A dynamic model for the COVID-19 with direct and indirect transmission pathways

Two common transmission pathways for the spread of COVID-19 virus are direct and indirect. The direct pathway refers to the person-to-person transmission between susceptibles and infectious individuals. Infected individuals shed virus on the objects, and new infections arise through touching a contaminated surface; this refers to the indirect transmission pathway. We model the direct and indirect transmission pathways with a S A D O R ode model. Our proposal explicitly includes compartments for the contaminated objects, susceptible individuals, asymptomatic infectious, detected infectious, and recovered individuals. We compute the basic reproduction number and epidemic growth rate of the model and determine how these fundamental quantities relate to the transmission rate of the pathways. We further study the relationship between the rate of loss of immunity and the occurrence of backward bifurcation. An efficient statistical framework is introduced to estimate the parameters of the model. We show the performance of the model in the simulation scenarios and the real data from the COVID-19 daily cases in South Korea.