A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment

Sunil Kumar, Ajay Kumar, Bessem Samet, J.F. Gómez-Aguilar and M.S. Osman

Chaos, Solitons & Fractals, 2020, vol. 141, issue C

Abstract: A tumor is most dangerous disease of medical science which is a mass or lumps of tissue that’s formed by an accumulation of abnormal cells. A famous fractional tumor-immune model is interpreting the dynamics of tumor and effector cells. In this work, we provide a comparative and chaotic study of tumor and effector cells through fractional tumor-immune dynamical model. A new arbitrary operator based on the Mittag-Leffler law is assumed for this study. Again, we examine the interactions among distinct tumor cell inhabitants and immune structure through a model of real world problem of medical science. We First investigate the dynamical effect of the activation of the effector immune and tumor cells by using Adams-Bashforth-Moulton and Toufik-Atangana methods. Furthermore, this paper analyses the existence and uniqueness of given tumor-immune model of arbitrary order. Further, we have examined the dynamical behaviors of the fractional tumor-immunne model and obtained results are compared with exiting results by other methods. Numerical simulations are executed by Adams-Bashforth-Moulton and Toufik-Atangana methods using popular Atangana-Baleanu fractional derivative. Our obtained results will be useful for biologists to the treatment of cancer disease.

Keywords: Fractional tumor-immune model; AB derivative; Existence and uniqueness results; Adams-Bashforth-Moulton method; Toufik-Atangana method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307177

DOI: 10.1016/j.chaos.2020.110321

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