A theoretical examination of the relative importance of evolution management and drug development for managing resistance

Abstract

Drug resistance is a serious public health problem that threatens to thwart our ability to treat many infectious diseases. Repeatedly, the introduction of new drugs has been followed by the evolution of resistance. In principle, there are two complementary ways to address this problem: (i) enhancing drug development and (ii) slowing the evolution of drug resistance through evolutionary management. Although these two strategies are not mutually exclusive, it is nevertheless worthwhile considering whether one might be inherently more effective than the other. We present a simple mathematical model that explores how interventions aimed at these two approaches affect the availability of effective drugs. Our results identify an interesting feature of evolution management that, all else equal, tends to make it more effective than enhancing drug development. Thus, although enhancing drug development will necessarily be a central part of addressing the problem of resistance, our results lend support to the idea that evolution management is probably a very significant component of the solution as well.

Keywords: chemotherapy; drug resistance; pharmaceuticals; treatment strategies.

Figure 1.

Timeline for antimalarials and antibiotics [–14]. The times of drug introduction and the subsequent evolution of resistance are indicated by the ends of the bars. The faded region is meant to show that the first observation of resistance does not absolutely equate with complete loss of treatment efficacy. (Online version in colour.)

Figure 2.

Schematic of the model. A timeline defining the time to failure, T, and drug availability, ρ. ‘Effective treatment available’ means that there is at least one effective drug in the portfolio. (Online version in colour.)

Figure 3.

Effects on time to failure from enhancing drug development and slowing evolution with estimates from antimalarial data (see the electronic supplementary material). (a) The effect on the time to failure density f_T(t) when the average drug inter-arrival time is reduced by 2 years (ΔE[D]) and the average drug lifespan is extended by 2 years (ΔE[L]) compared with baseline conditions (E[L] = 5 years, E[D] = 8.3 years). (b) The change in expected time to failure (E[T]) resulting from additive perturbations in E[L] and E[D] plotted for varying current drug availability (ρ). (Online version in colour.)

Figure 4.

Histogram of time to failure from numerical simulations of a gamma-distributed drug inter-arrival time, D, and drug lifespan, L. Baseline conditions are given as k = 2, α = 1/5, β = 1/2. (a) The effect on time to failure from an additive change decreasing E[D] by 2 years (k = 2, α = 1/4; ΔE[D]) or increasing E[L] by 2 years (k = 2, β = 1/3; ΔE[L]). (b) The effect on time to failure from a multiplicative change halving E[D] (k = 2, α = 2/5; ΔE[D]) or doubling E[L] (k = 2, β = 1/4; ΔE[L]). The last bar of the histogram represents all remaining values of time to failure in the simulation. Vertical lines represent average length of time to failure for baseline conditions (grey solid line) and perturbations decreasing E[D] (black dotted line) or increasing E[L] (black solid line).

Figure 5.

Histogram of time to failure from numerical simulations of a variable rate of drug development as inversely related to the size of the drug portfolio. Baseline conditions are given as α = 1/10, β = 1/4. (a) The effect on time to failure from an additive change decreasing E[D] by 2 years (α = 1/8; ΔE[D]) or increasing E[L] by 2 years (β = 1/6; ΔE[L]). (b) The effect on time to failure from a multiplicative change halving E[D] (α = 1/5; ΔE[D]) or doubling E[L] (β = 1/8; ΔE[L]). The same ‘fast rate’ of drug development (θ = 1/3) was used in the simulations when there were two or fewer drugs remaining in the drug portfolio at the time of the last drug arrival. The last bar of the histogram represents all remaining values of time to failure in the simulation. Vertical lines represent average length of time to failure for baseline conditions (grey solid line) and perturbations decreasing E[D] (black dotted line) or increasing E[L] (black solid line).