Models of Applied Population Dynamics

The paper is an overview of our recent results achieved with different coauthors, concerning several research lines of applied population dynamics we initiated some years ago, and mostly published in 2010. First, based on the classical Leslie population model, a dynamic demographic model including controlled immigration is recalled, and applying the Perron-Frobenius theory of nonnegative matrices, a convergent optimal control algorithm is given, in order to address the sustainability problem of the considered pay-as-you-go pension system. Then, concerning the monitoring problem of particular population systems, observer design for certain trophic chains is presented. Furthermore, considering a fish population with a reserve area, we deal with the problem of steering the population into a desired new equilibrium, applying a timedependent fishing effort as a control function. To this end, an optimal control problem is set up, which is numerically solved using an optimal control toolbox developed for MatLab. Finally, for the analysis of the efficiency of certain agents to be applied in biological pest control, corresponding mathematical models are presented that describe the dynamics of the interaction between predator, parasitoid and pest insect populations.