The Gompertz model is a mathematical equation that describes the growth of a solid tumor. It takes into account the initial growth rate of the tumor, the carrying capacity of the environment, and the tumor's growth rate as it approaches the carrying capacity.

The logistic model of tumor growth assumes that tumor growth is limited by environmental factors, such as the availability of nutrients and space.

The metastasis model is a mathematical equation that describes the spread of cancer cells through the bloodstream. It takes into account the rate of cancer cell shedding from the primary tumor, the rate of cancer cell survival in the bloodstream, and the rate of cancer cell colonization at secondary sites.

Mathematical models are used in cancer research to predict tumor growth and spread, to design new cancer treatments, and to understand the mechanisms of cancer development.

Fractal analysis is a mathematical technique that is used to analyze the spatial distribution of cancer cells within a tumor. It can be used to identify patterns of cancer cell growth and to predict the likelihood of metastasis.

The main challenge in developing mathematical models of cancer is the complexity of cancer biology, the lack of data on cancer, and the computational cost of running the models.

A combined model is used to describe the growth of a tumor under the influence of chemotherapy. This model takes into account the cell-cycle model, the pharmacokinetic model, and the pharmacodynamic model.

The goal of using mathematical models in cancer immunotherapy is to predict the response of a patient to immunotherapy, to design new immunotherapy strategies, and to understand the mechanisms of immunotherapy.

A combined model is used to describe the evolution of cancer cells under the influence of targeted therapy. This model takes into account the mutation-selection model, the adaptive therapy model, and the resistance model.

The main challenge in developing mathematical models of cancer metastasis is the complexity of the metastatic process, the lack of data on metastasis, and the computational cost of running the models.

The linear-quadratic model is used to describe the growth of a tumor under the influence of radiation therapy. This model takes into account the linear and quadratic components of radiation-induced cell death.

The goal of using mathematical models in cancer epidemiology is to identify risk factors for cancer, to predict the incidence and prevalence of cancer, and to evaluate the effectiveness of cancer prevention strategies.

The lymphatic model is a mathematical equation that describes the spread of cancer cells through the lymphatic system. It takes into account the rate of cancer cell shedding from the primary tumor, the rate of cancer cell survival in the lymphatic system, and the rate of cancer cell colonization at secondary sites.

The main challenge in developing mathematical models of cancer dormancy is the lack of data on cancer dormancy, the complexity of the dormancy process, and the computational cost of running the models.

The surgical model is a mathematical equation that describes the growth of a tumor under the influence of surgery. It takes into account the size of the tumor, the extent of the surgery, and the rate of tumor regrowth.