the reaction-diffusion dynamics of uninfected, actively infected, and latently infected T-cells as well as free virus within the LN parenchyma and the blood, and distinguishes between latently infected cells created before ARV therapy and during ARV therapy. We simulated suppressive therapy beginning in year 5 post-infection. Each LN sanctuary site had a volume of 1 ml, and we considered cases of 1ml, 30ml, and 250ml total volume, which represent a single active sanctuary site, moderate systemic involvement, and involvement of the total lymphoid tissue. Viral load in the blood rapidly dropped and remained below the limit of detection in all cases but remained high in the LN sanctuary sites. Novel latent cells increased systemically over time but very slowly, taking between 25 and 50 years to reach 5% of the total latent pool, depending on the volume of lymphoid tissue involvement. Putative sanctuary sites in LNs are limited in volume and produce novel latent cells slowly. Assays to detect genetic drift due to such sites would require very deep sequencing if sampling only from the blood. Previous studies showing a lack of genetic drift are consistent with the expected contribution of ongoing replication in lymph node sanctuary sites.