Modelling the impact of antimalarial quality on the transmission of sulfadoxine-pyrimethamine resistance in Plasmodium falciparum.

BACKGROUND: The use of poor quality antimalarial medicines, including the use of non-recommended medicines for treatment such as sulfadoxine-pyrimethamine (SP) monotherapy, undermines malaria control and elimination efforts. Furthermore, the use of subtherapeutic doses of the active ingredient(s) can theoretically promote the emergence and transmission of drug resistant parasites.
METHODS: We developed a deterministic compartmental model to quantify the impact of antimalarial medicine quality on the transmission of SP resistance, and validated it using sensitivity analysis and a comparison with data from Kenya collected in 2006. We modelled human and mosquito population dynamics, incorporating two Plasmodium falciparum subtypes (SP-sensitive and SP-resistant) and both poor quality and good quality (artemether-lumefantrine) antimalarial use.
FINDINGS: The model predicted that an increase in human malaria cases, and among these, an increase in the proportion of SP-resistant infections, resulted from an increase in poor quality SP antimalarial use, whether it was full- or half-dose SP monotherapy.
INTERPRETATION: Our findings suggest that an increase in poor quality antimalarial use predicts an increase in the transmission of resistance. This highlights the need for stricter control and regulation on the availability and use of poor quality antimalarial medicines, in order to offer safe and effective treatments, and work towards the eradication of malaria.

Introduction

The spread of antimalarial resistance is hampering malaria control and elimination efforts globally (Ambroise-Thomas, 2012, World Health Organization, 2010a). Poor quality antimalarials can be categorised into three main groups: falsified; substandard; and degraded (WorldWide Antimalarial Resistance Network, 2010). Each of these can be a source of subtherapeutic doses of the active ingredient(s), which promote the emergence and transmission of drug resistant parasites through selection pressures (Barnes et al., 2008, Simpson et al., 2000, White et al., 2009). Falsified antimalarials are those that are fraudulently made and typically contain an incorrect amount of active ingredient, incorrect active ingredient, toxic substances, or no active ingredient. Substandard antimalarials are those made by licenced companies but use poor manufacturing practices. Degraded antimalarials degrade from their initial quality due to inadequate storage conditions, such as excessive heat. In addition, within poor quality antimalarials, we include those that are not recommended in the World Health Organization (WHO) guidelines.

Approximately 30% of antimalarial medicines in Africa and Asia are considered to be falsified or substandard (Ambroise-Thomas, 2012, Newton et al., 2009). The outcome for those receiving poor quality antimalarials ranges from prolonged malaria symptoms, unexpected side effects, financial strain due to loss of income or healthcare costs, or even death (Ambroise-Thomas, 2012, Newton et al., 2006, Tabernero et al., 2014). In Kenya, prior to 2004, sulfadoxine-pyrimethamine (SP) had been recommended as first-line for treatment of malaria. Due to increasing resistance to SP, stemming from mutations in the P. falciparum dihydrofolate reductase (DHFR) gene, which affects pyrimethamine, and the dihydropteroate synthase (DHPS) gene, which affects sulfadoxine, Kenya adopted artemether-lumefantrine (AL) as its first-line treatment in 2004. In 2001, WHO recommended the use of artemisinin-based combination therapies (ACTs) as first-line policy (World Health Organization, 2010b). In December 2007, a report was produced surveying the antimalarial medicines available in Kenya and their quality. The researchers identified a wide range of products on the market, the majority of which were not in-line with the new national guidelines, and a high proportion were either un-registered or of low quality (Ministry of Health Republic of Kenya, 2007).

The effect of antimalarial use on the transmission of resistance has been modelled previously (Hastings, 2006, Klein, 2014, Koella and Antia, 2003, Mackinnon and Hastings, 1998, Tchuenche et al., 2011). Notably, the models currently available do not take into account the quality or percentage of antimalarial active ingredient and its effect on transmission. As summarised by Koella and Antia (2003), part of the issue preventing these resistance transmission models from being developed and used is a lack of complete, comprehensive datasets for key parameters. Since their model was published, work has been carried out to look at the effect of drug quality on resistance within mice (Huijben et al., 2010a, Huijben et al., 2013) and the effect of treatment in humans with SP-resistant infections (Barnes et al., 2008, Barnes et al., 2008, Méndez et al., 2007).

Here we develop a new model to explore the impact of antimalarial quality, defined as poor quality SP, as defined above, and good quality AL, on the transmission of SP antimalarial resistance in Plasmodium falciparum. To assist in more realistic parameterisation of the model, we applied the model to Kenya in 2006, rather than Kenya being a focus for actual predictions. The model assumes that low to moderate SP-resistance conferred by mutations in the DHFR gene, the target of pyrimethamine, has already been established within both human and mosquito populations.

Materials and methods

Model structure

We developed a deterministic compartmental model to explore the impact of antimalarial quality on the transmission of P. falciparum SP resistance (Fig. 1). The model quantifies the transmission dynamics of SP-sensitive (denoted ) and SP-resistant (denoted ) P. falciparum between female Anopheles mosquitoes and humans. The human-mosquito system is modelled using ordinary differential equations (ODEs) (Eq. (A1), Appendix A1). Humans may be infected by SP-sensitive strains , SP-resistant strains , or both . Resistance to SP was defined as the presence of DHFR-51 and DHFR-108 pyrimethamine resistance-conferring mutations (Méndez et al., 2007), used as proxy for all low to moderate SP-resistant conferring mutations in P. falciparum (Sridaran et al., 2010). At baseline, the percentage of humans and mosquitoes with SP-resistant infections was set to 42% (Kum et al., 2013, Spalding et al., 2010) and mixed infections was set to 8% (Kum et al., 2013).

Fig. 1

A summary of the structure of the mathematical model showing the movement between compartments of SP-sensitive and SP-resistant Plasmodium falciparum in humans and female Anopheles mosquitoes (blue solid line). The transmission of gametocytes (infected human to susceptible mosquito) and sporozoites (infected mosquito to susceptible human) during a blood meal, is depicted by the red dotted line for SP-sensitive, and a dark green dotted line for SP-resistant.

