Modeling treatment of cancer using virotherapy with generalized logistic growth of tumor cells
TL;DR: In this article, a deterministic mathematical model was proposed to understand the dynamics of Virotherapy in cancer treatment, which eliminates tumor cells without harming the healthy cells without causing any side effects.
Abstract: Virotherapy is an effective strategy in cancer treatment. It eliminates tumor cells without harming the healthy cells. In this article, a deterministic mathematical model to understand the dynamics...
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04 Aug 2020
TL;DR: From analysis and simulation of the NTIUNHDM, it can be deduced that instability of the response stage, due to a weak immune system, is classified as one of the main reasons for the coexistence of abnormal cells and normal cells.
Abstract: Changes in diet are heavily associated with high mortality rates in several types of cancer. In this paper, a new mathematical model of tumor cells growth is established to dynamically demonstrate the effects of abnormal cell progression on the cells affected by the tumor in terms of the immune system’s functionality and normal cells’ dynamic growth. This model is called the normal-tumor-immune-unhealthy diet model (NTIUNHDM) and governed by a system of ordinary differential equations. In the NTIUNHDM, there are three main populations normal cells, tumor cell and immune cells. The model is discussed analytically and numerically by utilizing a fourth-order Runge–Kutta method. The dynamic behavior of the NTIUNHDM is discussed by analyzing the stability of the system at various equilibrium points and the Mathematica software is used to simulate the model. From analysis and simulation of the NTIUNHDM, it can be deduced that instability of the response stage, due to a weak immune system, is classified as one of the main reasons for the coexistence of abnormal cells and normal cells. Additionally, it is obvious that the NTIUNHDM has only one stable case when abnormal cells begin progressing into early stages of tumor cells such that the immune cells are generated once. Thus, early boosting of the immune system might contribute to reducing the risk of cancer.
13 citations
TL;DR: This study incorporates environmental noise and stochastic effects to the basic deterministic model and proposes a stoChastic model for viral therapy in terms of Ito stochastically differential equations, which is conducted using boundary methods.
Abstract: The complexity of oncolytic virotherapy arises from many factors. In this study, we incorporate environmental noise and stochastic effects to our basic deterministic model and propose a stochastic model for viral therapy in terms of Ito stochastic differential equations. We conduct a detailed analysis of the model using boundary methods. We find two combined parameters, one describes possibilities of eradicating tumors and one is an increasing function of the viral burst size, which serve as thresholds to classify asymptotical dynamics of the model solution paths. We show there are three ergodic invariant probability measures which correspond to equilibrium states of the deterministic model, and extra possibility to eradicate tumor due to strong variance of tumor growth rate and medium viral burst size. Numerical analysis demonstrates several typical solution paths with biological explanations. In addition, we provide some medical interpretations and implications.
12 citations
TL;DR: The results of the analysis and simulation of the TNVM showed a case of coexistence between normal cells and tumor cells occur if an individual consumes a regular rate of vitamins that have been simulated to be 87% per day from a natural food source.
Abstract: The natural sources of the vitamins, which come from a balanced diet (as recommended by the World Cancer Research Fund and the American Institute for Cancer Research) contribute to protecting the body from advancing progressive of cancer stages. Thus, in this study, we analyze the effect of the intervention of vitamins on delaying the growth of cancer cells based on the dynamics of a normal cell cycle when the tumor cells appear in a tissue as a resulting for progressing abnormal cells due to the weak response of the immune system. We developed a mathematical model, called tumor-normal-vitamins model (TNVM), which is governed by a system of ordinary differential equations and refers to two main populations normal cells and tumor cells. This model considers the intervention of vitamins as a moderating factor within thirty days. The models are discussed analytically and numerically by utilizing the Runge-Kutta method to simulate them. The results of the analysis and simulation of free model illustrate that the model will be stable if the tumor cells succeed in eliminating normal cells in the tissue. Whereas, the analysis and simulation of the TNVM showed a case of coexistence between normal cells and tumor cells occur if an individual consumes a regular rate of vitamins that have been simulated to be 87% per day from a natural food source. Even though the response of the immune system is weak, the daily consumption of enough vitamins can play an essential role in delaying the development of an early stage of cancer. This study contributes to the increasing awareness regarding a healthy diet to reduce the risk of some deadly diseases, especially cancer.
7 citations
Cites background from "Modeling treatment of cancer using ..."
...Based on this model, several other models have been proposed to evaluate the dynamic system by applying various therapeutical types, such as virotherapy, chemotherapy, and immunotherapy [12]–[15]....
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TL;DR: A mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative to treatment of a glioma using a specialist virus that attacks only tumor cells is proposed.
Abstract: In this paper, we propose a mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative to treatment of a glioma. The main idea is to incorporate the virotherapy after the first or second chemotherapy session using a specialist virus that attacks only tumor cells. Some simulations are presented. Based on the results, we conclude that with this combined therapy may reduce the number of chemotherapy sessions and may lead to obtain better results in the fight against gliomas.
6 citations
TL;DR: A mathematical model for treatment of cancer by using oncolytic virotherapy is proposed and analyzed and it is found that for some set of parameters model system exhibits periodic oscillations.
Abstract: Oncolytic virotherapy is emerging as a promising new method for cancer treatment. In the present study, we propose and analyze a mathematical model for treatment of cancer by using oncolytic viroth...
