Model of dynamics of the insect cellular immune system

A mathematical model for the dynamics of functioning of an insect immune subsystem is considered. It is assumed that the interaction between hemocytes and bacteria corresponds to the Volterra principle of "pair interactions": the rate at which bacteria enter the system decreases in proportion to the rate of interaction of hemocytes with bacteria. In the absence of interaction, the intrinsic dynamics of bacteria is described by the Malthus law. Dynamic regimes of the model for different values of the parameters were analyzed. In particular, it was shown that, depending on the initial values of variables and the values of the parameters, there exist two regimes, the regime of death of the organism and the regime of elimination of bacteria.