Dynamic Analysis of Mathematical Model in Brain Cancer Treatment by Zika Virus Oncolysis

Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus–host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.

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Dynamic Analysis on a Cable-Driven Interventional Active Catheter Using Kane's Method Combined with Screw Theory

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.527.140 ◽

2014 ◽

Vol 527 ◽

pp. 140-145

Author(s):

Da Xu Zhao ◽

Bai Chen ◽

Guo Zhong Shou ◽

Yu Qi Gu

Keyword(s):

Mathematical Model ◽

Dynamic Analysis ◽

Motion Control ◽

Screw Theory ◽

Driving Forces ◽

Structure Design ◽

Kinematics And Dynamics ◽

Existing Problems ◽

Blind Area ◽

The Mathematical Model

In view of the existing problems of traditional interventional catheters, particularly poor activity, operation difficulty and mass blind area, a novel interventional catheter with a cable-driven active head-end is proposed, and a prototype was built to verify the performance. This paper deals with the kinematics and dynamics of the cable-driven prototype, a dynamic model based on Kanes method combined with screw theory was presented in this paper. According the mathematical model and the prototypes structure, the analysis of kinematics and dynamics of active head-end-end is done in the environment of Mathematica. The needed driving forces of every joint when the system moving along planned trajectory are calculated. The results can provide a basis for the structure design and motion control of the interventional active catheter.

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Photodynamic characterization and optimization using multifunctional nanoparticles for brain cancer treatment

10.1117/12.2005530 ◽

2013 ◽

Cited By ~ 1

Author(s):

Kristen Herrmann ◽

Yong-Eun Lee Koo ◽

Daniel A. Orringer ◽

Oren Sagher ◽

Martin Philbert ◽

...

Keyword(s):

Cancer Treatment ◽

Brain Cancer ◽

Multifunctional Nanoparticles

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Simulation of cancer treatment using the MATLAB SimBiology application

Modeling of systems and processes ◽

10.12737/2219-0767-2021-14-3-90-96 ◽

2021 ◽

Vol 14 (3) ◽

pp. 90-96

Author(s):

Anastasia Goncharova ◽

Maria Vil'

Keyword(s):

Mathematical Model ◽

Cancer Treatment ◽

Interference Competition ◽

The Body ◽

Continuous Treatment ◽

Constant Concentration ◽

Application Package ◽

The Mathematical Model ◽

Cancerous Cells

The paper presents the implementation of the mathematical model of cancer taking into account interference competition and the model of continuous treatment with a constant concentration of the drug in the patient's blood. The implementation was carried out using the MATLAB SimBiology application package. The principle of implementation of different stages of the course of the disease within the framework of one model is described. On the basis of the constructed models and SimBiology tools, a modification was carried out that implements the discrete administration of doses of the drug in courses and takes into account its dynamics in the body, taking into account the assumption that the drug is consumed only to suppress cancerous cells.

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Dynamic Analysis for the Design of CALM System in Shallow and Deep Waters

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2829062 ◽

1997 ◽

Vol 119 (3) ◽

pp. 151-157 ◽

Cited By ~ 3

Author(s):

Y.-L. Hwang

Keyword(s):

Mathematical Model ◽

Dynamic Analysis ◽

Model Test ◽

Time Domain ◽

Time Domain Analysis ◽

Mooring Lines ◽

Deep Waters ◽

Wave Drift ◽

The Mathematical Model ◽

Survival Condition

This paper presents a time domain analysis approach to evaluate the dynamic behavior of the catenary anchor leg mooring (CALM) system under the maximum operational condition when a tanker is moored to the terminal, and in the survival condition when the terminal is not occupied by a tanker. An analytical model, integrating tanker, hawser, buoy, and mooring lines, is developed to dynamically predict the extreme mooring loads and buoy orbital motions, when responding to the effect of wind, current, wave frequency, and wave drift response. Numerical results describing the dynamic behaviors of the CALM system in both shallow and deepwater situations are presented and discussed. The importance of the line dynamics and hawser coupled buoy-tanker dynamics is demonstrated by comparing the present dynamic analysis with catenary calculation approach. Results of the analysis are compared with model test data to validate the mathematical model presented.

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Modeling and analysis of fractional order Zika model

AIMS Mathematics ◽

10.3934/math.2022216 ◽

2021 ◽

Vol 7 (3) ◽

pp. 3912-3938

Author(s):

Muhammad Farman ◽

◽

Ali Akgül ◽

Sameh Askar ◽

Thongchai Botmart ◽

...

Keyword(s):

Mathematical Model ◽

Fixed Point ◽

Control Strategy ◽

Zika Virus ◽

Fixed Point Theory ◽

Point Theory ◽

Fractional Operator ◽

Modeling And Analysis ◽

Virus Model ◽

Positivity And Boundedness

<abstract> <p>We propose mathematical model for the transmission of the Zika virus for humans spread by mosquitoes. We construct a scheme for the Zika virus model with Atangna-Baleanue Caputo sense and fractal fractional operator by using generalized Mittag-Leffler kernel. The positivity and boundedness of the model are also calculated. The existence of uniquene solution is derived and stability analysis has been made for the model by using the fixed point theory. Numerical simulations are made by using the Atangana-Toufik scheme and fractal fractional operator with a different dimension of fractional values which support the theoretical outcome of the proposed system. Developed scheme including simulation will provide better understanding in future analysis and for control strategy regarding Zika virus.</p> </abstract>

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