Humans free of P. falciparum were classified as susceptible and denoted by . When transmission of sporozoites occurs from female An. mosquitoes to humans during a blood meal, the human moves into the exposed class ( at the rate . The script indicates a SP-sensitive ( is ) or SP-resistant ( is ) P. falciparum infection. Due to the difference in the latent periods for asexual P. falciparum and gametocytes, it is assumed that antimalarial treatment is sought while in the exposed class to treat malaria symptoms as part of the asexual lifecycle (Poser & Bruyn, 1999). There are four types of treatment available, each used as a proxy for ‘good quality’ or ‘poor quality’ treatments. Infected humans receive each treatment type with probability , where the subscript is for a full dose of AL (good quality); for a full-dose of SP monotherapy (poor quality); for a half-dose SP monotherapy (poor quality); and for no treatment, either through no antimalarial compound within the medicine sought or choosing not to seek treatment (poor quality). Following the gametocyte latency period, those in the exposed class move into the infectious class at rate , which is assumed to be equal for both SP-sensitive and SP-resistant infections. The length of infectiousness and probability of transmission of gametocytes from infected humans to mosquitoes are specified for each strain and treatment combination. The recovery rate is defined by . Natural immunity is gained at rate , among those who do not receive treatment (Bousema & Drakeley, 2011), and lost at rate . The protective nature and rates for gaining and losing natural immunity are also assumed to be independent of P. falciparum infection type.

Female Anopheles mosquitoes may be susceptible , exposed , or infected . Movement from susceptible to an exposed class, after the transmission of P. falciparum during a blood meal, occurs at rate ; where is for SP-sensitive parasites or for SP-resistant P. falciparum. The rate of transmission is defined as the product of the daily mosquito biting rate and the probability of transmission given parasite strain and drug treatment received by the human ( or ). We assume that An. mosquitoes can only be infected by one strain of P. falciparum gametocytes (i.e., no mixed infections), and in the occurrence that a susceptible mosquito feeds on a human host with a mixed infection, the probability of the SP-sensitive strain being selected over the SP-resistant strain and proceeding through the mosquito's midgut and onto the salivary gland, is set at 0.6, assigning a relatively small fitness cost to resistance (Appendix D1). Following the latent period, the mosquito enters the infectious class at rate , and it is assumed that they do not recover from their infection due to their short lifespans (Mandal, Sarkar, & Sinha, 2011). The parameters used in the model are defined in Table 1, Table 2. Additional parameters, including details on the calculations of mosquito and human demographic turnover rates can be found in Appendices B–E. The impact of SP on the level of gametocytes in humans has been extensively researched (Barnes et al., 2008, Barnes et al., 2008, Bousema and Drakeley, 2011, Méndez et al., 2007). We calculated an estimate for the length of gametocyte carriage and the probability of transmission when treated with a full dose pyrimethamine, half dose (using 50% or 37.5% of a full dose) of pyrimethamine, or no treatment (Huijben et al., 2010b, Huijben et al., 2013, Huijben et al., 2010a), and then calibrated these scenarios against human SP monotherapy studies (Barnes et al., 2008, Barnes et al., 2008, Méndez et al., 2007) (C2, C3).

Table 1

Human Parameters. A summary of the model parameters used to calculate the rates of change in human movement (daily) between model compartments, including: parameter definitions, symbols, parameter values used in the baseline model, and literature references or the section of the Appendices where the parameters are defined.

Parameter description	Symbol	Value	Reference
Human population size (initial)	N_H	1	Updated per iteration
Birth rate	Ω_H	1.1349 × 10−4	Appendix B1
Rate of humans becoming exposed to SP-sensitive sporozoites	β_H,w	0.0810	Appendix B2
Rate of humans becoming exposed to SP-resistant sporozoites	β_H,r	0.0810	Appendix B2
Rate of humans becoming infectious (gametocytes)	σ_H	0.0556	Appendix B3
Receiving AL (proportion, at baseline)	θ_q	0.70	Assumed, Appendix C1
Receiving full-dose SP monotherapy (proportion, at baseline)	θ_m	0.07	Demographic and Health Surveys (various), 2003–2012
Receiving full-dose SP monotherapy (proportion, at baseline)	θ_p	0.03	Minzi et al., 2003, Newton et al., 2006, Tabernero et al., 2014
Receiving no treatment (proportion, at baseline)	θ_n	0.20	Chuma et al. (2007)
Rate of human recovery from SP-sensitive P. falciparum having received AL	γ_w,q	0.1667	Appendix B4
Rate of human recovery from SP-sensitive P. falciparum having received full-dose SP monotherapy	γ_w,m	0.0588	Appendix B4
Rate of human recovery from SP-sensitive P. falciparum having received half-dose SP monotherapy	γ_w,p	0.0476	Appendix B4
Rate of human recovery from SP-resistant P. falciparum having received AL	γ_r,q	0.1667	Appendix B4
Rate of human recovery from SP- resistant P. falciparum having received full-dose SP monotherapy	γ_r,m	0.0096	Appendix B4
Rate of human recovery from SP- resistant P. falciparum having received half-dose SP monotherapy	γ_r,p	0.0096	Appendix B4
Rate of human recovery from mixed P. falciparum infection having received AL	γ_wr,q	0.1667	Appendix B4
Rate of human recovery from mixed P. falciparum infection having received full-dose SP monotherapy	γ_wr,m	0.0096	Appendix B4
Rate of human recovery from mixed P. falciparum infection having received half-dose SP monotherapy	γ_wr,p	0.0119	Appendix B4
Rate of recovery having received no treatment	γ_n	0.0149	Appendix B4
Overall transmission of SP-sensitive gametocytes (probability)	Ζ˜_w	0.1459	Appendix D2
Overall transmission of SP-resistant gametocytes (probability)	Ζ˜_r	0.1410	Appendix D2
Rate of acquired immunity	γ_R	6.0864 × 10−4	Appendix B5
Rate of loss of acquired immunity	ρ	0.0027	Labadin, Kon, & Juan (2009)
Rate of malarial mortality in humans	μ_I	8.2880 × 10−4	Appendix B6
Rate of “other” mortality in humans	μ_O	3.1779 × 10−5	Appendix B6

Table 2

Mosquito Parameters. A summary of the model parameters used to calculate the rates of change of movement (daily) of female An. mosquitoes between model compartments, including: parameter definitions, symbols, parameter values used in the baseline model, and literature references or the section of the Appendices where the parameters are defined.

Parameter description	Symbol	Value	Reference
Ratio of An. mosquito to human population (initial)	N_M	0.87	Updated per iteration
Rate female An. mosquitoes reach adulthood	Ω_M	0.0280	Chitnisa et al., 2008, Labadin et al., 2009
Biting rate of female An. Mosquitoes	c	0.4050	Anderson and May, 1991, Mandal et al., 2011
Rate of mosquitoes becoming exposed to SP-sensitive gametocytes	β_M,w	0.0591	Appendix E1
Rate of mosquitoes becoming exposed to SP-resistant gametocytes	β_M,r	0.0571	Appendix E1
Rate of mosquitoes becoming infectious (sporozoites at salivary gland)	σ_M	0.2000	Appendix E2
Rate of mortality of female An. mosquitoes	μ_M	0.0280	Mandal et al. (2011), Appendix E3

The model simulations were run at the 2006 baseline level for all parameters, with the initial conditions (Appendix A2) chosen to match surveillance data observed in Kenya in 2006. The system was solved for 1 year (2006), and the results analysed. All analysis were carried out in Mathworks Matlab 2012a, using the ODE15s solver.

