Optimal Control Harmony: Navigating Deterministic and Stochastic Realms With a Two-Strain Model Using Pontryagin’s Maximum Principle

In this paper, we study optimal control solutions using a two-strain SARS-CoV-2 deterministic epidemic model characterized by standard incidence, alongside a two-strain stochastic model incorporating a random transmission rate. We present proofs demonstrating the existence, uniqueness, and boundedness of a positive solution for any positive initial value for both models. An algorithm for simulating the ensemble average optimal control solution is introduced and its realism is compared to both stochastic and deterministic solutions. Additionally, we include graphical representations to illustrate the dynamics and outcomes of our models. Our findings suggest that ensemble average optimal control simulations may offer enhanced visualization and realism compared to both stochastic and deterministic solutions.