A hybrid deep learning method for controlled stochastic Kolmogorov systems with regime-switching

In this paper, we employ numerical methods based on deep learning algorithms for solving controlled stochastic Kolmogorov systems with regime-switching. Different from classical control problems, each component of the state in controlled Kolmogorov systems is nonnegative. Due to the nonlinearity and complexity of the controlled stochastic Kolmogorov systems, we develop a hybrid deep learning method to numerically solve the optimal controls under this system. Subsequently, we apply the hybrid deep learning method to solve a specific case of a controlled stochastic Kolmogorov system, specifically controlled SIS (susceptible-infected-susceptible) systems. Finally, the effectiveness of the proposed hybrid deep learning method is verified through numerical results.