Mathematical Ecology of Cancer

Hillen, Thomas; Lewis, Mark A.

doi:10.1007/978-3-319-03759-2_1

Cited by 3 publications

(2 citation statements)

References 66 publications

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“…Relating cancer to the ecological and evolutionary process, in a stable ecosystem (healthy body), if one of the species (cells) getaway from ecological restraints (immune system) and proliferates speedily, hence destroying the stability, precipitating the extinction of neighbouring species and therefore, collapse the ecosystem (disturbs body's balance, cause the death of healthy cells and made the body like acidic) called cancer [1,2]. The tumor growth cell mechanism depends upon how potentially cells are capable of availing the facilities and how profitably they construct a mechanism to escape the identification and extinction by the defense system of the body [3].…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

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

Khaliq

Iqbal

Bhat

2021

Preprint

View full text Add to dashboard Cite

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“…Furthermore, although the immune system routinely recognises and kills any dangerous host including cancer, mutations can provide cancer cells with the ability to avoid detection or immuno-suppress the environment, advantaging tumour progression or preventing eradication [1]. Processes involving mutations, cell growth and immune surveillance cumulatively result in the emergence of different cancer populations integrated in an environment made up of healthy tissue, immune cells and stroma [6,7].…”

Section: Introductionmentioning

confidence: 99%

Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions

Piretto

Delitala

Kim

et al. 2019

Mathematical Biosciences

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Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies.In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised.By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects

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A QSP model of prostate cancer immunotherapy to identify effective combination therapies

Coletti

Leonardelli

Parolo

et al. 2020

Sci Rep

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dependent on androgen signaling, androgen deprivation therapy, either by chemical or surgical castration, is the first-line treatment for advanced PCa 40. Although this therapy is initially highly effective in most of the patients, in some cases the tumor evolves into an androgen independent form that currently lacks efficacious therapeutic options 41. The transition from the androgen dependent to the androgen independent state may occur through several mechanisms that are not yet completely understood 42. In this context, immunotherapy represents a highly promising new treatment approach. Over the last few years, numerous pre-clinical and clinical studies have been performed to develop and test different PCa immunotherapies 43. A main achievement has been the US Food and Drug Administration (FDA) approval of sipuleucel-T, so far the only approved immunotherapy for PCa treatment 40. Compared with other types of cancer, PCa is relatively insensitive to the most popular immunotherapies and additional studies are needed to understand the mechanisms underlying this lack of immune responsiveness 44. Thus, evaluating combination therapies is another important step to improve therapeutic benefits 45. We herein propose a QSP model of prostate cancer that extends a previous one published by Peng et al. 46 based on data from a murine Pten prostate cancer model 47,48. Although Peng and coworkers already described the action of CTLs, dendritic cells, Tregs, androgens and interleukin-2 (IL-2) in the tumor microenvironment, we extended the characterization of the immune system by including MDSCs and Natural Killer (NK) cells as potential targets for new prostate cancer therapies. The main goal of this contribution is, indeed, to provide a mathematical model able to test the efficacy of several immunotherapies and their combinations. We incorporate a wide range of experimental data from literature 31,46,49-51 to implement seven treatments. The efficacy of therapies is assessed considering the model-predicted tumor inhibitory effect and the synergy of combination therapies. Synergy between treatments plays a crucial role to reduce the dosage of each drug maintaining a satisfactory overall treatment efficacy, improving patients' quality of life 52. The paper is organized as follows. In the result section we provide a description of the model diagram and a detailed explanation of the Ordinary Differential Equations (ODEs) constituting the mathematical model. We provide the model simulations to verify the reproducibility of the experimental data and to compare the predicted outcomes with known biological mechanisms. We identify the most effective treatment combinations for prostate cancer through the model-predicted tumor size and the treatment synergy. Moreover, we emphasize the androgen deprivation therapy as leading treatment in a decision tree to choose the best protocol to treat androgen independent prostate cancer. Finally, a discussion of the results and a description of the study limitations is provided. Results The mathema...

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Mathematical Ecology of Cancer

Cited by 3 publications

References 66 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

Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions

A QSP model of prostate cancer immunotherapy to identify effective combination therapies

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