Gametocyte carriage and infectiousness

The parameter values for the duration of gametocyte carriage and the probability a mosquito takes up a mature (infectious) gametocyte during a blood meal, given the infection-type and treatment received by the patient, utilised a combination of data from mice malaria studies for pyrimethamine (Huijben et al., 2010b, Huijben et al., 2013, Huijben et al., 2010a) and human SP studies (Barnes et al., 2008, Barnes et al., 2008, Méndez et al., 2007). Pyrimethamine (not in combination with sulfadoxine) mice studies were used to inform parameterisation due to the availability of data on pyrimethamine, with no such data was available on SP. This method is described in C2, C3.

The expected duration of gametocyte carriage, given treatment scenarios, were calculated and compared to the 2006 baseline treatment level (70% AL use (assumed, Appendix C1), 7% full-dose SP monotherapy (Demographic and Health Surveys (various), 2003–2012), 3% half-dose SP monotherapy (Minzi et al., 2003, Newton et al., 2006, Tabernero et al., 2014), and 20% no treatment (Chuma, Gilson, & Molyneux, 2007)), in Fig. 2A and Table 3. An increase in the use of full-dose or half-dose SP monotherapy use, or no treatment by 1% (with a corresponding 1% decrease in AL use), resulted in an increase in the duration of gametocyte carriage from baseline (16.1 days) of 2½ hour, 3 h and 16 h, respectively. However, exclusive use of either full-dose or half-dose SP (all other treatments set to 0%), results in the duration decreasing from baseline (3.3 days and 1.6 days, respectively); whereas increasing when no treatment is exclusively used by 50.9 days; indicating no treatment has a large impact on carriage. In contrast, as the percentage of AL treatment increases, a decrease in the average duration of gametocyte carriage is observed (2 h per 1% increase), down to an eventual duration of 2 days when used exclusively.

Fig. 2

(A) The impact of antimalarial quality on the average duration of gametocyte carriage in humans. (B–C) The impact of antimalarial quality on the infectiousness of humans to mosquitoes during a blood meal (probability), of (B) SP-sensitive and (C) SP-resistant gametocytes. Changes in the percentage use of full-dose SP monotherapy (, orange line) were adjusted for the use of 3% half-dose SP monotherapy , 20% receiving no treatment and the remainder AL treatment . Likewise, changes in half-dose SP monotherapy use (θ, purple line) were adjusted for and remainder; changes in those receiving no treatment (θ, blue line) were adjusted for and remainder; and changes in AL use (θ, green line) were adjusted for and remainder. The 2006 model baseline (black line) corresponds to and .

Table 3

The impact of changes in the percentage use of treatments (after 365 days), with percentage change, when compared to 2006 model baseline for: the average duration of gametocyte carriage; and the probability of mosquitoes taking up infectious gametocytes. The 2006 model baseline treatment use was set to 70% AL treatment , 7% full-dose SP monotherapy , 3% half-dose SP monotherapy and 20% no treatment . Changes in the percentage use of full-dose SP monotherapy were adjusted for and  = remainder; changes in the use of half-dose SP monotherapy use (θ) were adjusted for and remainder; changes in those receiving no treatment (θ) were adjusted for and remainder; and changes in AL use (θ) were adjusted for and remainder. For exclusive use of a treatment (100% use), all other treatments were set to 0%.

Drug Use Scenarios	Duration gametocyte carriage	Probability infectious gametocytes
		SP-sensitive	SP-resistant
2006 model baseline	16.1 days	0.1459	0.1410
+1% full-dose SP use	+2½ hours (0.6%)	+0.0016 (1.1%)	+0.0035 (2.5%)
+1% half-dose SP use	+3 hours (0.8%)	+0.0008 (0.5%)	+0.0002 (0.1%)
+1% no treatment	+16 hours (4.2%)	+0.0024 (1.6%)	+0.0021 (1.5%)
+1% AL use	− 2 hours (0.5%)	− 0.0015 (1.0%)	− 0.0034 (2.4%)
100% full-dose SP use	− 3.3 days (20.4%)	+0.0951 (65.2%)	+0.2830 (200.7%)
100% half-dose SP use	− 1.6 days (10.2%)	+0.0178 (12.2%)	−0.0498 (35.3%)
100% no treatment	+50.9 days (316.1%)	+0.1741 (119.3%)	+0.1390 (98.6%)
100% AL use	−14.1 days (87.6%)	−0.0600 (41.1%)	−0.0658 (46.7%)

The calculated probability of mosquitoes taking up infectious gametocytes during a blood meal also increased in response to greater use of full- and half-dose SP monotherapy, and no treatment (Fig. 2B–C, Table 3). In settings where SP resistance is already firmly established, a 1% increase in full-dose SP monotherapy resulted in a larger percentage increase in SP-resistant infectiousness, than sensitive infectiousness (2.5% v 1.1%). This is further highlighted under the scenario of exclusive use of full-dose SP, where results indicate a 200.7% increase in the probability of mosquitoes taking up SP-resistant P. falciparum, compared to a 65.2% increase in SP-sensitive P. falciparum. In contrast, 1% increases in half-dose SP or no treatment use had a greater percentage increase in the probability of mosquitoes taking up SP-sensitive P. falciparum (0.5% and 1.6%, respectively) compared to SP-resistant P. falciparum (0.1% and 1.5%, respectively). However, when used exclusively, half-dose SP had the greatest percentage increase in SP-resistant P. falciparum compared to SP-sensitive (35.3% v 12.2%); with exclusive use of no treatment resulting in a similarly large percentage increase for both (98.6% and 119.3%, respectively). Changes in the use of AL resulted in a greater decrease in the probability of SP-resistant P. falciparum being taken up by mosquitoes, compared to SP-sensitive P. falciparum (2.4% v 1.0%, for 1% increase; and 46.7% v 41.1%, when exclusively used).

Measuring the effect on transmission

The main outcome of interest is the impact of antimalarial quality on the total proportion of SP-resistant infections (resistant and mixed infections) in the human population (, Eq. (1)):

Here denotes the human classes (excluding acquired immunity), where the subscript and once again denote SP-sensitive and SP-resistant P. falciparum, respectively.

In addition to the proportion of SP-resistant infections, we also measured the expected number of malaria cases in humans.

