Mathematical Analysis of Diagnosis Rate Effects in Covid-19 Transmission Dynamics with Optimal Control

Many countries around the world are trying to fight Covid-19, and their main methods are lockdown, quarantine, isolation, and awareness programs to encourage people to adopt social distancing and maintain personal hygiene. The lockdown is aimed to restrict the movement of humans from or to certain places. Quarantine is aimed toward separating the susceptible humans from infected or exposed humans as much as possible, whereas isolation is aimed toward keeping the confirmed cases of infected humans away from the rest of the population. The confirmed cases are mainly identified through the diagnosis of individuals who showed symptoms of Covid-19 and sometimes through random checking of individuals hoping to identify either asymptomatic or pre-symptomatic cases, which is generally an expensive method. In this chapter, we develop a mathematical model to investigate the role of diagnosis rate in the transmission dynamics of Covid-19 together with the combined effects of quarantine and isolation. Our model will be fully analyzed both qualitatively and quantitatively in order to gain insight about the role of different model parameters in the disease transmission dynamics, especially those related to diagnosis and quarantine. The analysis will include the estimation of both the basic and the control reproduction numbers, and sensitivity analysis of the reproduction numbers to the corresponding model parameters. The optimal control theory will be also applied to the model to examine the role of some other optimal control strategies and to study the effect of diagnosis and quarantine rates in the effectiveness of these controls.