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.

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.

Credibility Trap: Japan today and China tomorrow

2006 ◽  
Vol 25 (1) ◽  
pp. 31-50
Author(s):  
Kensei Hiwaki ◽  
Junie Tong
Keyword(s):  
Human Development ◽  
Present Article ◽  
Socioeconomic Development ◽  
Sufficient Conditions ◽  
Theoretical Framework ◽  
Normative Framework ◽  
Specific Culture ◽  
Prevention And Cure ◽  
Necessary And Sufficient

This article provides a theoretical framework for a long-term socioeconomic lethargy (Credibility Trap) that results from the liquidation of holistic society-specific culture. As for example, it deals with the cases of Japan today and China tomorrow, elaborating on the slight of their respective society-specific cultures in a century-long process of “modernization”. The present theoretical framework primarily consists of three pivotal concepts, viz., Credibility Trap, society-specific cultures (Cultures) and market fundamentalism (Market), which facilitates a clear, concise and effective argument that the liquidation of their respective holistic Cultures may intimately relate to their actual and potential socioeconomic lethargy. Also, the present article concentrates on the elaboration of some promising avenues for prevention and cure of Credibility Trap. Such avenues comprise the necessary and sufficient conditions for a balanced socioeconomic development; a theoretical framework for a perpetual “virtuous” circle among cultural enrichment, comprehensive human development and balanced socioeconomic development; and a normative framework of multi-faceted value enhancement for vitality augmentation and cultural enrichment within a society.

Oscillation of the Riemann–Weber Version of Euler Differential Equations with Delay

2000 ◽  
Vol 7 (3) ◽  
pp. 577-584
Author(s):  
Jitsuro Sugie ◽  
Mitsuru Iwasaki
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Equations With Delay ◽  
Oscillation Of Solutions

Abstract Our concern is to consider delay differential equations of Euler type. Necessary and sufficient conditions for the oscillation of solutions are given. The results extend some famous facts about Euler differential equations without delay.

scholarly journals Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 61 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
All Solutions ◽  
Functional Differential ◽  
Delay Differential ◽  
Comparison Technique

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples.

scholarly journals Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
R. Rath ◽  
N. Misra ◽  
L. Padhy
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
T Tau

AbstractIn this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) $$\left[ {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

scholarly journals The Oscillation of a Class of the Fractional-Order Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qianli Lu ◽  
Feng Cen
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Analysis Method ◽  
Constant Coefficients ◽  
Delay Differential ◽  
Necessary And Sufficient

Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this,α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.

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