Dynamical modeling and optimal control strategies to reduce the spread of COVID-19

Abstract

In March 2020, the World Health Organization announced the occurrence of a pandemic caused by SARS-CoV-2, a coronavirus that results in COVID-19. This paper presents a compartmental model called SEQIRD used to analyse the transmission of the disease. SEQIRD divides the population into susceptible, exposed, quarantined, infected, recovered, and deceased categories.

The model possesses two equilibrium states: endemic and disease-free. We assessed stability around these equilibria using the Next Generation Matrix to determine the basic reproduction number, ℜ₀. Local stability was verified through the Routh-Hurwitz criteria. Lyapunov's method supported global stability analysis. The disease-free equilibrium is asymptotically stable if ℜ₀ is under one. Conversely, if ℜ₀ exceeds one, the endemic equilibrium is asymptotically stable. Three controls were applied: mask usage, vaccination, and medical treatment. Optimal control theory and the Pontryagin Maximum Principle were employed to minimize COVID-19 spread. Numerical simulations based on Central Java; Indonesia data validated the model. The reproduction number was calculated as 2.91, signifying endemic stability. Use of masks, vaccination, and treatment noticeably reduced exposure and infection in the simulations, demonstrating the effectiveness of these strategies for controlling spread.