EQUILIBRIUM AND QUASI-STATIONARY STATES OF NON-LINEAR AGE-STRUCTURED MONOCYCLIC CELL POPULATION MODEL

Last modified: 2014-03-28

#### Abstract

Our work devoted to the study of evolutionary dynamics of monocyclic age-structured cell population including effect of non-linear mortality (population growth feedback) and proliferation. The total population is considered as partitioned by fixing age into two subpopulations. Cells of first population are born, mature and at fixed age can divide with some probability; each of them can give birth for two new cells with null age. Cells of second subpopulation are older than dividing age and loose possibility to proliferate. This model was considered as the system of two initial boundary value prob-lems for non-linear transport equations with non-local boundary conditions. We obtained explicit “travel-ling wave” solution with restrictions for the set of incoming parameters which guarantee its continuity and smoothness. Explicit solution of system allowed us to perform numerical experiments with high ac-curacy exploiting the set of parameterized algebraic functions. We obtained and studied two different types of population dynamics. First is equilibrium, when the system attracts to the initial state due to bal-ance between effects of proliferation and non-linear mortality (like behaviour of microorganism popula-tion in the cases of asymptomatic or healthy carriers). Second is quasi-stationary state when the maxi-mum value of population density in time attracts to the constant value higher or lower than initial one. We studied also the influence of non-linear mortality parameters on the tremendous growth of population density followed by transition to quasi-stationary states (like infection generalization process in living organisms).

#### Keywords

Evolutionary dynamics. Monocyclic cell population. Non-linear mortality. Equilibrium and quasi-stationary states.