Modeling within-host effects of drugs on Plasmodium falciparum transmission and prospects for malaria elimination

Abstract

Achieving a theoretical foundation for malaria elimination will require a detailed understanding of the quantitative relationships between patient treatment-seeking behavior, treatment coverage, and the effects of curative therapies that also block Plasmodium parasite transmission to mosquito vectors. Here, we report a mechanistic, within-host mathematical model that uses pharmacokinetic (PK) and pharmacodynamic (PD) data to simulate the effects of artemisinin-based combination therapies (ACTs) on Plasmodium falciparum transmission. To contextualize this model, we created a set of global maps of the fold reductions that would be necessary to reduce the malaria R C (i.e. its basic reproductive number under control) to below 1 and thus interrupt transmission. This modeling was applied to low-transmission settings, defined as having a R 0<10 based on 2010 data. Our modeling predicts that treating 93-98% of symptomatic infections with an ACT within five days of fever onset would interrupt malaria transmission for ∼91% of the at-risk population of Southeast Asia and ∼74% of the global at-risk population, and lead these populations towards malaria elimination. This level of treatment coverage corresponds to an estimated 81-85% of all infected individuals in these settings. At this coverage level with ACTs, the addition of the gametocytocidal agent primaquine affords no major gains in transmission reduction. Indeed, we estimate that it would require switching ∼180 people from ACTs to ACTs plus primaquine to achieve the same transmission reduction as switching a single individual from untreated to treated with ACTs. Our model thus predicts that the addition of gametocytocidal drugs to treatment regimens provides very small population-wide benefits and that the focus of control efforts in Southeast Asia should be on increasing prompt ACT coverage. Prospects for elimination in much of Sub-Saharan Africa appear far less favorable currently, due to high rates of infection and less frequent and less rapid treatment.

Figure 1. Illustration of asexual, gametocyte, and human-to-mosquito infectivity model outputs.

The P. falciparum infection model was run six times to simulate three untreated individuals and another three treated with a hypothetical antimalarial. (A) Individual log₁₀ asexual blood stage parasitemias as a function of the number of days post emergence of parasites from the liver into the bloodstream. The inset depicts the first 50 days of infection; the triangles above indicate the first day of fever. In this example, three individuals were assumed to seek treatment a variable number of days after the onset of fever. The black line illustrates the approximate level of detectability by microscopy (∼10 parasitized red blood cells/µL). (B) Daily gametocytemias (sexual stage parasitemias) of the same six individuals. The hypothetical drug treatment was assumed to target early stages of gametocyte development more strongly than later stages. (C) Estimated probability of human-to-mosquito parasite transmission for treated (T) vs. untreated (U) individuals. Areas under the infectivity curves (AUIC) are equivalent to the number of fully infectious days. Net infectivity simulations yielded 1.0, 2.4, and 6.3 fully infectious days for treated (T) and 67.7, 6.5, and 28.6 days for untreated (U) individuals, respectively. The model outputs for untreated patients shown in panels A–C were previously reported in and are shown to compare with our modeling of treated patients.

Figure 2. Modeled pharmacokinetic and pharmacodynamic profiles of lumefantrine (LMF), mefloquine (MFQ) and chloroquine (CQ) against asexual blood stage parasites.

(A) Modeled plasma concentrations of LMF. The wide variability in concentrations reflects individual differences in absorption and clearance. The black line indicates population median drug concentrations. (B) Estimated parasite reduction ratios (PRR) over a 48 hr blood stage cycle for LMF as a function of time post onset of treatment. PRR is the fold reduction in asexual parasite densities due to drug action. PRR values were calculated from drug concentrations using a Hill function transformation. Each curve illustrates the PRR over time for a simulated individual; the black line illustrates the PRR for population median drug concentrations. (C–D) Plasma concentrations for MFQ and corresponding activities against asexual blood stage parasites. Drug concentrations reflect data from both plasma and whole blood studies. (E–F) Modeled plasma concentrations of both CQ and its metabolite monodesethyl-chloroquine (mdCQ) are shown in turquoise; PRR against asexual blood stages are in purple. All drug concentrations are in µg/ml.

