Nonlinear dynamics of estrogen receptor-positive breast cancer integrating experimental data: A novel spatial modeling approach.

Oncology research has focused extensively on estrogen hormones and their function in breast cancer proliferation. Mathematical modeling is essential for the analysis and simulation of breast cancers. This research presents a novel approach to examine the therapeutic and inhibitory effects of hormone and estrogen therapies on the onset of breast cancer. Our proposed mathematical model comprises a nonlinear coupled system of partial differential equations, capturing intricate interactions among estrogen, cytotoxic T lymphocytes, dormant cancer cells, and active cancer cells. The model's parameters are meticulously estimated through experimental studies, and we conduct a comprehensive global sensitivity analysis to assess the uncertainty of these parameter values. Remarkably, our findings underscore the pivotal role of hormone therapy in curtailing breast tumor growth by blocking estrogen's influence on cancer cells. Beyond this crucial insight, our proposed model offers an integrated framework to delve into the complexity of tumor progression and immune response under hormone therapy. We employ diverse experimental datasets encompassing gene expression profiles, spatial tumor morphology, and cellular interactions. Integrating multidimensional experimental data with mathematical models enhances our understanding of breast cancer dynamics and paves the way for personalized treatment strategies. Our study advances our comprehension of estrogen receptor-positive breast cancer and exemplifies a transformative approach that merges experimental data with cutting-edge mathematical modeling. This framework promises to illuminate the complexities of cancer progression and therapy, with broad implications for oncology.

New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach.

The existing work deals with the Jeffrey fluid having an unsteady flow, which is moving along a vertical plate. A fractional model with ternary, hybrid, and nanoparticles is obtained. Using suitable dimensionless parameters, the equations for energy, momentum, and Fourier's law were converted into non-dimensional equations. In order to obtain a fractional model, a fractional operator known as the Prabhakar operator is used. To find a generalized solution for temperature as well as a velocity field, the Laplace transform is used. With the help of graphs, the impact of various parameters on velocity as well as temperature distribution is obtained. As a result, it is noted that ternary nanoparticles approach can be used to increase the temperature than the results obtained in the recent existing literature. The obtained solutions are also useful in the sense of choosing base fluids (water, kerosene and engine oil) for nanoparticles to achieved the desired results. Further, by finding the specific value of fractional parameters, the thermal and boundary layers can be controlled for different times. Such a fractional approach is very helpful in handling the experimental data by using theoretical information. Moreover, the rate of heat transfer for ternary nanoparticles is greater in comparison to hybrid and mono nanoparticles. For large values of fractional parameters, the rate of heat transfer decreases while skin friction increases. Finally, the present results are the improvement of the results that have already been published recently in the existing literature. Fractional calculus enables us to control the boundary layers as well as rate of heat transfer and skin friction for finding suitable values of fractional parameters. This approach can be very helpful in electronic devices and industrial heat management system.

Numerical investigations of the nonlinear smoke model using the Gudermannian neural networks.

These investigations are to find the numerical solutions of the nonlinear smoke model to exploit a stochastic framework called gudermannian neural works (GNNs) along with the optimization procedures of global/local search terminologies based genetic algorithm (GA) and interior-point algorithm (IPA), i.e., GNNs-GA-IPA. The nonlinear smoke system depends upon four groups, temporary smokers, potential smokers, permanent smokers and smokers. In order to solve the model, the design of fitness function is presented based on the differential system and the initial conditions of the nonlinear smoke system. To check the correctness of the GNNs-GA-IPA, the obtained results are compared with the Runge-Kutta method. The plots of the weight vectors, absolute error and comparison of the results are provided for each group of the nonlinear smoke model. Furthermore, statistical performances are provided using the single and multiple trial to authenticate the stability and reliability of the GNNs-GA-IPA for solving the nonlinear smoke system.