Early transmission of Plasmodium vivax sensitive strain slows down emergence of drug resistance

Malaria remains endemic in multiple countries, in which interventions based on antimalarial drugs have had limited effect due to the spread of drug resistance. Majority of malaria cases are caused by the parasites Plasmodium falciparum and Plasmodium vivax and the evolution of drug resistance has a different temporal and geographic pattern between these Plasmodium species. In order to compare the different pattern, we develop here a compartmental model to estimate the effect of the monotherapies, combination therapies, the asymptomatic cases, the gametocytocidal use, the window of selection, the prophylactic period, and the resistance cost. The evaluation of the reproductive numbers and simulations showed the emergence of drug resistance in P. falciparum faster than P. vivax due to the highest effectiveness of the treatment against sensitive parasites but the delay to the emergence depends on the therapy. By contrast, the slower spread of drug resistance in P. vivax was produced by the transmission of sensitive parasites before the treatment and their transmission through the asymptomatic cases. These results suggest that improvements in the rapid attention can increase the risk of drug resistance and development of new therapies is necessary.

Introduction alaria mortality and morbidity rates produced about 435.000 deaths and 219 million human cases in 2017 [35]. Most cases are caused by Plasmodium vivax and Plasmodium falciparum parasites whose life cycles differ markedly. The development of antimalarial drugs has been the main strategy in malaria control allowing the decrease in the disease prevalence during the last decade. However, the emergence of drug resistance has decreased the antimalarial effectiveness, remaining as a challenge in the malaria control [36].
Currently, the evidence shows an evolution in drug resistance with different temporal and geographical patterns between P. vivax and P. falciparum parasites. For instance, the current first-line treatment suggested to treat the infection by P. vivax parasite in most endemic regions is the administration of chloroquine (CQ) [20]. In contrast, the suggested treatment for malaria infection by falciparum parasite is the artemisininbased combination therapy (ACT) because monotherapies as chloroquine (CQ) are ineffective due to reports of cloroquine resistance dating from 1950 in South America, Southeast Asia and subsequently spread to all endemic regions between 1960 to 1970 [37,38].
In the P. falciparum case, ACTs had their efficacy decreased in the Greater Mekong sub-region since the first report of treatment failure in 2008 [39,40]. On the other hand, CQ resistance by P. vivax has been confirmed in Indonesia and New Guinea but cases can be underestimated due to the recurrences in P. vivax infection are also caused by the hypnozoites relapse [41]. As a consequence of reports of CQ resistance in P. vivax, WHO has issued the use of ACTs to treat P. vivax cases as an alternative but CQ remains as the first-line option [20].
In order to explain how P. vivax and P. falciparum evolved towards drug resistance with different patterns, previous researches have evaluated a few biological factors associated with the parasite life cycle. An initial hypothesis involved different selection pressure by immune response against merozoites in P. falciparum and P. vivax caused by difficult recognition of P. vivax antigens [42]. Moreover, the early gametocyte relapse in P. vivax, i.e. before treatment, and longer life span in P. falciparum gametocytes were analyzed in an evolutionary model where a high frequency of 2/31 resistant P. falciparum parasites was achieved in less time than P. vivax due to the long selection period after treatment in P. falciparum [12].
Despite previous studies testing different evolution of drug resistance between Plasmodium species, most of the previous studies have been focusing in P. falciparum drug resistance [40]. This is the case of the evaluation of the selection force in P.
falciparum parasites through the window of selection, WoS, that represents the period post-treatment where the resistant parasites can emerge by the drug selection [13].
Additionally, previous studies evaluated the selection force in P. falciparum through the potential transmission showing that resistant strains have a reduction in the relapse of gametocytes between 0% to 60% in comparison to the wild type strains [18,19].
Another important property in the spread of drug resistance is the geographical pattern that is accelerated in zones of low transmission conditions as South America and Southeast Asia, in contrast with endemic zones in Africa [40]. Hamza et al. suggest that asymptomatic cases in high transmission conditions help to carry the population of wild-type parasites avoiding the spread of resistant strains [43].
Moreover, the existence of co-infection between sensitive and resistant strains in high transmission conditions make a competitive advantage to the wild-type due to the fitness cost associated with the resistance [26].
In order to estimate the effect of determinants in the spread of drug resistance and the malaria transmission, mathematical models have been a useful tool to evaluate this dynamic [44]. This kind of models have evaluated the emergence and the spread of drug resistance according to the selection force of some treatment regimens [12,13,25,32,44,[52][53][54][55]. Besides, models of transmission dynamics in human populations have allowed to estimate the effect of campaigns with drug administration to achieve malaria control and elimination [4-7, 15, 16, 22]. However, these models have been developed to P. falciparum transmission only. We compare the effect of the drug campaigns on populations affected by P. falciparum and P. vivax parasites to find determinants in their different pattern of drug resistance. Moreover, the results can be extended to make suggestions in the control programs using antimalarials.

