Modelling the role of HIV and its treatment in non-Hodgkin lymphoma growth dynamics

Aogo, Rosemary Akinyi (2015-12)

Thesis (MSc)--Stellenbosch University, 2015

ENGLISH ABSTRACT : HIV/AIDS associated cancers are cancers whose incidences are much higher in HIV/AIDS patients than in the general population. HIV as one of the chronic infections involves chronic antigenic stimulation by persistent self-antigens or foreign antigens and the stimulation activates B cells and induces their uncontrollable growth. Cancer and HIV co-existence both in vivo and in vitro in a cancer immune environment leads to specific cytokines being produced by various immune cells and the cancer cells. In this thesis, we develop a mathematical model describing the cancer-immune system interaction in the presence of HIV and HIV treatment. In particular, we focus on the most common cancer in AIDS patients; the non-Hodgkin’s lymphoma (NHL). The formulated model, described by non-linear ordinary differential equations, shows existence of multiple equilibria whose stability and bifurcation analysis are presented. Our results suggest existence of a low endemic state (non-aggressive) and a higher endemic (aggressive state). At a low cancer state, patients can live for a longer period of time with the cancer. However, initiation of HIV treatment in patients with NHL is observed to reduce the cancer cell density to lower endemic states and this might explain why some of the HIV-infected patients can live with cancer for many years. Highly active antiretroviral therapy (HAART) used for HIV treatment is a combination therapy ("cocktail" of drugs), that includes reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) in different proportions; it is more effective in treating HIV than a single drug therapy. In many communities in sub-Saharan Africa, HAART is available but not anti cancer drugs. We explore how effective the combination therapy in HIV associated cancer is in reducing cancer growth. Our model simulations show how to best choose the proportions of RTI and PI in order to maintain an acceptable level of CD+4 T cells and, at the same time, reduce the growth of cancer cells as much as possible. The results obtained also give an estimate of the efficacies of the drugs in the HAART regimen given to people living with HIV. In addition, the results also explain why late initiation of HIV treatment might not be helpful to cancer patients. Furthermore, in case of chemotherapeutic intervention, our results might explain why a few of these chemotherapeutic drugs are more effective when given at a slow continuous rate. The models present some interesting research outcomes on treatment of HIV related cancers that can influence their treatment and management.

AFRIKAANSE OPSOMMING : MIV/VIGS-verwante kankers is kankers wie se voorkoms in MIV/VIGS pasiënte baie groter is as in die algemene bevolking. MIV, as een van die kroniese infeksies, vereis kroniese antigeniese stimulasie deur aanhoudende self- of vreemde antigene. Hierdie stimulasie aktiveer B-selle en gee aanleiding tot hul onbeheerbare groei. Die saambestaan van kanker en MIV, beide in vivo en in vitro, in ‘n kanker- immuunomgewing lei tot die produsering van spesifieke sitokiene deur verskeie immuunselle en die kankerselle. In hierdie tesis ontwikkel ons ‘n wiskundige model wat die kanker-immuunstelsel se interaksie in die teenwoordigheid van MIV en MIV behandelings toon. Ons fokus, in die besonder, op die mees algemene kanker in MIV pasiënte: nie-Hodgkin se limfoom (NHL). Die geformuleerde model, wat nie-lineêre gewone differensiaalvergelykings beskryf, toon die bestaan van verskeie ewewigte wie se stabiliteit en bifurkasie analise verskaf word. Ons resultate dui op die bestaan van ’n lae endemiese staat ( nie- aggressiewe ) en ‘n hoer endemies (aggressiewe staat). Op ‘n lae kanker toestand is, kan pasiënte leef vir ‘n langer tydperk van die tyd met die kanker. Dit word egter waargeneem in pasiënte met NHL dat die begin van MIV- behandeling hierdie lae epidemiese state van die kankerselle verminder. Hoogs aktiewe antiretrovirale terapie (HAART) wat gebruik word vir MIV behandeling is ’n kombinasie terapie (“cocktail"van geneesmiddels) wat omgekeerde transkriptase inhibeerder (RTI) en protease-inhibeerder (PI) in verskeie proporsies insluit; dit is meer effektief in die behandeling van MIV as ’n enkele geneesmiddelterapie. In baie van die gemeenskappe in sub-Saharan Afrika is HAART, eerder as antie-kanker geneesmiddels, beskikbaar. Ons ondersoek hoe effektief die kombinasie terapie in HIV-verwante kankers is om kankergroei te verminder. Ons modelsimulasies toon hoe om die beste proporsie van RTI en PI te kies om ’n aanvaarbare vlak van CD+4 selle te handhaaf, en ter selfde tyd, die groei van kankerselle soveel as moontlik te verminder. Die resultate toon ook ‘n beraming van die effektiwiteit van die geneesmiddels in die HAART prosedure wat gegee word aan die wat MIV het. Ook verduidelik die resultate hoekom die MIV behandeling nie so nuttig onder kankerpasiënte, wat die behadeling laat begin, is nie. Bykomend, in die geval van chemoterapeutiese intervensie, mag ons resultate verduidelik hoekom sommige van die chemoterapeutiese geneesmidelle meer effektief is wanneer dit teen ’n stadige deurlopende tempo verskaf word. Die model toon interressante uitkomste van die navorsing oor die behandeling van MIV-verwante kankers wat hul behandeling en bestuur kan beïnvloed.

Thesis

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