Stability analysis and numerical simulations via fractional calculus for tumor dormancy models

摘要: Abstract Fractional calculus is a field of mathematics in considerable expansion and has been understood as tool with wide range applications, including biological systems. Cancer dormancy state which cancer cells have an intrinsic rate reduced proliferation over period time, after they arise accelerated growth rate, usually triggering metastases. This work investigates via fractional two proposed ordinary differential equation systems calculus, address dynamics between tumor the immune system. Analyses comparison processes are performed through analytical study about equilibrium points each model numerical simulations by Nonstandard Finite Difference (NSFD) method. The results show important behaviors associated dormancy. first refers to qualitative changes stability point, strongly depend on order derivative represent scenarios where there no escape. second behavior damping some solutions, can longer periods time exit In this case, different orders used derivatives investigated, well their influence solutions against main parameters model.