Adherence to antiretroviral HIV drugs: how many doses can you miss before resistance emerges?

Abstract

The question of determining how many doses may be skipped before HIV treatment response is adversely affected by the emergence of drug-resistance is addressed. Impulsive differential equations are used to develop a prescription to minimize the emergence of drug-resistance for protease-sparing regimens. A threshold for the maximal number of missable doses is determined. If the number of missed doses is below this threshold, then resistance levels are negligible and dissipate quickly, assuming perfect adherence subsequently. If the number of missed doses exceeds this threshold, even for 24h, resistance levels are extremely high and will not dissipate for weeks, even assuming perfect adherence subsequently. After this interruption, the minimum number of successive doses that should be taken is determined. Estimates are provided for all protease-sparing drugs approved by the US Food and Drug Administration. Estimates for the basic reproductive ratios for the wild-type and mutant strains of the virus are also calculated, for a long-term average fractional degree of adherence. There are regions within this fraction of adherence where the outcome is not predictable and may depend on a patient's entire history of drug-taking.

Figure 1

Example dose–effect curves for the wild-type (solid curve), 10-fold resistant (dashed curve) and 50-fold resistant (dot–dashed curve) viral strains. Note that the x-axis is on a logarithmic scale. When drug concentration R is less than R₁ (region 1), the probability that a T cell absorbs sufficient drug to block infection is negligible for all strains. Between thresholds $R_1<R<R_2^{(10)}$ (region 2), only the wild-type strain has a non-negligible probability of being blocked by the drug. For $R>R_2^{(10)}$ (region 3) both the wild-type and 10-fold resistant strains have non-negligible probability of being blocked by the drug (the dose–effect curves in these regimes are much closer to linear than suggested by this semi-log plot). The threshold $R_2^{(50)}$ represents the equivalent threshold for the 50-fold resistant viral strain. IC₅₀ values for Abacavir were used in this example.

Figure 2

Viral load and drug levels for therapy interruption. Therapy was allowed to reach the impulsive periodic orbit before being interrupted. Data used is for the drug Didanosine. (a, top) Viral load for the wild-type (solid line) and the mutant (dashed line) strains. (b, top) Drug levels on a log scale. (a) Eleven doses were missed, allowing drug levels to enter region 2 briefly before subsequent doses were taken. In this case, the emergence of the mutant strain is negligible and diminishes quickly. (b) Thirteen doses were missed, allowing drug levels to remain in region 2 for 24 h before subsequent doses were taken. In this case, the resistant strain reach almost 60 000 μmol l⁻¹ and was not eliminated for some weeks. Data used were n_I=262.5 day⁻¹, ω=0.7, r_I=0.01 day⁻¹, r_Y=0.005 day⁻¹, d_V=3 day⁻¹, d_S=0.1 day⁻¹, d_I=0.5 day⁻¹, r_P=r_R=r_Q=80 μM⁻¹ day⁻¹, λ=180 cells μl⁻¹ day⁻¹, m_RI=m_RY=log(2) day⁻¹, in addition to data found in table 1.

Figure 3

Upper and lower bounds for each strain of the virus. In the absence of drugs (p=0), the wild-type virus dominates. As the fraction of adherence increases, the mutant may dominate. For a sufficiently high fraction, both strains have a basic reproductive ratio of less than 1 and hence the virus is controlled. However, there are regions where the upper and lower bounds of one strain interfere with the bounds of the other strain. In these cases, it is not possible to predict which strain will dominate and the outcome will depend on the patient's entire history of drug-taking.

Figure 4

The sensitivity of results to the history of drug-taking. The solid lines represent T cells infected with the wild-type strain of the virus and the dashed lines represent T cells infected with the mutant strain. (a) In this case the wild-type strain dominates. Data used was n_I=262.5, ω=0.8, r_I=0.02, r_Y=0.01, d_V=3, d_S=0.1, d_I=0.5, r_R=40, r_Q=10.4, d_R=log(2)/2, λ=180, m_RI=24 log(2)/8, m_RY=24 log(2)/8, R₁=3, R₂=6, IC₅₀ (wild-type)=0.053, IC₅₀ (mutant)=0.53, β_T=0.0014, β_Y=0.001, τ=4, Rⁱ=4, p=0.255. (b) The same data was used and the same program run. However, in this case, the mutant strain dominates. The difference in results is due to the history of drug taking, modelled as a random variable drawn from a uniform distribution. Small changes in the random variable can have a dramatic impact on the outcome.