Understanding the spread of color blindness via population genetics model

Abstract

Color blindness is a lifelong disease caused by damage to the eye’s nerve cells’ pigment that reacts to color and light. As a result, a person suffering from this disease will have difficulty distinguishing specific or all colors. Although only a small number of people suffer from this disease, and it does not harm the sufferers, this disease can interfere with their daily activities. Interestingly, the proportion of color-blind people varies by ethnicity, geographic area, and gender. We construct a mathematical model to understand population dynamics in the spread of genetic-based color blindness with a particular concern of gender factors, involving a random mating process between men and women. The stability of the equilibrium point is analyzed in detail, and the model’s suitability with the Hardy-Weinberg equilibrium principle is examined. We found that the proportion of colorblind people in the future (equilibrium) depends on the initial conditions of the population and is more sensitive to the initial condition of the color blind women than that in men or carrier women. Furthermore, we also found that the ratio of color blindness in men is constantly higher than in women. Finally, the numerical simulations of data in Korea and Northern European countries are presented to confirm our analytical results.