Publication Date



Open access

Degree Type


Degree Name

Doctor of Philosophy (PHD)


Mathematics (Arts and Sciences)

Date of Defense


First Committee Member

Chris Cosner

Second Committee Member

Huseyin Kocak

Third Committee Member

Shigui Ruan

Fourth Committee Member

Lawrence Boise


Multiple myeloma is a malignant bone marrow plasma cell tumor which is responsible for approximately 12,000 deaths per year in the United States and two percent of all cancer deaths. It is recognized clinically by the presence of more than ten percent bone marrow plasma cells, the detection of a monoclonal protein (M-protein), anemia, hypercalcemia, renal insufficiency, and lytic bone lesions. The disease is usually preceded by a premalignant tumor called monoclonal gammopathy of undetermined significance (MGUS), which is present in one percent of adults over the age of fifty, three percent over the age of seventy and ten percent of those in the tenth decade. MGUS is also recognized by the detection of M-protein, but with less than ten percent bone marrow plasma cells and without the other features exhibited by myeloma. The majority of MGUS patients remain stable for long periods without ever developing myeloma. Only a small percentage of patients with MGUS eventually develop multiple myeloma. However, the reason for this is not yet known. Once the myeloma stage is reached, a sequence of well-understood mutational evets eventually lead to the escape of the tumor from the control of the immune system. We propose a mathematical model of tumor-immune system interactions at the onset of the disease in an effort to better understand the early events that take place and their influence on the outcome of the disease. The model is calibrated with parameter values obtained from available data and we study the resulting dynamics. Next, we study how the behavior of the system is affected as parameters are varied. Finally, we interpret the results and draw some conclusions.


Tumor; Multiple Myeloma; Monoclonal Gammopathy Of Undetermined Significance; MGUS; Cancer Model