TMNT: Dynamic Models of Cancer and HIV

TMNT: Dynamic Models of Cancer and HIV

Differential equations are used to build dynamic mathematical models for systems and nonlinear phenomena, which dynamically change with time. Ordinary differential equations describe a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable. Applications of those models are found in biological systems. In one study, homogeneous mathematical models are used to describe the interactions between cancerous cells and the immune system. Modeling using differential equations will allow better understanding of the behavior and spreading of those malignant cells. The models will investigate the dynamics of populations of cancer cells, the mechanism of immune surveillance, whereby the immune system identifies and kills foreign cells, the interactions between cancer cells, immune cells, and other type of cells or signaling proteins and the interacting components of the tumor microenvironment. These mathematical models of differential equations will provide a simpler framework within which to explore the interactions among tumor cells and the different types of immune and healthy tissue cells. Another application of models is in HIV dynamics, which have aided significantly in AIDS research. Deterministic dynamic models are used to study the viral dynamic process for understanding the pathogenesis of HIV Type 1 infections as well as antiviral treatment strategies. This study estimates the parameters of a long-term HIV dynamic model containing constant and time varying parameters by using HIV viral load and CD4 + T cell counts.