In this paper we propose and analyse a model of the competition between cancer and the acquired immune system. The model is a system of integro-differential bilinear equations. The role of the humoral response is analyzed. The simulations are related to the immunotherapy of tumors with antibodies.
The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the...
We consider a mathematical model of autoimmune disease. The model is described by a bilinear system of four integro-differential equations of Boltzmann type. We present numerical results illustrating several typical outcomes of autoimmune disease. In particular, special attention is devoted to the role of viral infections for development of autoimmune diseases.
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