A stochastic model for cancer metastasis: branching stochastic process with settlement

Stochastic analysis of a COVID-19 model with effects of vaccination and different transition rates: Real data approach

This paper presents a stochastic model for COVID-19 that takes into account factors such as incubation times, vaccine effectiveness, and quarantine periods in the spread of the virus in symptomatically contagious populations. The paper outlines the conditions necessary for the existence and uniqueness of a global solution for the stochastic model. Additionally, the paper employs nonlinear analysis to demonstrate some results on the ergodic aspect of the stochastic model. The model is also simulated and compared to deterministic dynamics. To validate and demonstrate the usefulness of the proposed system, the paper compares the results of the infected class with actual cases from Iraq, Bangladesh, and Croatia. Furthermore, the paper visualizes the impact of vaccination rates and transition rates on the dynamics of infected people in the infected class.

Application of a count data model to evaluate the anti-metastatic efficacy of QAP14 in 4T1 breast cancer allografts

Dopamine D1 receptor (D1DR) is proved to be a promising target to prevent tumor metastasis, and our previous studies showed that QAP14, a potent anti-cancer agent, exerted inhibitory effect on lung metastasis via D1DR activation. Therefore, the purpose of the study was to establish count data models to quantitatively characterize the disease progression of lung metastasis and assess the anti-metastatic effect of QAP14. Data of metastatic progression were collected in 4T1 tumor-bearing mice. Generalized Poisson distribution best described the variability of metastasis counts among the individuals. An empirical PK/PD model was developed to establish mathematical relationships between steady plasma concentrations of QAP14 and metastasis growth dynamics. The latency period of metastasis was estimated to be 12 days after tumor implantation. Our model structure also fitted well to other D1DR agonists (fenoldopam and l-stepholidine) which had inhibitory impact on breast cancer lung metastasis likewise. QAP14 40 mg/kg showed the best inhibitory efficacy, for it provided the longest prolongation of metastasis-free periods compared with fenoldopam or l-stepholidine. This study provides a quantitative method to describe the lung metastasis progression of 4T1 allografts, as well as an alternative PD model structure to evaluate anti-metastatic efficacy.

Investigating Optimal Chemotherapy Options for Osteosarcoma Patients through a Mathematical Model

Simple Summary

Osteosarcoma is a rare type of cancer with poor prognoses. However, to the best of our knowledge, there are no mathematical models that study the impact of chemotherapy treatments on the osteosarcoma microenvironment. In this study, we developed a data driven mathematical model to analyze the dynamics of the important players in three groups of osteosarcoma tumors with distinct immune patterns in the presence of the most common chemotherapy drugs. The results indicate that the treatments’ start times and optimal dosages depend on the unique growth rate of the tumor, which implies the necessity of personalized medicine. Furthermore, the developed model can be extended by others to build models that can recommend individual-specific optimal dosages.

Abstract

Since all tumors are unique, they may respond differently to the same treatments. Therefore, it is necessary to study their characteristics individually to find their best treatment options. We built a mathematical model for the interactions between the most common chemotherapy drugs and the osteosarcoma microenvironments of three clusters of tumors with unique immune profiles. We then investigated the effects of chemotherapy with different treatment regimens and various treatment start times on the behaviors of immune and cancer cells in each cluster. Saliently, we suggest the optimal drug dosages for the tumors in each cluster. The results show that abundances of dendritic cells and HMGB1 increase when drugs are given and decrease when drugs are absent. Populations of helper T cells, cytotoxic cells, and IFN-γ grow, and populations of cancer cells and other immune cells shrink during treatment. According to the model, the MAP regimen does a good job at killing cancer, and is more effective than doxorubicin and cisplatin combined or methotrexate alone. The results also indicate that it is important to consider the tumor’s unique growth rate when deciding the treatment details, as fast growing tumors need early treatment start times and high dosages.

Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment

Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known as metastatic blow-up. Recent clinical evidence has shown that the immune response can have strong tumor promoting effects. In this work, we investigate if the pro-tumor effects of the immune response can have a significant contribution to metastatic dormancy and metastatic blow-up. We develop an ordinary differential equation model of the immune-mediated theory of metastasis. We include both anti- and pro-tumor immune effects, in addition to the experimentally observed phenomenon of tumor-induced immune cell phenotypic plasticity. Using geometric singular perturbation analysis, we derive a rather simple model that captures the main processes and, at the same time, can be fully analyzed. Literature-derived parameter estimates are obtained, and model robustness is demonstrated through a time dependent sensitivity analysis. We determine conditions under which the parameterized model can successfully explain both metastatic dormancy and blow-up. The results confirm the significant active role of the immune system in the metastatic process. Numerical simulations suggest a novel measure to predict the occurrence of future metastatic blow-up in addition to new potential avenues for treatment of clinically undetectable micrometastases.