Mathematical analysis of COVID-19 dynamics with undetected asymptomatic cases and re-Infection

Abstract

In this article, we formulated a mathematical model for the transmission dynamic of COVID-19 using a deterministic approach that incorporates transmission by infectious individuals who are asymptomatic but embedded in the exposed class. Our model is an SEIRE model, which comprises five systems of ordinary differential equations. The major qualitative analyses, like the basic reproduction number, the disease-free and endemic equilibrium points and their stability analysis and sensitivity analysis, were rigorously analyzed. We analyzed the effect of the disease cycle on the backward bifurcation of the model. Our result shows that an increase in the recycle rate causes the model to exhibit backward bifurcation. When the scaling factor is between 0 and 0.555, it is impossible to eradicate the disease. When the scaling factor is between 0.556 and 0.680, there exists a critical value in which the basic reproduction number must be lower than before the disease can be wiped out. When the scaling factor is between 0.690 and 1.000, the bifurcation moves forward, and it is easier to eradicate the disease. