About a modification of Rogers model of parasite-host system dynamics

摘要

In current publication there is the consideration of mathematical model of parasite-host system dynamics for the populations with non-overlapping generations. Within the framework of considering model it is assumed that appearance of individuals of new generation correlates with the death of individuals of the previous one. It is also assumed that between time moments of appearance of individuals of new generations there are the monotonous and independent decreasing of population sizes of interacting species in a result of influence of self-regulative mechanisms and natural death. All survived individuals of the host produce the eggs synchronically, and part of these eggs is attacked by parasites. In model it is assumed that the time for the appearance of hosts and parasites from the eggs is much less than the length of time interval between closed generations. It allows describing of the process of appearance of new generations as "jumps" in changing of population's sizes. For considering model the dynamic regimes of interacting populations are analyzed for various values of model parameters and various assumptions about mechanism of interaction of species. In particular, there is the determination of conditions for parameters when the regimes of population outbreaks are observed in model.