Results and Discussion

Using our four evaluation criteria, we compared a single, two, and three first-line therapies over a randomly sampled set P of 5,000 parameter combinations spanning a range over the basic reproductive number (1.1 ≤ R₀ ≤ 100; see ref. 29), de novo mutation rate (10⁻⁶ ≤ σ_i ≤ 10⁻¹), fraction of clinical cases that are treated (0.2 ≤ f ≤ 1.0), the cost of resistance (0.05 ≤ s_i ≤ 0.20; see ref. 34), and the parasite population's inbreeding coefficient (0.0 ≤ F ≤ 1.0); drug-specific parameters are subscripted by i. Using three first-line therapies minimized failed treatments and overall clinical disease for 92.6% of the parameter combinations tested; this means that, without any knowledge of mutation rates or costs of resistance for particular resistant phenotypes, the odds are 14:1 that we would obtain a better clinical outcome by simply treating one-third of the population with drug 1, one-third with drug 2, and the final one-third with drug 3. When the σ_i are equal, an MFT strategy with three therapies is optimal under all four criteria 99.7% of the time (a single first-line therapy could be better in the comparisons on P when σ₁ is low but σ₂ and σ₃ are high). See Fig. 2 for a typical picture of the dynamics of resistance evolution under single and multiple therapies.

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Fig. 2.

Differences between single and multiple first-line therapies. Here, R₀ = 3, s_i = 0.1, σ_i = 10⁻⁵, f = 0.6, and F = 1.0. System is started at its endemic equilibrium, and treatment is begun at time 0. (Top) Percentage of hosts undergoing a clinical episode of malaria (red line) and percentage of all hosts that are infected (black line); red axis labels correspond to red line. (Middle) Frequency of single- (thin black line), double- (medium black line), and triple-resistant strains (thick black line); a thicker line indicates more resistance. The magenta lines in the second row indicate the fraction of incident treated cases that receive a failing treatment. (Bottom) ϕ the fraction of infections that are currently in a clinical state and possibly being treated by drugs. As in a classic resistance epidemic, a quick initial decrease in disease prevalence and clinical cases is followed by a period of low prevalence, which is followed by a period when prevalence creeps back up almost to pretreatment levels; disease prevalence will not attain its full pretreatment level as long as there is some cost to resistance. The major difference among the treatment strategies is the pattern of fixation in the middle row. Here and in the model in general, resistance evolution begins later and occurs more slowly when more first-line therapies are used.

In attempting to understand resistance evolution in a multidrug context, we must first understand the features of our system that have the most important effects of drug-resistance evolution in general.

One of the key epidemiological variables that drives resistance evolution in malaria is the fraction ϕ of infected hosts that have clinical malaria (Fig. 2 Bottom), because only hosts with symptoms receive drug treatment; the fraction ϕ is a measure of the selection pressure on the parasite population to evolve resistance. When ϕ is low, the high level of asymptomatic hosts causes natural selection to work against the resistant phenotypes, because competition between sensitive and resistant parasites occurs in the absence of drugs among asymptomatic hosts; in addition, when ϕ is low, there is little selection pressure for resistance because of the low probability that an individual parasite will encounter a drug. The effect of a low fraction of hosts with clinical disease was hypothesized to explain the regional absence of the dhfr Leu-164 mutation, which confers antifolate resistance (35).

The influence of malaria transmission intensity on ϕ is one of two key relationships that drives the dynamics of our model. As R₀ increases, ϕ decreases because of an increased level of host immunity (Fig. 3Right), which may help explain why resistance is more likely to arise in low transmission areas (36–38). The second relationship is that between R₀ and the equilibrium number of clinical cases Ĉ (Fig. 3 Left); Ĉ is maximized at an intermediate R₀, because Ĉ increases with higher prevalence but decreases with higher immunity, both of which increase with R₀. This relationship between the clinical burden of malaria and the transmission intensity is in general agreement with field data (28, 39).

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Fig. 3.

