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 demonstrate the positivity and boundedness of the
solution of the dynamical system. We compute the disease free equilibrium
point and analyze the stability behavior of the steady state solutions. We
compute the basic reproduction number (R₀) and show that for R < 1 the
disease dies out and for R > 1 the disease is endemic. The local stability
of the endemic equilibrium point is determined using center manifold theory.
The model exhibits a forward bifurcation and the sensitivity analysis
is performed. The sensitivity analysis we establish that R₀ is most sensitive
to the rate of protection and that a high level of protection needs to be
maintained as well as hospitalization to control the disease. Based on this
we devise optimal protection and hospitalization strategies. Characterization
of the optimal control is established using Pontryagin’s Maximum Principle. Numerical results for the COVID-19 outbreak dynamics and its optimal control revealed that a combination of protection and hospitalization is the best strategy to mitigate the spread of COVID-19 in the population.