Model accuracy

To validate our results, we performed a sensitivity analysis, and compared baseline model predictions against estimates found in the literature. A one-way sensitivity analysis was carried out, where each parameter was individually changed to the minimum and maximum value in its defined parameter range, and the change in the total proportion of SP-resistant infections in the human population was calculated. Parameters that inferred a change of greater than were considered to be significant during the sensitivity analysis.

Results

To quantify the impact of antimalarial quality on the transmission of SP resistance in P. falciparum, we varied the amount of good and poor quality antimalarial use in the population. Any change in antimalarial use that assists the survival and propagation of antimalarial resistance within human and mosquito populations highlights the need for better control and regulations of the use and availability of these medicines in order to offer safe and effective treatment.

Malaria cases (human)

At baseline, our model predicts 10,807,000 malaria cases in Kenya during 2006 (Fig. 3A, Table 4). An increase in the use of poor quality antimalarial use predicts a greater number of malaria cases, with the greatest increase observed under the scenario of full-dose SP being exclusively used (776.9%), followed by no treatment (773.6%) and the exclusive use of half-dose SP use (558.6%). This suggests that people may experience multiple malaria infections within one calendar year (population size 36,757,498 (The World Bank., 2006–2013g)). Under the exclusive use of AL, the model predicts that the number of malaria cases in Kenya for 2006 could have been 2,978,200 (a reduction of 72.5% from baseline). The proportion of malaria cases that contained SP-resistant P. falciparum reflects these increases under each scenario of SP use, where exclusive use of full-dose SP increases by 18.4% from baseline, and half-dose increases by 13.8% (Fig. 3B, Table 4). Decreases in the proportion of SP-resistant infections were observed when no treatment was used (−5.8%) and the exclusive use of AL (−1.8%).

Fig. 3

(A) The impact of antimalarial quality on the predicted number of human malaria cases in 2006. (B) The impact of antimalarial quality on the total proportion of SP-resistant infections in humans. Changes in the percentage use of full-dose SP monotherapy (, orange line) were adjusted for the use of 3% half-dose SP monotherapy , 20% receiving no treatment , and the remainder AL treatment . Likewise, changes in half-dose SP monotherapy use (θ, purple line) were adjusted for , and remainder; changes in those receiving no treatment (θ, blue line) were adjusted for and remainder; and changes in AL use (θ, green line) were adjusted for , and remainder. The 2006 model baseline (black line) corresponds to , and . Model simulations run for 365 days.

Table 4

The impact of changes in the percentage use of treatments (after 365 days) on the expected number of malaria cases in Kenya for 2006 and the proportion of resistant infections (percentage change), when compared to the 2006 model baseline. The 2006 model baseline treatment use was set to 70% AL treatment , 7% full-dose SP monotherapy , 3% half-dose SP monotherapy , and 20% no treatment ; and for the exclusive use of a treatment (100% use), all other treatments were set to 0%.

Drug Use Scenarios	Expected malaria cases (2006)	Proportion SP-resistant
2006 model baseline	10,807,000	0.8404
100% full-dose SP use	+83,964,000 (776.9%)	+0.1545 (18.4%)
100% half-dose SP use	+60,366,000 (558.6%)	+0.1157 (13.8%)
100% no treatment	+83,608,000 (773.6%)	−0.0491 (−5.8%)
100% AL use	−7,831,300 (−72.5%)	−0.0148 (−1.8%)

3.2 Results validation

Key 2006 baseline model output was compared to empirical estimates for the Kenyan population (Table 5), indicating our model predicted these outputs within an acceptable range. For the sensitivity analysis, parameters that inferred a change in the total proportion of SP-resistant infections in the human population of greater than were considered to be significant (Table 6). As seen with other malaria models (Mandal et al., 2011), our model was sensitive to mosquito parameters, such as the proportion of mosquitoes to humans, the daily rate female An. mosquitoes reach adulthood, and the probability of transmission of SP-sensitive and SP-resistant sporozoites during a blood meal. Additionally, the expected gametocyte clearances of SP-sensitive and SP-resistant gametocytes when treated with AL were found to significantly influence model outputs. The full sensitivity analysis is available in Appendix F.

Table 5

Results validation. A comparison of the baseline model outcomes with literature estimates for 2006 and the published reference, including the percentage error in the 2006 model estimate, for: the rate of population growth; the proportion of each strain of Plasmodium falciparum malaria in humans; the number of P. falciparum cases of malaria in humans; and the human mortality (total and malaria-specific).

Description	2006 Model Outcome	2006 Literature Value (Reference)	Difference (%)
Population growth, % (2006–2007)	2.7559	2.7 (The World Bank, 2006–2013b)	2
Malaria cases	10,857,000	8,926,058 (World Health Organization, 2010b)	22
Deaths (all)	500,980	404,332 (The World Bank, 2006–2013b)	24
Malaria-specific deaths	72,592	74,970 (The World Bank, 2006-2013b, World Health Organization, 2010b)	−3
Proportion of SP-sensitive infections in humans (w)	0.1625	0.05–0.5 (Kum et al., 2013)	Within range
Proportion of SP-resistant infections in humans (r)	0.8356	0.42–0.90 (Kum et al., 2013, Spalding et al., 2010)	Within range
Proportion of mixed infections in humans (wr)	0.0019	0–0.53 (Assumed)	Within range

Table 6

Sensitivity analysis summary. Results for the sensitivity analysis, where parameter range (minimum and/or maximum) resulted in a change in the proportion of SP-resistant infections in humans. Full sensitivity analysis results are available in Appendix F. A Largest value we could get a numerical solution for, actual literature range maximum value is 0.27.

Parameter	Range (literature range or ±10%)			Percentage change (%)
	Baseline	Minimum	Maximum	Minimum	Maximum
Ratio of mosquito to human population (initial, humans = 1) (N_M)	0.87	0.5	40	0.32	−20.55
Rate female An. mosquitoes reach adulthood (Ω_M)	0.028	0.020	0.1406 A	0.26	−36.20
SP-sensitive sporozoite transmission (probability) (T_w)	0.2	0.2	0.5	0.00	−86.98
SP-resistant sporozoite transmission (probability) (T_r)	0.2	0.2	0.5	0.00	17.90
SP-sensitive gametocyte clearance in humans treated with AL (ε_w,q)	14	7	28	9.20	−13.61
SP-resistant gametocyte clearance in humans treated with AL (ε_r,q)	14	7	28	−15.52	8.65

Discussion

Our model suggests that once SP resistance is widespread, as was the case in Kenya in 2006, an increase in poor quality antimalarial use (focusing on SP) results in an increase in: (i) the number of human malaria cases (Fig. 3A), and (ii) of these cases, an increase in the proportion of SP-resistant infections in humans (full- or half-dose SP used, Fig. 3B), when compared to good quality antimalarial use (AL). The predicted increase in malaria cases is of concern, where the scenario of full-dose SP being exclusively used (+776.9%), followed by no treatment (+773.6%) and the exclusive use of half-dose SP use (+558.6%), yield large increases; whereas the exclusive use of AL results in a marked decrease in the number of expected cases (−72.5%). The predicted increase in resistant-containing infections under SP drug pressure is supported by findings from Hastings (Hastings, 2006). Our findings suggest that a delay in P. falciparum clearance in humans, due to SP-resistance and/or inadequate antimalarial active ingredient, allows for prolonged transmission of SP-resistant gametocytes, hence ensuring their propagation throughout human and mosquito populations.

