A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment. (December 2020)

• Record Type: Journal Article
• Authors: Kumar, Sunil; Kumar, Ajay; Samet, Bessem; Gómez-Aguilar, J.F.; Osman, M.S.
• Is Part Of: Chaos, solitons and fractals. Volume 141(2020)
• Publication Date: 2020-12
• Subjects: Fractional tumor-immune model -- AB derivative -- Existence and uniqueness results -- Adams-Bashforth-Moulton method -- Toufik-Atangana method; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110321
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: A comparative and chaotic study of tumor and effector cells through fractional tumor-immune dynamical model was investigated. Performance was done using the strategy of Adams-Bashforth-Moulton and Toufik-Atangana methods. The existence and uniqueness of the given tumor-immune model of arbitrary order are analyzed. 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.