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1 Models of drug resistance dynamics In the current section, we present two models to represent the dynamics of malaria drug resistance to the cases of P. falciparum and P. vivax separately to compare the effect of the drug administration in the emergence and spread of drug resistance involving the differences between life cycles of these Plasmodium species. Both approximations were based in the compartmental Ross-Macdonald models with states in a human and mosquito populations [48]. Model parameters are described in the

Model features
In order to explain some model features, we listed a set of important key points involved in the modeling scope.
• Resistance cost: the modifications in a resistant genotype can imply a fitness cost in the parasite development. This cost is measured as a reduction in the growth rate, parasite density and parasite persistence that produce a decline in the infectiousness and the infectious period [19].
• Prophylaxis period: after applications of an antimalarial, the patient takes a period of time to eliminate the drug. This period is denominated prophylaxis period because the drug continues acting and it confers a temporally protection against new infection. This period varies with the applied treatment [57].
• Window of selection (WoS): a period during the prophylaxis when the drug concentration eliminates sensitive parasites while partial resistant parasites can emerge [32]. During this period, the resistant parasites can be transmitted.
• Asymptomatic contribution: these individuals are considered as parasite reservoirs because they are be able to transmit the parasite without the control of antimalarials [8]. This condition is associated with the immunological evolution of the host by the frequent exposition to the pathogen. Nevertheless, the infectious capacity of an asymptomatic host can be considered lower than a symptomatic [58]. infected mosquitoes by sensitive strain and I mf r infected mosquitoes by resistant strain states, as shown in Figure 1. This model represents a wild type strain (sensitive) and a resistant strain that can be originated by the parasite selection during the window of selection in the prophylaxis state P f s . 5/31 Where the human population N h and the mosquito population N m are The equations of the model are presented from the equations 1 to 8, and the model parameters are described in Table 1. In the model, the resistant strain has transmission probability lower than the sensitive strain because the decrease in the gametocytes density as consequence of resistance cost [19]. To model this behavior, we define the term (1 − ) that reduces the transmission rates between infected humans by resistant strain and susceptible mosquitoes in a percentage. Furthermore, our model includes a prophylaxis state in humans representing individuals treated for a prophylaxis period of time. This prophylaxis state takes into account the effect of the parasite selection within human host post-treatment. In this state, humans remain infectious because gametocytes remain in the blood while the drug is eliminating during the WoS at 1/κ rate [12]. In fact, the selection given from the drug allows the humans in prophylaxis state by sensitive parasite to develop a resistant parasite that can be transmitted to a susceptible mosquito with a ν probability that varies according to the drug therapy [21]. Nevertheless, a human in P f s state is able to transmit a sensitive parasite with a likelihood of 1 − ν.
A human infected by resistant strain has the same recovery time from an infected by the sensitive strain but it has n recurrences due to resistance effect with rate γ f r = γ f s /(n + 1). Hence, the average infectious period in I f r is (1/γ f s )(n + 1) .
Moreover, the average time of prophylaxis (or infectious period in prophylaxis) by the resistant strain depends on the number of recurrences (k(n + 1)).
Finally, we made the transmission blocking effect of the inclusion of a gametocytocidal as primaquine (PQ) [20]. Consider the parameter ϕ as the proportion of treated humans with gametocytocidal that do not have the potential to transmit the parasite. The treated humans correspond to the P f s and P f r states and we penalized the infectious potential to susceptible mosquitoes multiplying the falciparum case, the resistant strain can be originated by the parasite selection during the prophylaxis state P vs .
Where the human population N h and the mosquito population N m are The latent state represents the humans that were infected by P. vivax but they remain with hypnozoites that are be able to produce new recurrences of the disease.
An individual stays in latent state for hypnozoites development in either an untreated human or a treated human. The equations of L vs and L vr include that the untreated proportion of infected humans ((1 − ησ v )I v ) has a φ u probability of passing to latent state after it recovers. On the other hand, when an infected human is treated and progress to prophylaxis state, there is a probability φ t (1 − ϕ) that the infection will turn to latent state. In the P. vivax case, we assume that gametocitocydal also attacks hypnozoites as the primaquine works and for this reason we join the (1 − ϕ) term [20].

