Perturbing Coupled Multivariable Systems

All populations in nature experience different types of external perturbations that regulate their abundance and dynamics. These can range from environmental changes to demographic events such as migration. In interacting populations such as the host-parasite system, harvesting, culling, vaccination, quarantine, and segregation type of events are commonly used to control population abundance. There has been much work on the role of migration on population dynamics, and several parasitic diseases have been modeled to describe and predict the spatiotemporal spread of host-parasite populations. But a comparative study of the response of each variable (i.e. the host and parasite) to external perturbations such as described above is not available—both in theory and experiments (epidemiological data). We have studied the discrete host-parasite model where the host follows the logistic growth and the parasite grows only on the host. The dynamic response of this system to constant external perturbation is studied mathematically and numerically. We have shown the role of constant addition/removal of individuals from populations in controlling the complex dynamics that is exhibited by this discrete host-parasite system. Our results show that the response of the host and parasite populations to specific (i.e. when only one of the populations is affected) and to general (that acts on both host and parasite populations) perturbations are quite different. Thus reducing the parasite population and segregating the hosts from the population may have opposite effects. We also demonstrate the effect on lattice metapopulation models of the host-parasite system. Our results imply that the dynamic response of nonlinearly coupled multivariable systems to external perturbation depends not only on the type of the perturbation but also on the specific variable being perturbed and the interaction among them. This may help plan intervention strategies in host-parasite populations.