In these graphs, s_i = 0.1, σ_i = 10⁻⁵, F = 1.0, and the model was run for 20 years; f = 0.6 for the solid lines and f = 0.0 for the dashed lines. Left shows the clinical outcomes DPC (black lines) and NTF (red line) as a function of R₀. Right shows the time to emergence (T_.05) and time to fixation (T_.95) as a function of R₀; the dashed red line shows the equilibrium value of ϕ when there is no treatment or resistance. Red lines correspond to red axis labels. For higher R₀, ϕ is lower; thus, there is less selection pressure favoring the resistants and their time to emergence/fixation is longer. This relationship breaks down for very low R₀ where the parasites' generation time is long and evolution is slow. The inner axis labels correspond to NTF (red numbers) and years until resistance reaches 5% or 95% (black numbers).

Increasing R₀ has two basic effects on resistance evolution: it shortens the parasites' generation time, thus making any type of evolution faster, and it lowers ϕ weakening the selection pressure for resistance. Fig. 3 Right shows how these two opposing effects balance. In general, decreasing R₀ when it is large will lead to earlier treatment failure and resistance emergence, as suggested elsewhere (40). In our model, this behavior is explained by an immunogenic mechanism (as opposed to a recombination mechanism in other models), whereby lowering R₀ decreases population-wide immunity and increases the proportion of clinical cases among infecteds (ϕ). However, any increased risk of resistance with lower R₀ needs to be balanced against the benefit of reduced transmission. As Fig. 3 Left shows, reducing transmission below R₀ = 200 yields a reduction in clinical cases and failed treatments even when resistance evolution is taken into account. Note that reducing R₀ from 5,000 to 200 causes an increase in clinical cases and failed treatments; this occurs in our model because (i) lowering R₀ in this range reduces immunity but has little effect on prevalence, and (ii) for the 20-year timeframe we have chosen, resistance barely emerges for these extremely high R₀ values, and the clinical outcomes for these situations can be compared in the absence of resistance evolution.

In addition to the transmission intensity described by R₀, a second influential parameter in our model is the fraction f of clinical cases that are treated by drugs. Depending on the price of treatment and the local population's access to clinics and pharmacies, f will vary greatly from region to region. When more cases are treated, resistance and treatment failure arrive more quickly (see Fig. 4), and we obtain the standard result that treating the fewest patients results in the least resistance.

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Fig. 4.

In these graphs, R₀ = 3, σ_i = 10⁻⁵, F = 1.0, and the model was run for 20 years. The black line corresponds to MFT with three drugs, the medium gray line to MFT with two drugs, and the light gray line to a single first-line therapy. Note that using more therapies has a bigger advantage when the cost of resistance is higher. Fig. S2 in SI Appendix shows the bottom row without discounting.

However, when considering the clinical outcomes DPC and NTF, it is no longer optimal to treat the fewest patients. Fig. 4 Lower shows that it is optimal to treat all patients when the cost of resistance is high (s > 0.2) and approximately one-half of patients when the cost of resistance is low (s < 0.2); the optimal treatment fraction f* is sensitive to the length of the outlook period. Consider Fig. 4 where s = 0.1. Here, when the treatment fraction is low (f < 0.2), resistance does not emerge, and NTF depends only on the fraction of cases treated and is unaffected by treatment strategy; if there is no resistance, there is no benefit to using MFT over a single first-line therapy or vice versa. For f > 0.4, it becomes clear that MFT strategies result in fewer failed treatments (and fewer clinical cases; data not shown). When everyone receives treatment, using three first-line therapies results in a 49% reduction in failed treatments (and clinical cases) compared with a single first-line therapy. Note that, as we move from a single first-line therapy to two and three first-line therapies, the optimal treatment fraction f* moves rightward on the graph, which means that, as we add more first-line therapies into our treatment strategy, we will be able to treat a higher proportion of clinical cases without “overtreating” and driving the evolution of resistance too strongly.

