Mathematical Modeling of the Effect of Inbreeding on Homozygosity of Recessive Disease-Associated Alleles: A Case Study of Afghanistan

Consanguineous marriage can increase the probability of offspring homozygosis for recessive disease-associated alleles. However, parental relatedness, genetic homozygosis, and clinical disease are distinct concepts. This study develops a probabilistic framework to examine their relationships while distinguishing modeled outcomes from individual clinical risk. A single-locus model defines the probability of homozygosis as , where q is the allele frequency and F is the inbreeding coefficient. A modeled index, , is introduced to represent the simplified role of penetrance. The framework also considers multilocus homozygosity, an alternative threshold model, and the distinction between pedigree inbreeding and population structure. The case study draws on published cross-sectional data from couples in eight Afghan provinces, where consanguineous marriages accounted for of the sample and the mean inbreeding coefficient was . Monte Carlo simulation and sensitivity analysis were conducted using and samples, respectively. Under the illustrative distributions , , and , the simulated mean of R was approximately The results indicate that increases with when and are held constant. These findings demonstrate how probabilistic modeling can clarify the relationship between inbreeding and homozygosity under specified assumptions. However, the modeled index is not an epidemiological estimate of disease prevalence or individual clinical risk in Afghanistan; such interpretations require independent genetic and clinical data.