2022/11/09 by Tinaw Tilahun Asmamaw, Kiros Gebreargawi, Gebreargawi, Kiros
Mathematics · Medicine · #COVID-19 #COVID-19 epidemiological studies #Forward bifurcation #Mathematical and Theoretical Epidemiology and Ecology Models #Optimal control #Protection #SARS-CoV-2 and COVID-19 Research #Sensitivity analysis #Stability analysis
paper · doi:10.20372/8xv6na04
openalex publication_date 2022/11/09 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/01
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.