There are clear examples of substandard SP circulating in east Africa and elsewhere (see http://www.wwarn.org/aqsurveyor/#0). A common problem has been impaired drug dissolution due to poor manufacturing, despite having the correct amounts of SP in the tablet, which result in low blood SP drug levels (Leslie et al., 2009, White et al., 2009). The impacts described here for reduced dosage of SP will also apply to this situation of reduced bioavailability. In addition, systematic under-dosing of antimalarials, common in pregnancy and young children, has been shown to impact efficacy, with theoretical impacts of the selection of drug resistance (Barnes et al., 2008, Sambol et al., 2015). In all these cases, the key variable will be the antimalarial levels parasites are exposed to, reflecting both antimalarial content and bioavailability.

The impact of antimalarial quality on mortality could not be explicitly explored as the model assumes that the proportion of malaria-specific mortality is proportional to the prevalence of malaria and hence driven by this relationship. This additionally acts to drive the overall mortality.

The accuracy of the model indicated larger percentage errors in the predicted malaria cases and malaria deaths for 2006 (Table 5). However, this simulated number of malaria cases is below the 15 million cases estimated to have occurred in Kenya in 2006 (World Health Organization, 2010b), where under-reporting is considered a factor. This under-reporting is also assumed for malarial deaths, where there are discrepancies between the estimated (overall) deaths in Kenya in 2006 (The World Bank, 2006-2013c, World Health Organization, 2010b) (Appendix B6).

The parameterisation of the transmissibility and infectiousness of gametocytes under each treatment type utilised a combination of data from mice malaria studies for pyrimethamine (Huijben et al., 2010b, Huijben et al., 2013, Huijben et al., 2010a) and human SP studies (Barnes et al., 2008, Barnes et al., 2008, Méndez et al., 2007). The use of these calculated estimates introduces a margin of error; as well as the possible under-estimation of the transmissibility and infectiousness of those receiving a half-dose of SP (Appendix C3.2). The impact of antimalarial quality on the duration of gametocyte carriage seems plausible, with the largest increase predicted from increases in those who receive no treatment. Increases in carriage duration were observed with increases in the percentage SP use, with half-dose SP monotherapy showing more marked increases in carriage duration than full-dose SP monotherapy. This may be explained by SP-sensitive infections being cleared more slowly following sub-therapeutic concentrations of antimalarial medicine, then when using full-dose SP, thereby providing a longer period for gametocytes to remain in circulation. Interestingly, this relationship was not observed when considering pyrimethamine-resistant gametocyte density in mice, despite peak density and carriage often being correlated (Huijben et al., 2013). The limitations in approximating these parameters further highlight the need for more data in this area, as well as other more currently utilised antimalarial drugs.

The model assumed that SP-resistance is conferred by mutations in the DHFR gene, omitting other possible mutations conferring sulfadoxine-resistance, or other mutations in the DHFR gene such as C59R or the high level resistance-conferring I15L mutation (Rosenthal, 2013). The selection of low to moderate SP resistance was due to the availability of data (or lack thereof), highlighting the need for further research in this area.

It must be noted that both symptomatic and asymptomatic infections (Bousema, Okell, Felger, & Drakeley, 2014), as well as those with acquired immunity (Klein, Smith, Boni, & Laxminarayan, 2008), harbour gametocytes. The transmission potential of asymptomatic or acquired immune individuals were not included as a source of transmission, as they are outside of the scope of this study. Additionally, the model parameterised the mortality of mosquitoes irrespective of infection-status; did not allow mixed infections within the mosquito population; and a fitness-cost was assigned to SP-resistant gametocytes when mixed infections were taken up during a blood meal. A more detailed discussion of these assumptions and limitations is provided in Appendix G.

The effect of antimalarial treatment on gametogenesis and infectiousness differs depending on the antimalarial class. A key assumption in using poor quality SP as a proxy for the use of all poor quality antimalarial use is that we assume that all antimalarials have the same propensity to generate gametocytes and effect on gametocyte infectiousness, which is not the case. For example, ACT use is associated with a lower rate of gametocyte carriage (Bousema & Drakeley, 2011), highlighting the need for further studies.

Conclusions

The model predicts that an increase in the use of poor quality antimalarials, for which SP is an appropriate proxy, results in an increase in the transmission of antimalarial resistant malaria, providing insight into the link between poor quality antimalarial medicine use and resistance. The loss of antimalarial effectiveness is hampering malaria eradication efforts worldwide, and the continued availability and use of falsified, substandard, degraded and non-WHO recommended antimalarials are highly likely to facilitate the spread of resistance. In order to continue to effectively eradicate malaria, the availability and use of these antimalarials must be addressed by drug regulatory authorities and international organisations.

Competing interests

We declare no competing interests.

Authors' contributions

ARB, AE and JVR conceived the study, SP and AG assisted with further refinement. ARB, JVR, SG, DPD and AG contributed to the model design. ARB parameterised the model with assistance from JVR and SP. ARB, JVR, SG, DPD and AG contributed to the production of the results, which were interpreted by ARB, JVR, SP and AE. ARB drafted the manuscript. AE, JVR, SP, SG, DPD and AG reviewed and suggested modifications to the manuscript. All authors reviewed and approved the final version.

Funding

AR Brock was supported by a University of South Australia stipend.

Table A2.1

Initial Conditions. The initial values of each class in the model (i.e. when time is set to 0).

