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Analysis of immunotherapy models in the context of cancer dynamics

100%

Szymańska Z.

International Journal of Applied Mathematics and Computer Science

2003

tom 13

nr 3

407-418

A basic mathematical model of the immune response when cancer cells are recognized is proposed. The model consists of six ordinary differential equations. It is extended by taking into account two types of immunotherapy: active immunotherapy and adoptive immunotherapy. An analysis of the corresponding models is made to answer the question which of the presented methods of immunotherapy is better. The analysis is completed by numerical simulations which show that the method of adoptive immunotherapy seems better for the patient at least in some cases.

Models of interactions between heterotrophic and autotrophic organisms

63%

Foryś U. , Szymańska Z.

Applicationes Mathematicae

2009

tom 36

nr 3

279-294

We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.

Model of AIDS-related tumour with time delay

51%

Bodnar M. , Foryś U. , Szymańska Z.

Applicationes Mathematicae

2009

tom 36

nr 3

263-278

We present and compare two simple models of immune system and cancer cell interactions. The first model reflects simple cancer disease progression and serves as our "control" case. The second describes the progression of a cancer disease in the case of a patient infected with the HIV-1 virus.