Environment change, geographic migration and sickle cell anaemia

The classic model describing the interaction between sickle cell anaemia and malaria is one of the most notable achievements of population genetics. Nevertheless, only panmictic populations in steady environments have been studied theoretically to date. In this paper, environment change and geographic inhomogeneity are introduced. The rate of decrease of mutation after environment improvement is obtained. The kinetics of the spread of disease after the initial mutation, together with the genetic composition profile near the borders of malaria areas, are calculated. The results are compared with the empirical data on the mutation level in African and African-American populations. It is shown that the spread of disease and decrease in mutation are highly asymmetric: the mutation level increases exponentially and decreases much more slowly (as a power function). The mathematical and biological reasons for this behaviour are discussed.[PUBLICATION ABSTRACT]