We consider a gene with two alleles. Allele A is normal, allele S is abnormal. Individuals with genotype SS have a severe disease called sickle-cell disease. Individuals with genotype AS are not sick, and it is thought that they are more resistant to malarial infection than individuals with genotype AA. This could explain why the allele S has persisted in regions where malaria is endemic. We use a stochastic spatial process to test this hypothesis. For our model, we show that if the genotype AS has an advantage over the genotype AA, then the allele S will persist in the population even if the genotype SS is not viable.
"A stochastic spatial process to model the persistence of sickle-cell disease." Ann. Appl. Probab. 9 (2) 319 - 330, May 1999. https://doi.org/10.1214/aoap/1029962744