Modeling treatment of cancer using oncolytic virotherapy with saturated incidence
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...
Citations
More filters
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
Cites background from "Modeling treatment of cancer using ..."
...In recent years, several attempts have been made to characterize viral dynamics for oncolytic virotherapy using stochastic differential equations (SDEs) such as Yuan and Allen [14], Kim et al [15], and Rajalakshmi et al [16, 17]....
[...]
...A uthor M anuscript A uthor M anuscript A uthor M anuscript A uthor M anuscript characterize viral dynamics for oncolytic virotherapy using stochastic differential equations (SDEs) such as Yuan and Allen [14], Kim et al [15], and Rajalakshmi et al [16, 17]....
[...]
TL;DR: In this article , a stochastic Hopf bifurcation without parameters (SHB) without parameters was proposed to analyze the effect of perturbations and uncertainties related to immune responses.
3 citations
TL;DR: In this article , deterministic and stochastic models were proposed to explain the complexity of interactions in cancer virotherapy and outcomes of current preclinical and clinical trials of oncolytic viral treatments.
2 citations
References
More filters
TL;DR: The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods.
Abstract: MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows one to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, and fold bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore-Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created. The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods. The MATLAB environment makes the standard MATLAB Ordinary Differential Equations (ODE) Suite interactively available and provides computational and visualization tools; it also eliminates the compilation stage and so makes installation straightforward. Compared to other packages such as AUTO and CONTENT, adding a new type of curves is easy in the MATLAB environment. We illustrate this by a detailed description of the limit point curve type.
1,320 citations
"Modeling treatment of cancer using ..." refers methods in this paper
...The bifurcation diagrams by considering d and l as bifurcation parameters are produced using MATCONT in combination with MATLAB [12] and are demonstrated in Figures 6 and 7....
[...]
TL;DR: The models considered for the spread of an infectious disease in a population are of SIRS or SIS type with a standard incidence expression and have density-dependent restricted growth due to a decreasing birth rate and an increasing death rate as the population size increases towards its carrying capacity.
Abstract: The models considered for the spread of an infectious disease in a population are of SIRS or SIS type with a standard incidence expression. The varying population size is described by a modification of the logistic differential equation which includes a term for disease-related deaths. The models have density-dependent restricted growth due to a decreasing birth rate and an increasing death rate as the population size increases towards its carrying capacity. Thresholds, equilibria and stability are determined for the systems of ordinary differential equations for each model. The persistence of the infectious disease and disease-related deaths can lead to a new equilibrium population size below the carrying capacity and can even cause the population to become extinct.
180 citations
"Modeling treatment of cancer using ..." refers methods in this paper
...The logistic growth is modeled by considering the model discussed in Gao and Hethcote [10]....
[...]
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
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
...V22 1⁄4 P3 þ P4 þ P6 1⁄4 bX1X3 gþ X1 þ d þ 1þ a ð Þ r K X1 þ X2 ð Þ X2 þ 2X2 rþ X4 X4, V33 1⁄4 P5 þ P11 1⁄4 aX2 þ xX3, V44 1⁄4 P9 þ P10 þ P12 1⁄4 c1X1X4 þ c2X2X4 þ lX4: We follow the approach discussed in [11] and construct a matrix M such that X 1⁄4 MMT , where M is a 4 5 matrix....
[...]