A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator.

By Dumitru Băleanu, Amin Jajarmi, Samaneh Sadat Sajjadi, Dorota Mozyrska. Chaos, 2019

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In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined.

Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/c189f61dae659025c33cc46e32da917ac669047f

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Citations in the corpus

Lyapunov functions for fractional-order systems in biology: Methods and applications (2020, positive): “and long-range interactions, which exist in most biological systems. For this reason, fractional diﬀerential equations have recently been used to model more accurately such real processes: see, e.g., [5, 8, 35, 38]. As is well known, stability analysis is an important performance metric for any dyna”
A finite difference scheme for the nonlinear time‐fractional partial integro‐differential equation (2020, methodology): “(4) Having the Caputo derivative C0 D 𝛼 t in the generalized Equation (1) can improve the modeling accuracy for describing physical phenomena involving viscoelastic forces.”