Поредната сбирка на Националния семинар по стохастика ще се проведе на 19 юни 2019 г. (сряда) от 14:00 часа в зала 403 на ИМИ – БАН. Доклад на тема:
A decomposable multi-type Bellman-Harris branching process
with mutations. Application in modeling of cancer evolution
ще изнесе Калоян Витанов (докторант във ФМИ-СУ).
Поканват се всички интересуващи се.
Резюме: A prominent feature of biological systems is their capacity to adapt and mutation is a key mechanism for achieving adaptation. As a continuation of [3] we propose a decomposable multi-type Bellman-Harris branching process, which incorporates a possibility for mutation.
Metastasis, the spread of cancer cells from a primary tumour to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. We consider a metastasized cancer cell population after some medical treatment (e.g. chemotherapy). Arriving in a di erent environment the cancer cells may change their characteristics concerning lifespan and reproduction, thus they may di erentiate into di erent types. Even if the treatment is e ective (resulting in subcritical reproduction of all cancer cell types), however, it is possible during cell division for mutations to occur. These mutations can produce a new cancer cell type that is adapted to the treatment (having supercritical reproduction). Cancer cells from this new type may lead to a non-extinction process.
We model the above scenario with the proposed model. Expanding [1] and [2] we investigate relevant quantities such as the probability of extinction of the process until time t and as t approaches in nity, the number of occurred supercritical mutants until time t and as t approaches in nity, the time until the rst occurrence of a mutant starting a non-extinction process and the immediate risk for the process to escape extinction. We also propose numerical schemes for performing calculations.
Keywords: Mutations, Decomposable multi-type branching process, Probability of extinction, Waiting time to escape mutant, Immediate risk of escaping extinction
Acknowledgements: The research of these authors was supported, in part, by the Bulgarian National Science Fund at the Ministry of Science and Education, Grant No. KP-06-H22/3.
References
[1] K. Vitanov, M. Slavtchova-Bojkova, Multitype branching processes in continuous time as models of cancer, Annuaire de l’Universite de So a \St. Kl. Ohridski”, Fac. Math and Inf., 104, 2017, 193-200.
[2] M. Slavtchova-Bojkova, K. Vitanov, Modelling cancer evolution by multi-type age-dependent branching processes, Compt. rend. de l’acad. bulgare des Sci. 71, 2018, 1297{1305.
[3] M. Slavtchova-Bojkova, P. Trayanov, S. Dimitrov, Branching processes in continuous time as models of mutations: Computational approaches and algorithms, Computational Statistics and Data Analysis, 113, 2017, 111{124.