A Robust Study of Tumor-Immune Cells Dynamics through Non-Integer Derivative

Abstract

It is renowned that the immune reaction in the tumour micro environment is a complex cellular process that requires additional research. Therefore, it is important to interrogate the tracking path behaviour of tumor-immune dynamics to alert policy makers about critical factors of the system. Here, we use fractional derivative to structure tumor-immune interactions. Furthermore, in our research, we concentrated on the qualitative investigation and time series analysis of tumor-immune cell interactions. The solution routes are examined using a new numerical technique to emphasis the impact of the factors on tumor-immune system. We focused on the behaviour of the system with fluctuation of different values. The most crucial components of the proposed system are identified and policymakers are advised. The outcomes of the present study are the strong predictor of clinical success and the in-out of immune cells in a tumour is also critical to treatment efficacy. As a result, studying the behaviour of tumor-immune cell interactions is important to predict crucial factors for the prevention and management to the health officials.

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

“…Radhakrishnan, Kundu, and Lakshmanan initially introduced RKLE in 1976, and it has since been used in a wide variety of physics, chemistry, and engineering contexts. The Radhakrishnan-Kundu-Lakshmanan equation (RKLE) has been used widely by recent researchers in order to examine how optical solitons move along optical fibres [33] , [34] , [35] , [36] . The Radhakrishnan-Kundu-Lakshmanan equation (RKLE) may be used to study dispersive optical solitons exhibiting the Kerr law nonlinearity without the four-wave mixing (4WM) effect which is regarded as being the basic case of fibre nonlinearity.…”

Fractional‐calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers

“…Mathematical models have been built to conceptualize the transmission route and provide the most effective management measures. [4][5][6] Therefore, large number of epidemic models illustrating the dynamics of typhoid fever transmission have been introduced in the literature. [7][8][9][10][11][12] However, few researchers tried to introduce control measure for the prevention of typhoid fever in the society.…”

“…Mathematical models have been built to conceptualize the transmission route and provide the most effective management measures 4–6 . Therefore, large number of epidemic models illustrating the dynamics of typhoid fever transmission have been introduced in the literature 7–12 .…”

Optimal Control for Fractional Order Dynamics of Tumor Growth

“…Natural killer (NK) cells, dendritic cells (DCs), neutrophils, and macrophages are a few of the cells involved in this process. The neutrophils requires tissue in order to circulate on the host blood and eliminate bacteria [15]. DCs, macrophages, and NK cells are necessary for tumor detection.…”