Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

Abstract

The coronavirus disease 2019, started spreading around December 2019, still persists in the population all across the globe. Though different countries have been able to cope with the disease to some extent and vaccination for the same has been developed, it cannot be ignored that the disease is still not on the verge of completely eradicating, which in turn creates a need for having deeper insights of the disease in order to understand it well and hence be able to work towards its eradication. Meanwhile, using mitigation strategies like non-pharmaceutical interventions can help in controlling the disease. In this work, our aim is to study the dynamics of COVID-19 using compartmental approach by applying various analytical methods. We obtain formula for important tools like R0and establish the stability of disease-free equilibrium point for R0<1. Further, based on R0, we discuss the stability and existence of the endemic equilibrium point. We incorporate various control strategies possible and using optimal control theory, study their expected positive impacts on the spread of the disease. Later, using a biologically feasible set of parameters, we numerically analyse the model. We even study the trend of the outbreak in China, for over 120 days, where the active cases rise up to a peak and then the curve flattens.

Keywords

• COVID-19
• Epidemics
• Basic reproduction number
• Optimality
• Sensitivity analysis
• Delay