Interactions Between the Frequency of the Duffy Antigen and the Dynamics of P. vivax Malaria Infections

The malarial parasite Plasmodium vivax has infected humans for millennia. As such, alleles like the FY*O allele in the Duffy Antigen Receptor for Chemokines (DARC) andthe sickle cell allele (HbS) have been naturally selected for in malaria-endemic regions because they confer resistance to malaria, thereby increasing the survival and reproductive success of individuals carrying these protective alleles. As resistance becomes more common in a population, malaria incidence is expected to decline, reducing the evolutionary pressure for additional resistance. In this work, we explore the interaction between these processes. We construct a model with seasonality that tracks the frequency of Duffy genotypes and leverages fast/slow dynamics to analyze the coupled dynamics of malaria transmission and changes in the gene frequency of the DARC genotype. Specifically, we investigate how the burden of malaria changes with the fractions of people with the various DARC genotypes. We derive the basic reproduction number as the threshold condition for the stability of the disease-free equilibrium and interpret the R_0 as a weighted sum of the cases generated by infected individuals of each genotype. Additionally, we calibrate our model using data from the Amazonas region in Brazil, which has a polymorphic population with respect to DARC, and still reports a substantial number of P. vivax cases. Analysis of our model determines the proportion of the population that must be Duffy-negative in order for the entire population to be protected against P. vivax without any further interventions. Furthermore, we assess how different proportions of Duffy-negative individuals influence the monthly incidence of P. vivax cases.