Generalized Hukuhara derivative approach for Gompertz tumor growth with allee effect under fuzzy environment

Abstract

In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary from time to time, and in real life, it is very difficult to estimate the exact cell count. In this vague situation, the initial condition, coefficient, and both together are taken as the fuzzy number. In this paper, the GHD approach is used to solve the fuzzy tumor growth model in which four different cases are considered with respect to (i)-gH differentiability and (ii)-gH differentiability concept. The main objective of this study is to present a significant reduction in uncertainty while modeling the tumor growth in a fuzzy environment with the Allee effect. Finally, the proposed model and technique are illustrated by numerical simulation and analysis of tumor growth is conducted.

Keywords

• mathematical modeling
• gh-derivative approach
• fuzzy theory
• tumor growth
• allee effect
• differential equation
• soft computing