Population	Model Class	Initial Value (t=0)
Human	N_H	1.0000
	E(H)_wS(H)_r	0.0021
	I(H)_wS(H)_r	0.0009
	S(H)_wE(H)_r	0.0108
	E(H)_wE(H)_r	0.0000
	I(H)_wE(H)_r	0.0000
	S(H)_wI(H)_r	0.0046
	E(H)_wI(H)_r	0.0000
	I(H)_wI(H)_r	0.0000
	R(H)	0.0000
	D(H)_I	0.0000
	D(H)_O	0.0000
	S(H)_wS(H)_r	N_H−[E(H)_wS(H)_r+I(H)_wS(H)_r+S(H)_wE(H)_r+E(H)_wE(H)_r+I(H)_wE(H)_r+S(H)_wI(H)_r+E(H)_wI(H)_r+I(H)_wI(H)_r+R(H)+D(H)_I+D(H)_O]
Mosquito	N_M	0.8700
	E(M)_w	0.0002
	E(M)_r	0.0012
	I(M)_w	0.0017
	I(M)_r	0.0088
	D(M)	0.0000
	S(M)	N_M−[E(M)_w+E(M)_r+I(M)_w+I(M)_r−D(M)]

Table B.1

Human Parameters. A description of the parameters specific to the human population, in Kenya (2006). For parameter values where literature values were readily available, these values, along with the range of values and references are provided. For parameters that required further manipulation from the original source, the section of the Appendices where this parameter is discussed is noted. All parameter units are in days, unless otherwise stated.

Parameter description	Symbol	Value [range]	Reference
Human Kenyan population (count)	Y_K	36,757,498	The World Bank (2006–2013g)
Number of deaths in Kenya in 2006 (count)	D_K	11 per 1000	The World Bank (2006-2013c)
Births per year in Kenya	χ	38 per 1000	The World Bank (2006-2013a)
Range of child-bearing ages (years of age): initial, final	λ_I, λ_F	15, 49	Ikamari, Izugbara, and Ochako (2013)
Fertility rate (births per woman)	ζ	4.9	The World Bank (2006-2013d)
Proportion of population that are female	ψ	0.501	The World Bank (2006-2013f)
Life expectancy of humans (days)	ξ_H	20,454	The World Bank (2006-2013e)
Kenyan 2006 malaria cases (count)	Y_M	8,926,058	World Health Organization (2010b)
Kenyan 2006 malarial deaths (count)	D_M	74,970	The World Bank, 2006-2013c, World Health Organization, 2010b
Latency period of asexual parasites in humans (days)	Π_Η	9 [9, 14]	Bloland and Williams (2002)
Delay in seeking treatment (days)	η	1 [0, 2]	Sumba, Wong, Kanzaria, Johnson, and John (2008)
Time to initial wave of gametocytes after the initial wave of asexual parasites (days)	G_I	7 [7, 15]	Bousema and Drakeley (2011)
Time for gametocytes to mature (days)	G_M	2 [2, 3]	Bousema and Drakeley (2011)
Total time until infectious gametocytes (days) from time of transmission from mosquito	υ	18 [18, 32]	Appendix B3
Rate of the loss of acquired immunity	ρ	0.0027	Labadin et al. (2009)
Allele frequency of SP-sensitive P. falciparum	F_w	0.50 [0.05, 0.50]	Kum et al. (2013)
Allele frequency of SP-resistant P. falciparum	F_r	0.42 [0.42, 0.90]	Kum et al., 2013, Spalding et al., 2010
Allele frequency of mixed P. falciparum	F_wr	0.08 [0, 0.08]	Kum et al. (2013)
The rate of building effective immunity	q	27.3774	Labadin et al. (2009)
The rate of recovery of P. falciparum infection	s	0.0018	Labadin et al. (2009)

Table C.1

Treatment parameters. A description of the treatment parameters used in the model. For parameter values where literature values were readily available, these values, along with the range of values and references are provided. For parameters that required further manipulation from the original source, the section of the Appendices where this parameter is discussed is noted. All parameter units are in days, unless otherwise stated.

Symbol	Parameter description	Value [range or ±10%]	Reference
1−θ_n	Probability of receiving treatment	0.80 [0.80, 0.91]	Chuma et al. (2007)
θ_n	Receiving no treatment (proportion, at baseline)	0.20 [0.09, 0.20]	Chuma et al. (2007)
θ_m	Receiving full-dose SP monotherapy (proportion, at baseline)	0.07 [0.063, 0.077]	Demographic and Health Surveys (various) (2003–2012)
θ_p	Receiving half-dose SP monotherapy (proportion, at baseline)	0.03 [0.027, 0.33]	Appendix C1
θ_q	Receiving AL (proportion, at baseline)	0.70 [0.63, 0.77]	Appendix C1
ε_w,q	SP-sensitive gametocyte clearance in humans treated with AL	14 [12.6, 15.4]	Appendix C2.1
ε_r,q	SP-resistant gametocyte clearance in humans treated with AL	14 [12.6, 15.4]	Appendix C2.1
ε_wr,q	Mixed infection gametocyte clearance in humans treated with AL	14 [12.6, 15.4]	Appendix C2.1
ε_w,m	SP-sensitive gametocyte clearance in humans treated with full-dose SP monotherapy	25 [21, 119]	Appendix C2.2
ε_r,m	SP-resistant gametocyte clearance in humans treated with full-dose SP monotherapy	112 [112, 882]	Appendix C2.2
ε_wr,m	Mixed infection gametocyte clearance in humans treated with full-dose SP monotherapy	25 [21, 119]	Appendix C2.2
ε_w,p	SP-sensitive gametocyte clearance in humans treated with half-dose SP monotherapy	29 [29, 162]	Appendix C2.2
ε_r,p	SP-resistant gametocyte clearance in humans treated with half -dose SP monotherapy	112 [112, 882]	Appendix C2.2
ε_wr,p	Mixed infection gametocyte clearance in humans treated with half -dose SP monotherapy	92 [92, 772]	Appendix C2.2
ε_n	Gametocyte clearance in humans not treated	75 [0, 730]	Anderson and May (1991)
Z_w,q	SP-sensitive gametocyte transmission when treated with AL (probability)	0.053705 [0.0183335, 0.053705]	Appendix C3.3
Z_r,q	SP-resistant gametocyte transmission when treated with AL (probability)	0.053705 [0.0183335, 0.053705]	Appendix C3.3
Z_wr,q	Mixed infection gametocyte transmission when treated with AL (probability)	0.053705 [0.0183335, 0.053705]	Appendix C3.3
Z_w,m	SP-sensitive gametocyte transmission when treated with full-dose SP (probability)	0.055 [0.0495, 0.0605]	Appendix C3.2
Z_r,m	SP-resistant gametocyte transmission when treated with full-dose SP (probability)	0.3 [0.424485, 0.4999]	Appendix C3.2
Z_wr,m	Mixed infection gametocyte transmission when treated with full-dose SP (probability)	0.31 [0.452, 0.527375]	Appendix C3.2
Z_w,p	SP-sensitive gametocyte transmission when treated with half-dose SP (probability)	0.0489 [0.04401, 0.05379]	Appendix C3.2
Z_r,p	SP-resistant gametocyte transmission when treated with half-dose SP (probability)	0.0147 [0.0125, 0.0147]	Appendix C3.2
Z_wr,p	Mixed infection gametocyte transmission when treated with half-dose SP (probability)	0.1913 [0.1639, 0.1913]	Appendix C3.2
Z_n	Gametocyte transmission with no treatment (probability)	0.2 [0.2, 0.5]	Mandal et al. (2011), Appendix C3.1

Table C2.2.1

Summary findings from gametocyte clearance studies. Gametocyte clearance time in human and mice studies, along with the parameter range ([minimum, maximum]), for SP-sensitive , SP-resistant and mixed infections in humans (Barnes et al., 2008, Barnes et al., 2008, Méndez et al., 2007); and pyrimethamine-sensitive , pyrimethamine-resistant and mixed infections in mice Huijben et al., 2013, Huijben et al., 2010a, Huijben et al., 2010b.