Basic reproduction number
Here we derive the basic reproduction number using the next generation matrix proposed in [3,50,51]. The first step is to assume a constant population in humans N h and mosquitoes N m where Λ h = 0, µ h = 0 and Λ m = µ m . In this way, we can use the 10/31 disease free disease-stable steady state where the human and mosquito populations are

Analysis of basic reproduction number R 0 for P. falciparum
We obtained two reproduction numbers associated with the sensitive strain R 0f s and the resistant strain R 0f r (equations 19 and 20).
For both compartments of infection due to sensitive or resistant strains, the basic reproduction number is proportional to the the number of mosquitoes per human, the biting rate and the transmission probabilities b, c a and c s . On the other hand, R 0 decreases with recovery rate in human and the death rate in the mosquito population.
In the R 0f s case, the expression 19 involves the κc s (1 − ν)(1 − ϕ)ησ f γ f s term that represents the transmission rate of a human in prophylaxis of a sensitive strain.
Actually, this term increases R 0f s because the strain has an additionally way to survive when a treatment is used without a gametocytocidal.
On the other hand, R 0f r involved a reduction by the resistance cost transmission with the product with the expression (1 − ). Similar to deriving R 0f s , R 0f r has a term that represents the contribution of humans in prophylactic state. In this manner, it is necessary increase the recovery rate using a treatment or implement programs to reduce the transmission rates to obtain malaria control.
The growth of the resistant strain depends on the reproduction number where the resistant strain increases its frequency above the sensitive strain when R 0f r > R 0f s .
The balance between strains depends on the drug coverage η where the condition to avoid the increase of resistant cases is R 0f s > R 0f r . In order to compare the basic reproduction number along the coverage variation with the effect of the resistance cost 11/31 , the gametocytocidal coverage ϕ,the window of selection κ and the symptomatic proportion of cases σ f , we calculated the basic reproduction numbers (see the Figure   3).  Table 2 The 2.2 Analysis of basic reproduction number R 0 for P. vivax As the P. falciparum case, we derive expressions for the basic reproduction number R 0vs in the case of sensitive strain and R 0vr in the case of resistant strain, as follows.

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The  (Figure 4). It is important to remark that the increase in the drug coverage decreases the reproduction number at less rate than the reproduction numbers of P. falciparum and it suggests that the drug coverage is less effective against the P. vivax parasite.
In the case of the resistance cost, R 0vs always is greater than R 0vr with resistant 13/31  Table 2 cost greater or equal than 0.  Table 2 3

.2 Campaigns against infected by P. vivax
We evaluated the P. vivax model without effect of superinfection in latent state such that most of the recurrences are produced by the hypnozoites release as observed in some endemic regions [22]. The results are in the Figure 6 where we can see longer periods of time before the emergence of the resistant strain in contrast to the P.
falciparum results. Nevertheless, the drug coverage against infected by P. vivax is less 16 Table 2 effective than the campaigns against P. falciparum because the proportion of infected by P. vivax were greater in all the scenarios.
The emergence of the resistant strain started around the 20 th year, when only monotherapy is applied. Also, in this case the proportion of I vs was 42% and L vs was 45%. Actually, the campaign effectiveness is poor in terms of the prevalence reduction because the large proportion of asymptomatic cases (1 − σ v = 0.66 → 66%) does not let the use of an effective drug coverage and it produces an underestimate of the real disease prevalence. Moreover, γ f s < γ vs produces a greater infectious period in an P.
vivax infected due to the premature relapse of gametocytes [12]. This situation allows

