Mathematical Model Formulation and Analysis for COVID-19 Transmission with Virus Transfer Media and Quarantine on Arrival

Abstract

An outbreak of severe acute respiratory syndrome (COVID-19) killed 287,355 with 4, 257,578 cases worldwide as of May 12, 2020. In this paper, we propose an $SEQ{I}_s{I}_{a}RM$ deterministic mathematical model which contains compartments for both human-to-human transmission and transmission through contaminated surfaces. Without intervention, the role of symptomatic and asymptomatic cases in humans is found to be very high in the transmission of the virus. Sensitive parameters which are associated with increased transmission of the COVID- $19$ virus were identified. According to the sensitivity results, the most sensitive parameters were disease-induced death rates of symptomatic and asymptomatic infectious people ( $\sigma$ ), the rate of removal of virus from surfaces and environment ( $\nu$ ), and the rate of infection by asymptomatic infectious people ( ${\lambda }_2$ ) and symptomatic infectious people ( ${\lambda }_1$ ). The numerical results of our model confirm the sensitivity results that there are more new incidences of asymptomatic cases than symptomatic cases, which escalates the transmission of the virus in the community. Combined interventions like increasing both the rate of removal of viruses from surfaces and environment and decreasing the rate of infection in asymptomatic cases can play a significant role in reducing the average number of secondary infection ( $R_0$ ) to less than unity, causing COVID- $19$ to die out.