scholarly journals A mathematical model of viral oncology as an immuno-oncology instigator

2019 ◽  
Author(s):  
Tyler Cassidy ◽  
Antony R Humphries
Keyword(s):  
Mathematical Model ◽  
Distributed Delay ◽  
Cycle Duration ◽  
Necessary And Sufficient Condition ◽  
Cell Cycle Duration ◽  
Viral Therapy ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
The Mathematical Model

Abstract We develop and analyse a mathematical model of tumour–immune interaction that explicitly incorporates heterogeneity in tumour cell cycle duration by using a distributed delay differential equation. We derive a necessary and sufficient condition for local stability of the cancer-free equilibrium in which the amount of tumour–immune interaction completely characterizes disease progression. Consistent with the immunoediting hypothesis, we show that decreasing tumour–immune interaction leads to tumour expansion. Finally, by simulating the mathematical model, we show that the strength of tumour–immune interaction determines the long-term success or failure of viral therapy.

scholarly journals A mathematical model of viral oncology as an immuno-oncology instigator

2018 ◽  
Author(s):  
Tyler Cassidy ◽  
Antony R. Humphries
Keyword(s):  
Mathematical Model ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Cycle Duration ◽  
Cell Cycle Duration ◽  
Viral Therapy ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Term Response

AbstractWe develop and analyse a mathematical model of tumour-immune interaction that explicitly incorporates heterogeneity in tumour cell cycle duration by using a distributed delay differential equation. Our necessary and sufficient conditions for local stability of the cancer free equilibrium completely characterise the importance of tumour-immune interaction in disease progression. Consistent with the immunoediting hypothesis, we show that decreasing tumour-immune interaction leads to tumour expansion. Finally, we show that immune involvement is crucial in determining the long-term response to viral therapy.

A Necessary and Sufficient Condition for the Oscillation of an Even Order Nonlinear Delay Differential Equation

1973 ◽  
Vol 25 (5) ◽  
pp. 1078-1089 ◽  
Author(s):  
Bhagat Singh
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Oscillatory Behavior ◽  
Necessary And Sufficient Condition ◽  
Even Order ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

In this paper we study the oscillatory behavior of the even order nonlinear delay differential equation(1)where(i) denotes the order of differentiation with respect to t. The delay terms τi σi are assumed to be real-valued, continuous, non-negative, non-decreasing and bounded by a common constant M on the half line (t0, + ∞ ) for some t0 ≧ 0.

Oscillation and Global Attractivity in a Periodic Delay Equation

1996 ◽  
Vol 39 (3) ◽  
pp. 275-283 ◽  
Author(s):  
J. R. Graef ◽  
C. Qian ◽  
P. W. Spikes
Keyword(s):  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
All Solutions ◽  
Periodic Delay ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractConsider the delay differential equationwhere α(t) and β(t) are positive, periodic, and continuous functions with period w > 0, and m is a nonnegative integer. We show that this equation has a positive periodic solution x*(t) with period w. We also establish a necessary and sufficient condition for every solution of the equation to oscillate about x*(t) and a sufficient condition for x*(t) to be a global attractor of all solutions of the equation.

scholarly journals The Solution of a Mathematical Model for Dengue Fever Transmission Using Differential Transformation Method

2019 ◽  
pp. 82-87
Author(s):  
Felix Yakubu Eguda ◽  
Andrawus James ◽  
Sunday Babuba
Keyword(s):  
Mathematical Model ◽  
Dengue Fever ◽  
Transformation Method ◽  
Vital Role ◽  
Differential Transformation Method ◽  
Linear Ordinary Differential Equations ◽  
Differential Transformation ◽  
Long Term Behavior ◽  
The Mathematical Model

Differential Transformation Method (DTM) is a very effective tool for solving linear and non-linear ordinary differential equations. This paper uses DTM to solve the mathematical model for the dynamics of Dengue fever in a population. The graphical profiles for human population are obtained using Maple software. The solution profiles give the long term behavior of Dengue fever model which shows that treatment plays a vital role in reducing the disease burden in a population.

The Mathematical Modeling Stages of Combining the Carriage of Goods for Indefinite, Fuzzy and Stochastic Parameters

2020 ◽  
Vol 12 (7) ◽  
Author(s):  
Sergiy Kotenko ◽  
◽  
Vitalii Nitsenko ◽  
Iryna Hanzhurenko ◽  
Valerii Havrysh ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Radical Change ◽  
Short Term ◽  
Best Value ◽  
Stochastic Parameters ◽  
Mode Of Transportation ◽  
Cargo Transportation ◽  
Risk Parameters ◽  
The Mathematical Model

Combined cargo transportation in Ukraine is characterized by the presence of uncertain risks. The aim of the article was to propose a mathematical model for choosing the mode of transportation that would correspond to the best value of the integral objective function in the presence of fuzzy, stochastic and uncertain risk parameters. The efficiency of the mathematical model provided the possibility of forming not only long-term forecasts that require significant time, but also short-term forecasts in real time. This allows to quickly change routes and conditions of transportation. Practical testing of the mathematical model revealed the assimilating nature of some uncertain risks. The results of the analysis are given in the article. The realization of such a risk leads to a radical change in all conditions of transportation. Long-term forecasts allow to predict new routes and conditions of transportation.

Modeling Colorectal Cancer

2013 ◽  
pp. 53-75 ◽  
Author(s):  
Svetoslav Nikolov ◽  
Mukhtar Ullah ◽  
Momchil Nenov ◽  
Julio Vera Gonzalez ◽  
Peter Raasch ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Colorectal Cancer ◽  
Mathematical Model ◽  
Systems Biology ◽  
Numerical Simulations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Extended Version ◽  
Necessary And Sufficient ◽  
The Mathematical Model

Mathematical modeling is increasingly used to improve our understanding of colorectal cancer. In the first part of this chapter, the authors give a review of systems biology approaches to investigate colorectal cancer. In the second part, the mathematical model proposed by Johnston et al. (2007) is expanded to include time delays and analysed for its stability. For both models, the original and the extended version, the authors obtain the necessary and sufficient conditions for stability. This is confirmed by numerical simulations. Thus, some new mathematical and biological results are obtained.

scholarly journals Necessary and sufficient conditions for oscillations of delay differential inequalities

1989 ◽  
Vol 39 (2) ◽  
pp. 161-165
Author(s):  
Jurang Yan
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Differential Inequalities ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Delay Differential Inequality

A necessary and sufficient condition is obtained for a first order linear delay differential inequality to be oscillatory. Our main result improves and extends some known results.

scholarly journals Strategic Factors in the Capital Structure of the Services and Communication Sectors in Mexico

2015 ◽  
pp. 33-50
Author(s):  
Juan Gaytán Cortés ◽  
Joel Bonales Valencia ◽  
Juan Antonio Vargas Barraza
Keyword(s):  
Mathematical Model ◽  
Empirical Study ◽  
Capital Structure ◽  
Stock Exchange ◽  
Theoretical Framework ◽  
Strategic Factors ◽  
Communication Sector ◽  
The Mathematical Model ◽  
The Capital Structure

The purpose of this research was to identify the strategic factors of the country and the companies, to incorporate long term debt in the capital structure of the companies of services and the communication sector that they quoted on the Mexican Stock Exchange in the periods 2000-2012.The mathematical model and the factors used in this empirical study were used in the investigations that were analyzed in the theoretical framework.

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