Model of lymphoma from stochastic analysis

In this work, the authors introduce a stochastic model of lymphoma. Two clonotypes of T cells of the immune system compete with each other and with other clonotypes for survival stimuli. One of the clonotypes is normal and the other is tumourous. To model the tumourous clonotype the authors include a rate of influx of new naive T cells (descendants of mutated precursor cells) from the thymus. The authors obtain a deterministic approximation to the stochastic model and analyse eight cases of competition between the two clonotypes of T cells. The authors obtain two possible scenarios, depending on the values of parameters: either both clonotypes survive in the repertoire or the clonotype of the normal T cells becomes extinct, meanwhile the clonotype of the tumourous T cells is maintained, after achieving some maximum level of growth. The authors show that if the income of the new tumourous T cells from the thymus is augmented, then the tumourous clonotype, would never be removed from the repertoire; meanwhile the normal clonotype could become extinct if it was not specialised enough to compete effectively for survival stimuli provided by professional cells.