Different initial conditions in fuzzy Tumor model

Esmaili, Somayeh Saraf; Nasrabadi, Ali Motie

doi:10.4236/jbise.2010.310130

Cited by 12 publications

(5 citation statements)

References 13 publications

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“…The concept of fuzzy is logic that is used to designate fuzziness rather than logic that is fuzzy. In oncology, related to tumor growth, fuzzy mathematical models have been used by A.M Nasarbadi in 2009 and 2010 in which fuzzy differential equations have been solved for tumor growth solutions [46,47].…”

Section: Fuzzy Theory and Applicationsmentioning

confidence: 99%

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Khaliq

Iqbal

Bhat

2021

Preprint

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Most of the cancer growth models have described the exponential growth patterns at the very initial stage with low cell population density. Eventually, decreasing the tumor growth rate at higher cell population densities because of deficiency in resources such as space and nutrients. However, recent studies at clinical and preclinical investigations of cancer initiation or reappaearance showed a population dynamics evincing that the growth rate increases as cell number increases. Hence, showing behaviour analogous to cooperative mechanism in the ecosystem and ecological effect called Allee effect. Based on these observations with two arguments i.e. change in initial population and growth rate. In this paper, the novel mathematical model of tumor growth kinetics with Allee effect under fuzzy environment is proposed. In this model the Generalized Hukuhara derivative approach is utilized to solve the fuzzy differential equations. Moreover, it is showen that the change in initial value and growth rate affects the cell density with the Allee effect under the fuzzy environment. Finally the superiority of model has been showen with the help of numerical simulation.

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Section: Fuzzy Theory and Applicationsmentioning

confidence: 99%

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Khaliq

Iqbal

Bhat

2021

Preprint

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“…It will vary depending upon the behavior of the model in both crisp and fuzzy. Many researchers have used a fuzzy concept of different nature: Somayeh Saraf Esmaili [24] used a fuzzy initial with a tumor model. Muhammad Zaini Ahmed [15] used a prey-predator model with a fuzzy initial population.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Two Species Model with Holling Type III Functional Response and Harvesting using Trapezoidal Fuzzy Numbers [TFN]

Vinothini

Kavitha

2023

Preprint

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Fuzzy dynamical modeling plays a major role in various fields, especially in biology. In our paper, we can formulate two species models with Holling type III functional response and harvesting as trapezoidal fuzzy numbers. Boundedness and positivity are found using a dynamic system. The existence of equilibrium points is existing in both crisp and fuzzy forms. Additionally, the parameters were defuzzed using a Graded Mean Value approach, and the dynamical system was reduced at various pessimistic levels. Equilibrium points and stability analysis are determined using a variational matrix in both crisp and fuzzy environments. Numerical simulations are carried out using MATLAB software. AMS Subject Classification: 34A07, 37N25, 92Bxx, 34K36.

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“…But ODE models just follow the average behavior of the system and cannot predict random noises or uncertainties of real systems. To overcome this deficiency of ODE models, fuzzy models [ 16 ], stochastic models [ 17 ] and ABM [ 1 ] can be used.…”

Section: Introductionmentioning

confidence: 99%

Extracting Mutual Interaction Rules Using Fuzzy Structured Agent-based Model of Tumor-Immune System Interactions

Allahverdy

Rahbar

Mirzaei

et al. 2019

jbpe

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Background: There are many studies to investigate the effects of each interacting component of tumor-immune system interactions. In all these studies, the distinct effect of each component was investigated. As the interaction of tumor-immune system has feedback and is complex, the alternation of each component may affect other components indirectly. Objective: Because of the complexities of tumor-immune system interactions, it is important to determine the mutual behavior of such components. We need a careful observation to extract these mutual interactions. Achieving these observations using experiments is costly and time-consuming. Material and Methods: In this experimental and based on mathematical modeling study, to achieve these observations, we presented a fuzzy structured agent-based model of tumor-immune system interactions. In this study, we consider the confronting of the effector cells of the adaptive immune system in the presence of the cytokines of interleukin-2 (IL-2) and transforming growth factor-beta (TGF-β) as a fuzzy structured model. Using the experimental data of murine models of B16F10 cell line of melanoma cancer cells, we optimized the parameters of the model. Results: Using the output of this model, we determined the rules which could occur. As we optimized the parameters of the model using escape state of the tumor and then the rules which we obtained, are the rules of tumor escape. Conclusion: The results showed that using fuzzy structured agent-based model, we are able to show different output of the tumor-immune system interactions, which are caused by the stochastic behavior of each cell. But different output of the model just follow the predetermined behavior, and using this behavior, we can achieve the rules of interactions.

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Different initial conditions in fuzzy Tumor model

Cited by 12 publications

References 13 publications

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Dynamics of a Two Species Model with Holling Type III Functional Response and Harvesting using Trapezoidal Fuzzy Numbers [TFN]

Extracting Mutual Interaction Rules Using Fuzzy Structured Agent-based Model of Tumor-Immune System Interactions

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