A Mathematical Model for the Transmission Dynamics of COVID-19 Pandemic Considering Protected and Hospitalized with Optimal Control

Abstract

In this paper, we propose a mathematical model to investigate coronavirus diseases (COVID-19) transmission in the presence of protected and hospitalized classes. We establish that the solution of the dynamical system remains positive and bounded. We compute the disease free equilibrium point and analyze the stability behavior of the steady state solutions. We determine the basic reproduction number (R) and demonstrate that the disease fades away when R₀ < 1 but persists in the population when R₁ > 1. The center manifold theory is used to assess the local stability of the endemic equilibrium. The model demonstrates a forward bifurcation, and a sensitivity analysis is conducted. The sensitivity analysis reveals that R₀ is highly influenced by the protection rate, highlighting the necessity of
maintaining a high level of protection along with hospitalization to effectively control the disease. We develop optimal strategies for
protection and hospitalization. The characterization of the optimal control is derived using Pontryagin’s Maximum Principle. Numerical results for the dynamics of the COVID-19 outbreak and its optimal control show that a combination of protection and hospitalization is the most effective strategy for reducing the spread of COVID-19 within the population.