Deterministic and stochastic approaches for a fat receptor-breast cancer model with crossover effects

Abstract

In this paper, the dynamics of a fat receptor-breast cancer model have been investigated by employing the deterministic and stochastic approaches. The existence of the endemic equilibrium, positivity of solutions and the calculation of the reproduction number are examined for the deterministic model and also the existence uniqueness of the stochastic model is discussed. Then, we will examine the crossover tendencies of the deterministic-stochastic model with the help of piecewise differential operators that take into account stochastic and power law processes followed by generalized Mittag-Leffler functions have been investigated. We employ a numerical scheme based on Newton polynomial to solve the deterministic-stochastic tumor growth model with fractional differential operators numerically. The graphical representations are simulated for different values of fractional order and the crossover tendencies of the deterministic-stochastic model are observed during the simulations.