In comparing the useful therapeutic lives of treatment strategies in Fig. 4 Upper, it becomes apparent that MFT strategies have longer UTLs, because they use more drugs. A more relevant comparison measures the UTL per drug rather than the UTL of the treatment strategy as a whole; at s = 0.1 and f = 0.6, for example, the per-drug UTL for a strategy of three first-line therapies is 3.32 years (one-third of the 9.95-year UTL of an MFT strategy with three therapies), whereas the per-drug UTL of a single first-line therapy is 3.54 years. Thus, it would seem optimal to use our single first-line therapies in sequence for a total UTL of 3.54 × 3 = 10.62 years. However, this simple calculation obscures the fact that when n drug therapies are used in sequence, their total UTL cannot be calculated by summing the UTLs of the individual therapies. In our example, using the drugs in sequence, the UTL of the first therapy would be 3.54 years, the second therapy 2.92 years, and the third therapy 2.83 years, for a total UTL of 9.29 years.

When using therapies in sequence, there is a particular aspect of parasite ecology that reduces the UTL of each subsequent therapy, even when there is no cross-resistance among the drugs. During the first treatment period, resistant parasites emerge and spread by competing for hosts with drug-sensitive wild-type parasites. During the second treatment period, parasites resistant to therapy 2 compete against a mixture of wild types and resistants left over from the previous treatment period, hence they emerge into a less competitive environment where they increase in frequency more quickly and cause high levels of treatment failure more rapidly. During the third treatment period, parasites resistant to therapy 3 emerge into an even less competitive environment than was present at the beginning of period 2, and treatment failure arrives even more quickly. From the perspective of parasite ecology, each resistant strain degrades the mean fitness of the parasite population (see Fig. 5) and constructs a niche in which it is easier for subsequent resistant strains to invade (41, 42). This fundamental ecological interaction among drug-resistant strains in a parasite population is a key reason why MFT strategies outperform drug-cycling strategies.

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Fig. 5.

Differences between MFT and cycling strategies; “adaptive cycling” means switching drugs at 10% treatment failure with a 1-year switch delay. Here, R₀ = 3, s_i = 0.1, σ_i = 10⁻⁵, f = 0.6, and F = 1.0. Top is as in Fig. 2. Middle tracks the total level of resistance in the parasite population (triple resistants count as fully resistant, double resistants count as 2/3 resistant, and so on); light gray lines show the “total resistance” line from the other two columns for comparison. Bottom tracks the parasites population's mean fitness, calculated in the absence of drug treatment, with a fitness of one assigned to drug-sensitive parasites; the light gray lines show the mean-fitness line from the other two columns for comparison.

In fact, compared with MFT policies, cycling policies have two fundamental disadvantages that can be understood in the light of evolution. Organisms evolve in response to environmental pressures, and cycling policies are more likely to create environments favorable to drug-resistant malaria in two ways. First, cycling lowers the mean fitness of the parasite population more quickly than MFT, thereby creating a less competitive environment that is more conducive to the invasion and spread of new resistant types. Second, from the perspective of the pathogen, cycling creates a less temporally variable environment that makes resistance evolution easier in the long term, as described by Bergstrom et al. (16). These are two distinct ecological-evolutionary effects: at the beginning of the second cycling period, newly emerged resistant parasites can invade and spread easily, because (i) they can count on a temporally invariable environment for some time; and (ii) they encounter weak competition, the mean fitness of the parasite population having been degraded in the previous cycling period.

To compare the health outcomes of cycling policies and MFT strategies, we ran our model for 20 years over the parameter set P and compared MFT with 10 variants of cycling policies (see SI Appendix); one such cycling strategy approximates the status quo pattern of switching drugs and is described here. For 75.1% of parameter combinations, MFT outperformed a cycling policy that switched first-line therapies at 10% treatment failure with a 1-year switch delay. Quantitatively, the NTF values under both strategies were quite close, within 5% of each other for 64.4% of parameter values. For 20.9% of parameter values, MFT enjoyed a 5–10% advantage, and for 9.5% of parameter values, MFT enjoyed a >10% advantage. For 3.6% of parameter values, MFT had a 5–10% disadvantage, and for 1.6% of parameter values, a >10% disadvantage. The most noticeable quantitative benefit of using multiple first-line therapies over cycling strategies was the increased delay in time to resistance emergence and treatment failure, which ranged from 2- to 4-fold (for equal σ_i). The longest delay in resistance emergence is achieved under an MFT policy with an even drug distribution, but some diversity is better than no diversity (see Fig. 6). For example, using three drugs in a 50/25/25 ratio almost doubles the time until resistance reaches 5%, compared with a single first-line therapy. Note in Fig. 6 that time to emergence is determined primarily by the frequency of the most frequently used drug.

