Wheldon model of CLM revisited

Abstract

The Wheldon model (1975) of a Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of recent discovery that this model has a major drawback. To reanimate the Wheldon model, we used late Wheldon´s remarks and M. C. Mackey ideas to introduce a new mechanism. To further enrich the model, we introduced time-varying microenvironment and time-dependent drug efficacies. The resulting model is a special class of nonautonomous nonlinear system of differential equations with delays. The global existence and positiveness of the solutions of the Wheldon model are examined. Furthermore, via topological methods, the existence of positive periodic solutions is proved.