Figure 3. Modeled post-treatment gametocyte prevalence and treatment effect sizes.

Treated and untreated malaria infections were simulated using our within-host malaria infection model. Modeled treatments differed according to the assumed level of gametocyte killing. Model treatment was assumed to start 5 days after the first onset of fever; all model outputs represent the mean of 1,000 runs. (A) The number of individuals predicted to be gametocyte positive by microscopy (threshold 5 gametocytes per µL) was tracked over time. Untreated model outputs are shown in black. Treatment was assumed to be a combination therapy with a short-lived component (active for 3 days) and a longer-lived component with the pharmacokinetic profile of mefloquine. The green line illustrates the effects of treatment assuming no gametocytocidal activity (‘Schizonticide’). The assumed gametocytocidal activity of each component was progressively increased and compared to field data to generate the rest of the curves, each labeled with their corresponding antimalarial (chloroquine, CQ; artemisinin-based combination therapy, ACT; primaquine, PQ). The curves labeled ‘ACT+PQ’ assumed the presence of a second short-lived partner that strongly killed both early and late stage gametocytes; the number indicates the day on which the simulated PQ component was administered. (B) Total effect sizes (fold-reductions in transmission) for each of the modeled drug parameterizations as a function of treatment coverage, including the oocidal effects of drugs, assuming net untreated infectivity of 30.5 days, and using the ‘Jeffery-Eyles’ density-to-infectivity parameterization for treated individuals (Table 2; [23]). Each drug class is depicted in a different color. The variation in each class is due to the different simulated levels of gametocytocidal activity for that drug type. Each line within a given drug class represents the result of 1,000 simulation runs; the black lines indicate the mean effect sizes for each class of drug. The horizontal line illustrates a six-fold reduction in transmission. The dotted vertical lines indicate the levels of treatment coverage needed to reach a six-fold reduction in total human-to-mosquito transmission for each drug class. The y-axis is in log-scale.

Figure 4. Worldwide map of the predicted probabilities that a five-fold effect size will interrupt malaria transmission.

This map shows the predicted probabilities that a five-fold reduction in transmission (‘five-fold effect size’) would interrupt malaria transmission over a given pixel. Map pixel size is 5 km². In order to interrupt malaria transmission in a given area, the basic reproductive number for malaria under control (R_C) needs to be reduced below 1. Probabilities for each pixel are calculated according to Bayesian posterior estimates of uncertainty . Probabilities have been binned into six categories for clarity. Areas with high transmission (defined as at last a 50% probability of R₀>10) are masked because our model results are applicable to regions of relatively lower transmission. Most of Sub-Saharan Africa is masked because of the very intense transmission. However, most of Sahelian Africa, as well as East Africa, parts of Southern Africa, most of India, as well as most of Southeast Asia and essentially all of South America have high probabilities of interruption at this control level. Note that local conditions (within a given pixel) may be more or less favorable to transmission than the per-pixel averages shown here, and so these maps are most applicable for regional or country-level planning, rather than local-level control efforts. Microenvironments or ‘hotspots’ might require additional interventions and/or greater treatment coverage than the per-pixel average . Data collection sites used to construct the maps are reported in . A partial database of the actual site locations and the measured levels of malaria endemicity can be found on the Malaria Atlas Project (MAP) website: www.map.ox.ac.uk.

Figure 5. Map of the predicted probabilities that five-fold reductions will interrupt transmission in Southeast Asia.

The predicted probabilities that a control effort with a five-fold reduction would interrupt transmission are shown for Southeast Asia, using the same masking of high transmission areas (R₀>10) and mapping assumptions as for Figure 4. Areas that appear to be uniform may have small-scale heterogeneities in transmission that are beyond the scale of this map. Map pixel size is 5 km².