Strain (i)	Human Studies		Mice Studies
	Full-dose SP	Full-dose SP	Full-dose Pyrimethamine	Half-dose Pyrimethamine
Drug Sensitive (w)	49 [21, 119]	14	11	15
Drug resistant (r)	315 [112, 882]	>28	22	22
Mixed Infection (wr)	315 [112, 882]	–	22	18
Reference(s)	Barnes et al., 2008, Barnes et al., 2008	Méndez et al. (2007)	Huijben et al., 2013, Huijben et al., 2010a, Huijben et al., 2010b	Huijben et al., 2013, Huijben et al., 2010a, Huijben et al., 2010b

Table C2.2.2

Expected gametocyte clearance in humans (days). The expected clearance of P. falciparum gametocytes in humans, using a linear interpolation of SP treatment in humans (Barnes et al., 2008, Barnes et al., 2008) and pyrimethamine treatment in mice studies (Huijben et al., 2010b, Huijben et al., 2013, Huijben et al., 2010a), using Eq. (C2.2.1). AEstimated using mice data where the 37.5% of a full-dose of pyrimethamine treatment used (Huijben et al., 2010b, Huijben et al., 2010a), whereas estimates from 50% of a full-dose of pyrimethamine treatment were used for the other parameter calculations (Huijben et al., 2013).

Strain (i)	Treatment (d)
	AL	Full-dose SP monotherapy	Half-dose SP monotherapy
Drug Sensitive (w)	28	49 [21, 119]	67 [29, 162] A
Drug resistant (r)	28	315 [112, 882]	315 [112, 882]
Mixed Infection (wr)	28	315 [112, 882]	258 [92, 722]

Table C3.2.1

Total area of average gametocyte density in Fig. C3.2.1, produced using estimates from Méndez et al. (2007).

Strain	Average gametocyte density
SP-sensitive (w)	0.055
SP-resistant (r)108-mutatnt	0.424485
SP-resistant (r) 51 & 108 mutant	0.4999

Table C3.2.2

The calculated total area of average gametocyte density in Fig. C3.2.3, produced using data from Huijben et al. (2013).

Strain	Treatment
	Full-dose pyrimethamine	Half-dose pyrimethamine
Pyrimethamine-sensitive (W)	4241.723	3769.852
Pyrimethamine-resistant (R)	6698.292	197.569
Mixed infection (WR)	10940.015	3967.421

Table C2.3.3.1

Infectiousness of gametocytes to mosquitoes after AL and SP treatment. Percentage of mosquitoes that become infected in membrane-feeding assays using blood samples from randomly selected children on day 7 post-treatment, by treatment arm. (Obtained from Table B.4 of Bousema et al. (2006).)

Treatment arm	Infected mosquitoes, % (proportion)	RR (95% CI)
SP	6.9 (52/750)	1
AL	3.6 (27/750)	0.52 (0.33–0.82)

Table C3.3.2

Infectiousness of gametocytes to mosquitoes after AL treatment. Gametocyte infectiousness among mosquitoes, by study arm. Blood samples taken on day 7 after initiation of treatment, with mosquitoes examined on day 7 after feeding. (Obtained from Table B.3 of Sawa et al. (2013).)

Variable	Proportion of Participants (%)
Individuals participating in membrane-feeding assays, no.	77
Microscopy finding on feeding day
Gametocyte prevalence	4.2 (3/72)
Gametocyte density, gametocytes/μL, geometric mean (95% CI)	39.5 (18.2–85.4)
Pfs25 QT-NASBA finding on feeding day
Gametocyte prevalence	21.7 (5/23)
Individuals infecting ≥1 mosquito	31.1 (24/77)
Infected mosquitoes, % (proportion)	1.9 (44/2293)
Oocysts in infected mosquitoes, no., mean [range]	1.3 [1, 2]

Table C3.3.3

A summary of the expected probability of transmission of each P. falciparum strain from human to mosquito during a blood meal, given the antimalarial treatment. ALow values believed to be a product of the experimental design to collect data.

Strain (i)	Treatment (d)
	AL (q)	Full-dose SP (m)	Half-dose SP (p)	No Treatment (n)
SP-sensitive (w)	0.05705	0.055	0.0489	0.200
SP-resistant (r)
108 mutant	0.05705	0.424485	0.0125 A
58 & 108 mutant		0.4999	0.0147 A	0.200
Mixed infection (wr)
108 mutant	0.05705	0.452	0.1639 A
58 & 108 mutant		0.527375	0.1913 A	0.200

Table D.1

Transmission parameters. A description of the transmission parameters used in the model. For parameter values where literature values were readily available, these values, along with the range of values and references are provided. For parameters that required further manipulation from the original source, the section of the Appendices where this parameter is discussed is noted. All parameter units are in days, unless otherwise stated.

Symbol	Parameter description	Value [range]	Reference
c	Biting rate of female An. Mosquitoes	0· 4050 [0.01, 0.5]	Anderson and May, 1991, Mandal et al., 2011
T_w	SP-sensitive sporozoite transmission (probability)	0.2 [0.2, 0.5]	Mandal et al. (2011)
T_r	SP-resistant sporozoite transmission (probability)	0.2 [0.2, 0.5]	Mandal et al. (2011)
Z˜_w	Overall transmission of SP-sensitive gametocytes (probability)	0.1459 [0.1313, 0.1605]	Appendix D2
Z˜_r	Overall transmission of SP-resistant gametocytes (probability)	0.1410 [0.1269, 0.1551]	Appendix D2
P_w	Fitness cost of resistance	0.6 [0.54, 0.66]	Appendix D1

Table E.1

Anopheles mosquito parameters. A description of the parameters specific to female An. mosquitoes used in the model. For parameter values where literature values were readily available, these values, along with the range of values and references are provided. For parameters that required further manipulation from the original source, the section of the Appendices where this parameter is discussed is noted. All parameter units are in days, unless otherwise stated.

Symbol	Parameter description	Value [range]	Reference
N_M	Initial ratio of mosquitoes to humans (humans = 1)	0.87 [0.5, 40]	Mandal et al. (2011)
ξ_Μ	Average life span of a female Anopheles mosquito in Kenya (days)	8–21	Labadin et al., 2009, Olayemi and Ande, 2008, Tchuinkam et al., 2010, Wanji et al., 2003
μ_Μ	Daily mortality rate of female mosquitoes	0.0280 [0.05, 0.5]	Mandal et al. (2011), Appendix E3
Ω_Μ	Daily rate female An. mosquitoes reach adulthood	0.0280 [0.020, 0.27]	Chitnisa et al., 2008, Labadin et al., 2009
Π_Μ	Latent period of mosquitoes (days)	5 [5, 15]	Mandal et al. (2011)
Γ_Μ	Proportion of mosquitoes that are infected with P. falciparum	0.40 [0.38, 0.83]	Mbogo et al. (2003)

Table F.1

Sensitivity analysis results. The changes in the predicted percentage of SP resistant-containing infections in humans during 2006, due to changes in parameter values. When required, values are reported to 4 d.p. A The literature parameter range is 0.020–0.27, however there were computational restrictions that only permitted a range of 0.020–0.1406 days for the sensitivity analysis.

Symbol	Description	Range (known range or ±10%)			Percentage change
		Baseline	Minimum	Maximum	Minimum	Maximum
N_H	Human population size (initial)	1	0.9	1.1	0.10	−0.12
N_M	Ratio of mosquito to human population (initial)	0.87	0.5	40	0.32	−20.55
P_w	Fitness cost in mosquito midgut	0.6	0.5	0.7	5.12	−6.60
μ_Μ	Mortality rate of female An. mosquitoes	0.028	0.0476	0.125	0.29	0.24
Ω_Μ	Rate female An. mosquitoes reach adulthood	0.028	0.020	0.1406A	0.26	−36.20
Π_Μ	Latent period of An. mosquitoes	5	5	15	0.00	0.20
D_M	Kenyan 2006 malaria deaths	74,970	67,473	82467	0.00	0.00
Y_M	Kenyan 2006 malarial cases	8,926,058	8,033,452.2	9818663.8	0.00	0.00
Ω_Η	Birth rate for humans	1.1349 × 10−4	1.0411 × 10−4	7.8811 × 10−4	0.00	−0.11
μ_Ι	Rate of malarial mortality in humans	0.0011	0.0010	0.0012	0.00	0.00
μ_Ο	Rate of “other” mortality in humans	3.1779 × 10−5	2.86 × 10−5	3.50 × 10−5	0.00	0.00
Π_Η	Latency period of asexual parasites in humans	9	9	14	0.00	−0.04
G_M	Maturing of gametocytes	2	2	3	0.00	−0.01
η	Delay in seeking treatment	1	0	2	−0.01	−0.04
c	Biting rate of female An. mosquitoes	0.405	0.01	0.5	0.19	−1.43
T_w	SP-sensitive sporozoite transmission (probability)	0.2	0.2	0.5	0.00	−86.98
T_r	SP-resistant sporozoite transmission (probability)	0.2	0.2	0.5	0.00	17.90
θ_n	Receive no treatment (proportion, at baseline)	0.2	0.09	0.2	0.57	0.00
θ_m	Receiving full-dose SP monotherapy (proportion, at baseline)	0.07	0.063	0.077	−0.52	0.54
θ_p	Receiving half-dose SP monotherapy (proportion, at baseline)	0.03	0.027	0.033	0.00	0.00
ε_w,q	SP-sensitive gametocyte clearance in humans treated with AL	14	7	28	9.20	−13.61
ε_r,q	SP-resistant gametocyte clearance in humans treated with AL	14	7	28	−15.52	8.65
ε_wr,q	Mixed infection gametocyte clearance in humans treated with AL	14	7	28	0.05	−0.04
ε_w,m	SP-sensitive gametocyte clearance in humans treated with full-dose SP monotherapy	25	21	119	0.52	−1.56
ε_r,m	SP-resistant gametocyte clearance in humans treated with full-dose SP monotherapy	112	112	882	0.00	0.26
ε_wr,m	Mixed infection gametocyte clearance in humans treated with full-dose SP monotherapy	112	21	119	0.01	0.00
ε_w,p	SP-sensitive gametocyte clearance in humans treated with half-dose SP monotherapy	29	29	162	0.00	−0.52
ε_r,p	SP-resistant gametocyte clearance in humans treated with half-dose SP monotherapy	112	112	882	0.00	0.12
ε_wr,p	Mixed infection gametocyte clearance in humans treated with half-dose SP monotherapy	92	92	772	0.00	0.00
ε_n	Gametocyte clearance in humans not treated	75	30	720	−0.04	0.02
Z_w,q	SP-sensitive gametocyte transmission when treated with AL (probability)	0.0537	0.0183	0.0537	5.69	0.00
Z_r,q	SP-resistant gametocyte transmission when treated with AL (probability)	0.0537	0.0183	0.0537	5.69	0.00
Z_wr,q	Mixed infection gametocyte transmission when treated with AL (probability)	0.0537	0.0183	0.0537	5.69	0.00
Z_w,m	SP-sensitive gametocyte transmission when treated with full-dose SP monotherapy (probability)	0.055	0.0495	0.0605	0.11	−0.11
Z_r,m	SP-resistant gametocyte transmission when treated with full-dose SP monotherapy (probability)	0.3	0.4245	0.4999	2.30	3.58
Z_wr,m	Mixed infection gametocyte transmission when treated with full-dose SP monotherapy (probability)	0.31	0.452	0.5274	−0.56	−0.87
Z_w,p	SP-sensitive gametocyte transmission when treated with half-dose SP monotherapy (probability)	0.0489	0.0440	0.0538	0.05	−0.04
Z_r,p	SP-resistant gametocyte transmission when treated with half-dose SP monotherapy (probability)	0.0147	0.0125	0.0147	−0.01	0.00
Z_wr,p	Mixed infection gametocyte transmission when treated with half-dose SP monotherapy (probability)	0.1913	0.1639	0.1913	0.05	0.00
Z_n	Gametocyte transmission with no treatment (probability)	0.2	0.2	0.5	0.00	−4.27
γ_R	Rate of acquired immunity	6.0864 × 10−4	5.4778 × 10−4	6.6950 × 10−4	0.00	0.00
ρ	Rate of loss of acquired immunity	0.0027	0.0024	0.0030	0.00	0.00