T model of growth and its application in systems of tumor-immune dynamics

Mohammad A Tabatabai1, Wayne M Eby, Karan P Singh

  • 1Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA. mtabatabai@cameron.edu

Related Concept Videos

Tumor Immunotherapy01:27

Tumor Immunotherapy

Immunotherapy is a treatment that boosts or manipulates the immune system to fight diseases, including cancer. For instance, by stimulating an immune response through vaccinations against viruses that cause cancers, like hepatitis B virus and human papillomavirus, these diseases can be prevented. Nonetheless, some cancer cells can avoid the immune system due to their rapid mutation and division. The immune response to many cancers involves three phases: elimination, equilibrium, and escape.
The Tumor Microenvironment02:17

The Tumor Microenvironment

Every normal cell or tissue is embedded in a complex local environment called stroma, consisting of different cell types, a basal membrane, and blood vessels. As normal cells mutate and develop into cancer cells, their local environment also changes to allow cancer progression. The tumor microenvironment (TME) consists of a complex cellular matrix of stromal cells and the developing tumor. The cross-talk between cancer cells and surrounding stromal cells is critical to disrupt normal tissue...
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
Tumor Progression02:07

Tumor Progression

Tumor progression is a phenomenon where the pre-formed tumor acquires successive mutations to become clinically more aggressive and malignant. In the 1950s, Foulds first described the stepwise progression of cancer cells through successive stages.
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...