A Stability Mathematical Model of Nasopharyngeal Carcinoma on Cellular Level

This paper discussed the stability of “Tumorigenesis Models†to link between EBV and carcinoma of the nasopharyngeal from normal cell to invasive carcinoma. The review on this case accomplished the previous theorem of equilibrium point on “Tumorigenesis Modelsâ€

Modelling Inhibition of AKT Phosphorylation in Acute Myeloid Leukemia

Constitutive activation of PI3K/AKT signaling pathway has been observed in Acute Myeloid Leukemia (AML) that caused by the mutation of Fms-like Tyrosine Kinase 3 in internal tandem duplication (FLT3-ITD). Constitutive activation of AKT resulted in the regulation of apoptosis by the growth of abnormal cells that uncontrollably (AML blast). In our previous work we had consider a mathematical model of PI3K/AKT signaling pathways in phosphorylation AKT. In this paper we carry out a modification of the model by including synthesis and degradation of proteins as well as the effect of small molecule inhibitor of PI3K/AKT pathways. Perifosine is one of a small molecule inhibitor which has been widely known in the treatment of AML as AKT inhibitor. Our simulation result suggested that the administration of Perifosine may reduce the activity of AKT Phosphorylation. This result also support of the hypothesis that PI3K/AKT pathways is a potential target theraphy in AML. REFERENCE

Link of Nasopharyngeal Carcinoma and Epstein-Barr Virus

Nasopharyngeal Carcinoma (NPC) is a cancer that occurs in nasopharynx which is associated with Epstein-Barr Virus (EBV). Mutation agents in nasopharyngeal neoplasms occur because of EBV infection. Transformation of B-cells due to EBV causes hormone imbalance in lymphoid cells or nasopharyngeal epithelial tissue. Rates of EBV infection have been shown to be prognostic to NPC. The basic level of EBV DNA can be used for stratification prognosis, with higher titers showing greater disease severity and worse outcomes. With mathematical models, there is a correlation between the increase in Epstein-Barr Virus and the increase in Invasive Carcinoma Cells or increase in Nasopharyngeal Carcinoma Cells

A mathematical model of phosphorylation AKT in Acute myeloid leukemia

In this paper we consider a mathematical model of PI3K/AKT signaling pathways in phosphorylation AKT. PI3K/AKT pathway is an important mediator of cytokine signaling implicated in regulation of hematopoiesis. Constitutive activation of PI3K/AKT signaling pathway has been observed in Acute Meyloid Leukemia (AML) it caused by the mutation of Fms-like Tyrosine Kinase 3 in internal tandem duplication (FLT3-ITD), the most common molecular abnormality associated with AML. Depending upon its phosphorylation status, protein interaction, substrate availability, and localization, AKT can phosphorylate or inhibite numerous substrates in its downstream pathways that promote protein synthesis, survival, proliferation, and metabolism. Firstly, we present a mass action ordinary differential equation model describing AKT double phosphorylation (AKTpp) in a system with 11 equations. Finally, under the asumtion enzyme catalyst constant and steady state equilibrium, we reduce the system in 4 equation included Michaelis Menten constant. Simulation result suggested that a high concentration of PI3K and/or a low concentration of phospatase increased AKTpp activation. This result also indicates that PI3K is a potential target theraphy in AML

An age-structured SIPC model of cervical cancer with immunotherapy

Immunotherapy is a targeted therapy that can be applied to cervical cancer patients to prevent DNA damage caused by human papillomavirus (HPV). The HPV infects normal cervical cells withing a specific cell age interval, i.e., between the $G_1$ to $S$ phase of the cell cycle. In this study, we developed a new mathematical model of age-dependent immunotherapy for cervical cancer. The model is a four-dimensional first-order partial differential equation with time- and age-independent variables. The cell population is divided into four sub-populations, i.e., susceptible cells, cells infected by HPV, precancerous cells, and cancer cells. The immunotherapy term has been added to precancerous cells since these cells can experience regression if appointed by proper treatments. The immunotherapy process is closely related to the rate of T-cell division. The treatment works in the same cell cycle that stimulates and inhibits the immune system. In our model, immunotherapy is represented as a periodic function with a small amplitude. It is based on the fluctuating interaction between T-cells and precancerous cells. We have found that there are two types of steady-state conditions, i.e., infection-free and endemic. The local and global stability of an infection-free steady-state has been analyzed based on basic reproduction numbers. We have solved the Riccati differential equation to show the existence of an endemic steady-state. The stability analysis of the endemic steady-state has been determined by using the perturbation approach and solving integral equations. Some numerical simulations are also presented in this paper to illustrate the behavior of the solutions

Analysis of a Mathematical Model of the Interaction between PIP3, AKT, and FOXO3a in Acute Myeloid Leukemia

Yudi Ari Adi, Lina Aryati, Fajar Adi-Kusumo, and Mardiah Suci Hardiant

Cox Proportional Hazard Regression Interaction Model and Its Application to Determine The Risk of Death in Breast Cancer Patients after Chemotherapy

Introduction: This research is based on medical record data of breast cancer patients who seek treatment at the Central General Hospital, dr. Sardjito Yogyakarta, from 2018-2021 has as many as 105 patients. Several risk factors for cancer include demographic factors, clinical factors, tumor factors, and therapy. These factors lead to different psychological states of patients, resulting in the rate of recovery and death of patients. Objective: To determine the risk of death in breast cancer patients after chemotherapy. Methods: The method used in this study is Cox Proportional Hazard survival analysis with an interaction model. The variables studied were age, marital status, profession, insurance, BMI, comorbidities, duration of chemotherapy, chemotherapy agent, chemotherapy type, and tumor size. Results: The analysis results using SPSS software obtained the best hazard and survival model with four significant variables, namely the duration of chemotherapy, chemotherapy agents, chemotherapy types, and the interaction between BMI and chemotherapy types. Conclusions: The most significant risk factor for death was palliative chemotherapy type with HR 27.195 and 3-5 chemotherapy agents with HR 4.997. Meanwhile, the long duration of chemotherapy and the interaction between lean BMI and palliative chemotherapy reduced the risk of death by HR 0.967 and 0.128, respectively