Distribution of Recirculating Lymphocytes: A Stochastic Model Foundation

Interest in mathematical immunology has been growing. This is reflected in the several monographs that have been published and the conferences that have been held lately. Examples of recent work are available in Bell, Perelson and Pimbley (1978), Merrill (1980), Mohler, Bruni and Gandolfi (1980), DeLisi (1983), Marchuk (1983), Marchuk and Belykh (1983), Marchuk, Belykh and Zuev (1985), and Mohler (1987). The mathematical study of events that are involved at the cellular level in transmission of information seems to be generally missing in the literature, the reference here being to the study of recirculation of lymphocytes. These events functionally interconnect many of the parts of the immune response by physically and biochemically conveying information and providing defense. This paper is concerned with a particular approximation for the distribution of recirculating lymphocytes. Besides the healthy state of an organism such distribution is also of significance for disease states. Any maldistribution could be a symptom of a disease, for example, in humans, Hodgkin’s disease, hepatitis B, psoriasis, and chronic lymphocytic leukemia. Thus quantification of the norm of distribution pattern, statistical analysis of the deviation from the norm and/or maldistribution, and modeling and identification of the models can be useful in diagnosis and estimation of disease severity, and in the classification and differential diagnosis of abnormalities in migratory patterns of lymphocytes.