Population Dynamics of Children and Adolescents without Problematic Behavior

In this work we suggest a simple mathematical model for the dynamics of the population of children and adolescents without problematic behavior (criminal activities etc.). This model represents a typical population growth equation but with time dependent (linearly decreasing) population growth coefficient. Given equation admits definition of the half-life time of the non-problematic children behavior as well as a criterion for estimation of the social regulation of the children behavior. It is well-known [1-3] that population of the children and adolescents without problematic behavior (criminal activity, use of the alcohol and narcotic drugs, etc.) has an interesting dynamics. This population firstly (till some critical time moment) increases and later (after given critical time moment) quickly decreases during time. (Given population dynamics correlates to dynamics of the positive influence of the parents and society at children and adolescents.) In this work we shall suggest a simple mathematical model for given population dynamics. This model represents a typical population growth equation but with time dependent (linearly decreasing) population growth coefficient. Given equation admits definition of the half-life time of the nonproblematic children behavior as well as a criterion for estimation of the social regulation of the children behavior. So, we suggest the following first order differential equation d(x − c) dt = (a − bt)(x − c). (1)