Narrow Results

Some special cases of Marchuk's model of an infectious disease are studied. A paralysis effect is neglected, and the model reduces to 3 ordinary differential equations with time delay and initial data corresponding to a healthy organism infected by some dose of the antigen at time 0. It is proved that, if the immune system is very strong and the antigen reproduction rate is not too large, then every solution has a finite limit, which is equal to the stationary state describing the healthy organism. If the antigen reproduction rate is large, then all solutions have average values equal to the values corresponding to the chronic form of the disease.

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.

Angiogenesis, or the formation of new blood vessels from pre-existing vasculature through sprouting or invagination, is a complex process involving many factors. The role of angiogenesis in the progression of cancer has been extensively explored, and it is now well established that elevated levels of angiogenesis in many solid tumors correlates with poor prognosis. Similarly, recent evidence suggests that blood vessel formation plays a pivotal role in the progression of hematological malignancies, including the plasma cell malignancy, multiple myeloma. Several studies have shown that bone marrow angiogenesis is significantly increased in patients with active multiple myeloma and is indicative of poor prognosis. Malignant myeloma cells are known to secrete several angiogenic factors which may play a role in the increased angiogenesis in the bone marrow of myeloma patients. Anti-angiogenic therapy with thalidomide is now considered to be a standard therapy for advanced myeloma patients and a number of new anti-angiogenic therapies are currently undergoing clinical trials for use in this disease.