scholarly journals A Class of Solutions for the Hybrid Kinetic Model in the Tumor-Immune System Competition

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Carlo Cattani ◽  
Armando Ciancio
Keyword(s):  
Immune System ◽  
Kinetic Model ◽  
Density Function ◽  
Hybrid System ◽  
Kinetic Models ◽  
State Transition ◽  
Transition Density ◽  
Realistic Model ◽  
Transition Density Function ◽  
Competing Populations

In this paper, the hybrid kinetic models of tumor-immune system competition are studied under the assumption of pure competition. The solution of the coupled hybrid system depends on the symmetry of the state transition density which characterizes the probability of successful occurrences. Thus by defining a proper transition density function, the solutions of the hybrid system are explicitly computed and applied to a classical (realistic) model of competing populations.

scholarly journals Stochastic Volatility Effects on Correlated Log-Normal Random Variables

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Yong-Ki Ma
Keyword(s):  
Stochastic Process ◽  
Density Function ◽  
Process Model ◽  
Numerical Study ◽  
Correction Term ◽  
Order Term ◽  
Splitting Method ◽  
Transition Density ◽  
Analytic Approximation ◽  
Transition Density Function

The transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. In this paper, we incorporate an ergodic process displaying fast moving fluctuation into constant volatility models to express volatility clustering over time. We obtain an analytic approximation of the transition density function under our stochastic process model. Using perturbation theory based on Lie–Trotter operator splitting method, we compute the leading-order term and the first-order correction term and then present the left and right skew scenarios through numerical study.

scholarly journals Separable Transition Density in the Hybrid Model for Tumor-Immune System Competition

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Carlo Cattani ◽  
Armando Ciancio
Keyword(s):  
Immune System ◽  
Density Function ◽  
Tumor Cells ◽  
Explicit Form ◽  
Hybrid Model ◽  
Transition Density ◽  
System Of Equations ◽  
Volterra System ◽  
Separable Functions ◽  
Concrete Application

A hybrid model, on the competition tumor cells immune system, is studied under suitable hypotheses. The explicit form for the equations is obtained in the case where the density function of transition is expressed as the product of separable functions. A concrete application is given starting from a modified Lotka-Volterra system of equations.

Kinetic Aspects of the Interplay of Cancer and the Immune System

2019 ◽  
Vol 14 (02) ◽  
pp. 101-114 ◽  
Author(s):  
Vladimir P. Zhdanov
Keyword(s):  
Stem Cells ◽  
Immune System ◽  
Kinetic Model ◽  
Human Population ◽  
Lifetime Risk ◽  
Risk Of Cancer

The understanding of the interplay between cancer and the immune system is still limited. Herein, I focus on two aspects of this interplay. First, I propose a kinetic model describing the likely role of the immune system in the lifetime risk of cancer at the level of the whole human population. For each tissue, the risk is predicted to be influenced by the heterogeneity of the population and to depend exponentially on time. The expression for the risk does not, however, depend explicitly on the total number of divisions of the corresponding stem cells. For this reason, the correlation with the latter number can only be indirect. Second, using another kinetic framework, I describe how the growth of a few tumors can depend on their interaction via the immune system. The analysis shows that depending on specific details, the tumors of different sizes tend either to reach the same size or remain to be of different sizes.

scholarly journals Kinetic aspects of virus targeting by nanoparticles in vivo

2021 ◽  
Author(s):  
Vladimir P. Zhdanov
Keyword(s):  
Immune System ◽  
Kinetic Model ◽  
Order Of Magnitude ◽  
Eradication Of Infection ◽  
Infected Cells

AbstractOne of the suggested ways of the use of nanoparticles in virology implies their association with and subsequent deactivation of virions. The conditions determining the efficiency of this approach in vivo are now not clear. Herein, I propose the first kinetic model describing the corresponding processes and clarifying these conditions. My analysis indicates that nanoparticles can decrease concentration of infected cells by a factor of one order of magnitude, but this decrease itself (without feedback of the immune system) is insufficient for full eradication of infection. It can, however, induce delay in the progress of infection, and this delay can help to form sufficient feedback of the immune system.

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