optimal control Alzheimer's Disease reaction-diffusion equation
Abstract:
The objective of this paper is to identify the most effective therapy strategies for inhibiting the growth of Amyloid-beta concentration in the brain. To achieve this, we utilize a reaction- diffusion model that characterizes the diffusion and proliferation of Amyloid-beta, and formulate an optimization problem that minimizes both the concentration and potential side-effects. We establish the existence of an optimal solution and analyze the necessary conditions for obtaining an optimal solution. Subsequently, we propose an algorithm and present numerical simulations based on our algorithm. Specifically, we compute an explicit solution in a special scenario for comparison with the outcome of our algorithm.