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Fig. 6.

Results of 1,000 simulations, with R₀ = 3, σ_i = 10⁻⁵, f = 0.6, s_i = 0.1, and F = 1.0, where the drug distribution of three drugs was chosen randomly. Certain drug distributions are highlighted in Upper. Lower shows the same simulations plotted against the frequency of the most used drug. Drug diversity is measured as − p_i Σ log p_i, where p_i is frequency of use of drug i. The 60/20/20 strategy has the same diversity measure as the 45/45/10 strategy, but resistance arrives sooner under the former because one drug has such a high frequency of use.

In addition to the clinical and drug lifespan benefits of deploying multiple first-line therapies, MFT strategies may enjoy some operational advantages, because they do not incur the economic costs involved in switching therapies and maintaining a high level of surveillance (43). Moreover, cycling strategies are sensitive to the length of the cycling period and implementation delay (Fig. S1 in SI Appendix), and they may incur a higher level of treatment failure than noted in the modeling if there are delays in phasing out a failed first-line therapy. Note that the MFT strategy analyzed in this study is a nonadaptive strategy. In the context of the same surveillance networks available to cycling strategies, the clinical benefits of an adaptive MFT over cycling strategies could be much greater.

An important challenge in applying this type of theoretical work is that we will usually not know the de novo mutation rate to resistant strains (σ_i) or the resistant types' fitness cost of resistance (s_i), and we may have to rely on our best judgment to make a conservative but effective recommendation. Moreover, not all factors in malaria control—imperfect compliance with treatment regimens, delays in implementing policy switches, recommended use of second-line drugs, likely use of cheap but ineffective drugs such as chloroquine, varying levels of surveillance available to detect resistance or treatment failure–have been included in our model; model-influenced regional recommendations should take into account regional variations in drug-use patterns and malaria epidemiology.

The pharmacokinetic/pharmacodynamic (PK/PD) aspect of malaria treatment has also been omitted from the model presented here. In reality, some drugs remain in the system for days, whereas others linger for weeks. When designing MFT strategies, drugs with longer half-lives should be used more sparingly to distribute the drugs as uniformly as possible in the parasites' environment; this way, the parasite has the lowest probability of encountering the same drug twice in a row. More importantly, the increasing use of ACTs makes it critical to analyze the effects of mismatched half-lives in combination therapies (4). The short half-life of the artemisinin component in ACTs may make it possible to use multiple ACTs in an MFT strategy, even though each therapy contains an artemisinin derivative. These suggestions should be evaluated with detailed within-host PK/PD modeling.

Our results suggest an important general principle for malaria treatment that holds across a broad parameter range and in other model formulations: compared with a single first-line therapy, multiple first-line therapies reduce total clinical cases and failed treatments, significantly delay resistance emergence and treatment failure, and slow resistance evolution once resistance emerges. Extrapolating our conclusions to use of multiple ACTs may yield even stronger results. Because resistance to the nonartemisinin partner drugs typically arises and spreads quite easily, the evolution of artemisinin resistance is likely to be followed in rapid succession by the evolution of resistance to all ACTs. Thus, in theory, the optimal strategy would be to deploy all available ACTs to reduce selection pressure on the partner drugs; protecting the partner drugs may extend the useful therapeutic lives of all ACTs. As new drugs are deployed, and as we are able to assess the levels of use in different countries, we should look toward identifying locations with drug-use patterns that would allow us to quantify the population-wide benefits of using multiple first-line therapies to treat malaria infections.