4 citations
Cites background from "Modeling treatment of cancer using ..."
...This work emphasizes the need of identifying the key parameters which can influence the success of CONTACT Mini Ghosh minighosh@vit.ac.in Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, Chennai, 600127, India....
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...ORCID Mini Ghosh http://orcid.org/0000-0001-9652-2409...
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...Further, Rajalakshmi and Ghosh [8] extended this model by considering generalized logistic growth of tumor cells and cell-cell fusion of uninfected and infected tumor cells....
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References
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01 Jan 1987TL;DR: A very brief tour of XPPAUT can be found in this paper, where the authors present a technique for writing ODE files for Differential Equations for differentially Equations.
Abstract: List of figures Preface 1. Installation 2 A Very Brief Tour of XPPAUT 3. Writing ODE Files for Differential Equations 4. XPPAUT in the Classroom 5. More Advanced Diffferential Equations 6. Spatial Problems, PDEs, and BVPs 7. Using AUTO. Bifurcation and Continuation 8. Animation 9 Tricks and Advanced Methods Appendix A. Colors and Linestyles Appendix B. The Options Appendix C. Numerical Methods Appendix D. Structure of ODE Files Appendix E. Complete Command List Appendix F. Error Messages Appendix G. Cheat Sheet References IndexAppendix C. Numerical Methods Appendix D. Structure of ODE Files Appendix E. Complete Command List Appendix F. Error Messages Appendix G. Cheat Sheet References Index.
1,606 citations
TL;DR: Fundamentals of mathematical modeling of tumor growth and tumor-host interactions are described, and some of the seminal and most prominent approaches are summarized.
Abstract: Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. So-called in silico trials that predict patient-specific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumor-host interactions, and summarize some of the seminal and most prominent approaches.
169 citations
"Modeling treatment of cancer using ..." refers background in this paper
...In [2], the authors discussed several mathematical models based on the ordinary and partial differential equations to describe the dynamics of tumor growth and treatment....
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TL;DR: This work uses numerical simulations to explore conditions for which the model predicts successful therapy and tumor eradication, and exhibits damped, as well as stable oscillations in a range of parameter values.
141 citations
"Modeling treatment of cancer using ..." refers background or methods in this paper
...[9], here too we consider the term byv in the third equation of our model keeping in view the fact that by infecting tumor cells, the virus particles will be lost and it will not contribute in infecting new tumor cells....
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...Numerical simulation For the numerical simulation of our models, the basic parameter values are adopted from [8, 9] and the additional parameters for example, c1, c2, q, l are taken from reference [7]....
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TL;DR: A mathematical model, based on population dynamics, that captures the essential elements of radiovirotherapy is developed and the existence of corresponding equilibrium points related to complete cure, partial cure, and therapy failure is proved and discussed.
Abstract: Cancer virotherapy represents a dynamical system that requires mathematical modeling for complete understanding of the outcomes. The combination of virotherapy with radiation (radiovirotherapy) has been recently shown to successfully eliminate tumors when virotherapy alone failed. However, it introduces a new level of complexity. We have developed a mathematical model, based on population dynamics, that captures the essential elements of radiovirotherapy. The existence of corresponding equilibrium points related to complete cure, partial cure, and therapy failure is proved and discussed. The parameters of the model were estimated by fitting to experimental data. By using simulations we analyzed the influence of parameters that describe the interaction between virus and tumor cell on the outcome of the therapy. Furthermore, we evaluated relevant therapeutic scenarios for radiovirotherapy, and offered elements for optimization.
131 citations
TL;DR: New stochastic models are developed for the dynamics of a viral infection and an immune response during the early stages of infection and it is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding.
Abstract: New stochastic models are developed for the dynamics of a viral infection and an immune response during the early stages of infection. The stochastic models are derived based on the dynamics of deterministic models. The simplest deterministic model is a well-known system of ordinary differential equations which consists of three populations: uninfected cells, actively infected cells, and virus particles. This basic model is extended to include some factors of the immune response related to Human Immunodeficiency Virus-1 (HIV-1) infection. For the deterministic models, the basic reproduction number, R0, is calculated and it is shown that if R0 1, the deterministic models predict the viral infection persists in the host. But for the stochastic models, there is a positive probability of viral extinction. It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding.
92 citations
Additional excerpts
...where the above diffusion matrix is symmetric, positive-definite and each component of this 4 4 diffusion matrix can be obtained as follows: V11 1⁄4 P1 þ P5 þ P6 þ P11 þ P12 1⁄4 bX1X3 þ qX2X1 þ 1X1X4 þ rX1 þ rX1 X1þX2 K ; V12 1⁄4 V21 1⁄4 P1 1⁄4 bX1X3; V13 1⁄4 V31 1⁄4 P1 1⁄4 bX1X3; V22 1⁄4 P1 þ P2 þ P4 1⁄4 bX1X3 þ dX2 þ 2X2X4; V23 1⁄4 V32 1⁄4 P1 1⁄4 bX1X3; V33 1⁄4 P1 þ P3 þ P9 1⁄4 bX1X3 þ aX2 þ xX3; V44 1⁄4 P7 þ P8 þ P10 1⁄4 c1X1X4 þ c2X2X4 þ lX4: We follow the approach discussed in [10] and construct a matrix M such that X1⁄4MM, where M is a 4 5 matrix....
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