Genetic-Mathematical Modelling of the Populations Interaction

The solution of a genetic-mathematical problem of interaction of the human population cells and virus population to a problem of pandemic COVID-19 is submitted. The mathematical model based on the Hardy - Weinberg law consisting of two interdependent differential equations is used. The equations reflect time dynamics of the human cells and virus populations during their interaction. Solutions of the differential equations are found and results of these solutions are analyzed. The estimation of duration pandemic is received at use of parameters of the human liver cells and a flu virus.

Inbreeding in a Family Tree and in a Population

On the basis of Hardy – Weinberg’s law the problem of inbreeding in a family tree and a population was investigated. With use of an inbreeding factor are received the discrete equation for a family tree and differential equation for a population. The numerical solution of the differential equation for a population was found and analyzed at various values of the inbreeding factor. Migration of inbred population is investigated in view of natural selection. It was shown that velocity of migration falls with increase of the inbreeding factor. Interrelation of the recessive allele frequency at woman for a migrating population with inbreeding factor and standard parameter of selection was found.

Migration of a Population

On the basis of Hardy – Weinberg law the problem of migration from the genetic point of view is considered. It is proved the linear differential equation of migratory process of a panmictic population. The phase of the solution of this equation is investigated. On the basis of the carried out analysis the dependence of migration velocity of a population on average time of alternation of generations is found. It is shown that migration of primitive people from Africa to Europe needed alternation the several hundred generations. The dependence of migration velocity of a population on the average area developed by a population for year is investigated. Lacks of the carried out analysis owing to absence of the account of natural selection and inbreeding are marked.

Natural Selection in a Population is a Problem of Nonlinear Genetics

The problem of natural selection against recessive homozygotes in a population is investigated. It is shown that natural selection of mutant alleles linked with the Х-chromosome in a population at women is described by the nonlinear differential equation of the third order. The order of the differential equation characterizes a power of selection. It is marked that the high order of the differential equation of natural selection allows level all mutational processes in Earth populations.

Genetic-Mathematical Modelling of Mutational Processes in a Population

Processes of genetic-mathematical modeling of a population development are considered. A basic distinction in the mathematical description of a family tree and a population is shown. In a family tree alternation of generations has discrete character. In a population there is a continuous alternation of generations. The method of the differential equations is applied for the description of a population. It is shown that mutational process in a population can be described with use of a Green’s function. For radiating influence on a population the universal evolutionary law is found.