Onkolitik Virüs ile Matematiksel Tümör Modeli

Abstract

Besin, sağlıklı hücreler, tümör hücreleri ve onkolitik virüs arasındaki etkileşim için verilen dört boyutlu matematiksel model [29], bu çalışmada beş boyutlu adi diferansiyel denklem sistemi şeklinde genişletilmiştir. Tümör hücreleri onkolitik virüs ile etkileşime geçtiğinden, enfekte olmuş tümör hücreleri de modele dâhil edilmiştir. Onkolitik virüsün tümörü yok etmedeki rolünü incelemek için, tümörün sistemde olmadığı durumlar için kararlılık analizi yapılmıştır. Tümör ve sağlıklı hücrelerden yoksun bir sistemin kararlılığının, sisteme verilen virüs dozunun minimum değerine bağlı olduğu tespit edilmiştir. Tümörün olmadığı ve sağlıklı hücrelerin var olduğu durumda ise, sistemin kararlılığı için elde edilen minimum virüs dozunun, bir önceki dozdan daha küçük olduğu gözlemlenmiştir. Böylece, sistemde sağlıklı hücrelerin bulunmasının, tümörün yok edilme şansını artırdığı ve gerekli ilaç dozunun azaltılmasını sağladığı sonucuna varılmıştır. Son olarak, elde edilen kararlılık analizi için nümerik sonuçlar elde edilmiş ve sistemin kararlılığı için örnekler sunulmuştur.

Keywords

• Tümör modeli
• kararlılık analizi
• onkolitik virüs
• viroterapi

A Mathematical Tumor Model with Oncolytic Virus

Abstract

In this study, a four-dimensional model [29] that is given for interactions between nutrient, healthy cells, tumor cells, and oncolytic virus, is extended with a five-dimensional ordinary differential equations system. Infected tumor cells are included in the model since oncolytic virus infects tumor cells. In order to investigate the role of oncolytic virus in eradication of tumor burden, stability analysis has been performed in case of no tumor cells in the system. It is determined that the stability of the system in case of no tumor cells and healthy cells is related with the minimum virus dosage injected into the host. In case of no tumor cells, but healthy cells, the minimum dosage is smaller than the previous case for stability of the equilibrium point. Therefore, this study demonstrates that existence of healthy cells in the host increases the chance of eradication of tumor cells, and it leads to a decrease in virus dosage. Finally, some numerical results have been obtained for the stability analysis and numerical findings have been presented.

Keywords

• Tumor model
• stability analysis
• oncolytic virus
• virotherapy

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