Modeling the SARS-CoV-2 parallel transmission dynamics: Asymptomatic and symptomatic pathways

Asymptomatic transmission of the coronavirus disease and the infected individual prediction has become very important in the COVID-19 outbreak study. The asymptomatic and symptomatic transmission studies are still ongoing to assess their impacts on disease monitoring and burden. However, there has been limited research on how asymptomatic and symptomatic transmissions together can affect the coronavirus disease outbreak. A mathematical model is therefore needed to be developed in order to assess the effect of these transmissions on the coronavirus disease dynamics. This paper develops a mathematical model concerning asymptomatic and symptomatic disease transmission processes in the COVID-19 outbreak. The model sensitivity has been analysed in terms of the variance of each parameter, and the local stability at two equilibrium points have been discussed in terms of the basic reproduction number (R₀). It is found that the disease-free equilibrium gets stable for R₀ < 1 whereas the endemic equilibrium becomes stable for R₀ > 1 and unstable otherwise. The proportion of the effect of asymptomatic and symptomatic transmission rates on R₀ is calculated to be approximately between 1 and 3. The results demonstrate that asymptomatic transmission has a significant impact compared to symptomatic transmission in the disease outbreak. Outcomes of this study will contribute to setting an effective control strategy for the COVID-19 outbreak.