Mathematical modeling and optimal intervention of COVID-19 outbreak

Background: The COVID-19 pandemic has become a formidable threat to global health and economy. The coronavirus SARS-CoV-2 that causes COVID-19 is known to spread by human-to-human transmission, and in about 40% cases, the exposed individuals are asymptomatic which makes it difficult to contain the virus. Methods: This paper presents a modified SEIR epidemiological model and uses concepts of optimal control theory for analysis of the effects of intervention methods of the COVID19. Fundamentally the pandemic intervention problem can be viewed as a mathematical optimization problem as there are contradictory outcomes in terms of reduced infection and fatalities but with serious economic downturns. Results: Concepts of optimal control theory have been used to determine the optimal control (intervention) levels of i) social contact mitigation and suppression, and ii) pharmaceutical intervention modalities, with minimum impacts on the economy. Numerical results show that with optimal intervention policies, there is a significant reduction in the number of infections and fatalities. The computed optimum intervention policy also provides a timeline of systematic enforcement and relaxation of stay-at-home regulations, and an estimate of the peak time and number of hospitalized critical care patients. Conclusion: The proposed method could be used by local and state governments in planning effective strategies in combating the pandemic. The optimum intervention policy provides the necessary lead time to establish necessary field hospitals before getting overwhelmed by new patient arrivals. Our results also allow the local and state governments to relax social contact suppression guidelines in an orderly manner without triggering a second wave.