The control and propagation of a genetic disease

Preventive health is an appealing method to better our quality of life. However, in the practice of preventive health, its probabilistic nature and the time lag for results lessen its appeal. The specter of genetic diseases also has a probabilistic nature but has a time lag that spans generations. Thus any preventive health effort for genetic diseases should be studied so the results can be predicted in advance. A number of mathematical genetic problems have been solved that include mutation and phenotype selection factors. This paper takes a large human population that has birth and death frequencies that vary with age and that operates under Mendelian genetics. Hypothetical mutation and backmutation rates are put into this population; this results in an adverse effect on the death rate for those individuals born with homogenously mutated genes. This is called a genetic defect. The mutated genes are carried in the gametes of individuals who are born with the genetic defect and those who are exposed to the mutation rates; their manifestation is an increased probability of producing method gametes for reproduction. The preventive health control effort is birth control after genetic counseling. Various combinations of birth control selection effectiveness are tried on the different genotypes. It is found that a high selection factor for homogenously mutated genotypes gives the best result for reducing excess deaths caused by the genetic defect, and that a selection factor for heterozygous genotypes is a counterproductive effort. This model, employing a set of difference equations, may be used to evaluate preventive health policies on the control of genetically linked diseases such as sickle cell anemia, which affect the death rate of afflicted individuals. Also, effects other than death rate may be incorporated to evaluate policies on genetic diseases such as retinal blastoma.