Models of nutrient-plankton interaction with a toxic substance that inhibits either the growth rate of phytoplankton, zooplankton or both populations are proposed and studied. For simplicity, it is assumed that both nutrient and the toxin have the same constant input and washout rate. The effects of toxin upon the existence, magnitude, and stability of the steady states are examined. Numerical simulations demonstrate that the system can have multiple attractors when phytoplankton's nutrient uptake rate is inhibited by the toxin.

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We investigate the effect of migration between local populations of a single discrete-generation species living in a ring or an array of habitats. The commonly used symmetric dispersal assumption is relaxed to include the biologically more reasonable asymmetric dispersion. It is demonstrated analytically that density independent migration has no effect on the equilibrium stability of individual populations. However, the positive equilibrium may be destabilizing if the migration is density dependent in such a way that it increases with increasing population density at the source patch.

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Immunotherapies are important methods for controlling and curing malignant tumors. Based on recent observations that many tumors have been immuno‐selected to evade recognition by the traditional cytotoxic T lymphocytes, we propose mathematical models of tumor–CD4+–cytokine interactions to investigate the role of CD4+ on tumor regression. Treatments of either CD4+ or cytokine are applied to study their effectiveness. It is found that doses of treatments are critical in determining the fate of the tumor, and tumor cells can be eliminated completely if doses of cytokine are large. Bistability is observed in models with either of the treatment strategies, which signifies that a careful planning of the treatment strategy is necessary for achieving a satisfactory outcome. Copyright © 2014 John Wiley & Sons, Ltd.