Antimalarial drugs have been used as one of the main strategies for controlling this disease. However, the spread of drug resistance in the Plasmodium falciparum parasite has generated major challenges for the control of malaria. For this reason, it is necessary to develop an efficient policy considering the parasite behavior in relation to drug treatment and epidemiological parameters. To achieve this goal, we propose a mathematical model that describes the dynamics of parasite population considering the transmission effects between mosquitoes and humans. In order to quantify the drug treatment effect on humans and the generation of new parasite genotypes within the mosquito, the parasite population was divided into those found in humans and mosquitoes. To test the model, we simulate several parasite populations, related with pyrimethamine resistance, in high and low transmission conditions. Simulation results show the dynamics of different parasite populations depending on drug coverage and the effect of epidemiological parameters. These results show that disease elimination may not be possible by using only pyrimethamine treatment, so we include different control strategies and we observe that reducing contacts between mosquitoes and humans helped the drug coverage to reduce the prevalence of disease. Finally, this model is used to propose an optimal policy that minimizes disease prevalence; the principal result is that the most effective coverage of the drug is around middle coverage. The model can also be used to evaluate not only pyrimethamine treatments, but it can be adapted for the study of resistance to other drugs.
Keywords: Drug resistence; Malaria; Mathematical model; Optimal control; Plasmodium falciparum; Pyrimethamine.
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