Discussion
The emergence of drug resistance in P. falciparum and P. vivax has happened with different patterns in time and efficacy. For instance, Chloroquine remains as the first-line treatment for malaria caused by the P. vivax parasite [20,23], though it has not been recommended for treatment of P. falciparum infections. Nevertheless, the P.
vivax resistance to chloroquine has been widespread in some endemic zones, as an evidence that this parasite has this selection possibility in a different rate from P.
In order to explain the pattern of resistance evolution, we studied the differences between life cycles, the kind of therapy, the resistance cost, the infectious period, the window of selection and the asymptomatic cases. Our results show that the drug 18/31  Table 2 resistance in P. falciparum appears faster than in P. vivax using the same treatment line.
First, we found that a resistance cost of 30% or less in the transmission allows a resistant strain to have a greater reproduction number than a sensitive strain where the emergence of drug resistance is imminent for both Plasmodium species. Our estimate value is within the range of the estimated resistant cost of previous research in the field of within host dynamics and transmission intensity [18,19,25,26]. Thus, resistance costs under transmission above 30% produces an imminent spread of drug resistance in a similar proportion to P. falciparum and P. vivax. Nevertheless, the period before the emergence of the resistant strain depends on the other factors as we can see in the previous section where we used a fixed resistance cost obtaining different emergence times in the resistant strain.
Our results show that the infectious period in infected humans is the most 19/31 important factor that enables a premature emergence of drug resistance in P.
falciparum. An infected human by P. vivax has an infectious period, longer than the one for P. falciparum, before receiving treatment, permitting transmission of sensitive parasites, and delaying the emergence of a resistant strain [12,27]. However, this infectious period before the treatment decreased the effectiveness of the drug therapy trials as we can appreciate in the reproduction numbers in P. vivax. Moreover, this statement implies that a reduction in a infectious periods before the treatment caused by the successful therapies, rapid attention and the rapid diagnostic test allows the increase of the risk in the spread of drug resistance.
As result of the evaluation between monotherapy and combined therapy, we remark the best effect of a combined therapy against the spread of drug resistance [20,28].
The explanation is the lower mutation probability against multiple components in a combined therapy than a monotherapy [21]. Currently, the first-line treatment against P. falciparum is the use of artemisinin based combination therapy (ACT) that has been administrated since the first decade of the 21 st century besides the resistance reports in the Greater Mekong sub-region [29]. Therefore, ACT is highly recommended after the emergence of CQ resistance to treat malaria caused by P.
vivax. In fact, accelerating the development of triple combination therapies to use against P. falciparum malaria deserves attention, due to reduction in the mutation probabilities [30].
The variation of the window of selection (WoS) did not have a relevant effect in the emergence of a resistant strain because it had the same impact against the reproduction numbers in both sensitive and resistant strains of both Plasmodium species. However, the competence between multiple strains in a single host could make differences between the strains development in presence of the drug administration but the current research do not achieve multiple infection and it can explain the obtained behaviour with respect at the WoS [26].
On the other hand, the inclusion of gametocytocidal produces in an acceleration in the emergence of resistant strain in overall simulated campaigns whereas it obtained a different performance against disease prevalence between the malaria species. In the P.
falciparum case, the gametocytocidal reduced the prevalence of infected humans, suggesting that the WHO recommendation of a single dose of primaquine (PQ) to 20/31 avoid the transmission of sexual stages has a beneficial effect in the malaria control [20]. By contrast, the gametocytocidal accelerates the emergence of the resistant strain in P. falciparum due to the reduction in the transmission of sensitive parasite during the prophylactic period. Moreover, premature drug resistance was also present in P. vivax but in this case primaquine has an additional effect to clear hypnozoites. The results in P. vivax shows the increase in the population of infected humans by the inclusion of gametocytocidal because the reduction in the humans in latent state produces a rise up in susceptible humans using the model structure.
On the other hand, the asymptomatic cases decreased the drug coverage and the effectiveness against the sensitive strain in both Plasmodium species. Thus, an elevated drug coverage would imply a less pronounced effect against the resistant strain producing the spread of drug resistance and the asymptomatic cases supports the transmission of the sensitive strain delaying the drug coverage outcome.
Furthermore, our results are in accordance that control of P. vivax using drug administration is difficult since most cases are asymptomatic [9]. Although the contribution of asymptomatic infections remains unclear and previous research shows a variable potential of asymptomatic in the transmission, our results achieve an estimation of the contribution in the parasite transmission [33,34].
Our findings suggest that the emergence of drug resistance can be delayed to the P.
vivax parasite but the malaria control against it is more difficult to achieve than to the P. falciparum parasite. We observe that more effectiveness in the campaign for reducing the prevalence of P. falciparum reaches a premature spread of drug resistance. By contrast, the simulated campaigns against P. vivax parasite shows less effectiveness in the reduction of the infection prevalence than P. falciparum but this result produces a delayed spread of drug resistance.
In order to compare the emergence of drug resistance, we found previous works that have monitored drug resistance in specific regions [46,47]. In Kenya CQ resistance is near 100% after more than ten years of administration, in accordance In conclusion, the current study shows that the drug resistance evolves faster in P.
falciparum because the treatment on the infected population decreases the transmission of sensitive parasites allowing a competitive advantage in resistant parasites. On the other hand, the slower spread of drug resistant in P. vivax was due to the transmission of sensitive parasites before the treatment and the higher proportion of asymptomatic infections than P. falciparum. Nevertheless, this behaviour in P. vivax implied that the campaigns against the disease prevalence were less effective than P. falciparum. Thus, the improvements in the rapid testing, drug coverage, primaquine use, treatments to asymptomatic cases can increase the risk of drug resistant and the development of new combination therapies is necessary to delay the spread of resistant strains. Transmission probability from an infected asymptomatic human to susceptible mosquito c s Transmission probability from an infected symptomatic human to susceptible mosquito ν Transmission probability of a resistant strain from a human in prophylactic state by sensitive strain to a susceptible mosquito. ψ Hypnozoite relapse rate ρ sr Probability of developing sensitive infection by the contact between an infected mosquito by sensitive strain and a human in latent state of the resistant strain ρ rs Probability of developing resistant infection by the contact between an infected mosquito by resistant strain and a human in latent state of the sensitive strain φ t Probability of a human in prophylaxis state of going to latent state φ u Probability of an untreated infected human of going to latent state µ vl Clearance rate of hypnozoites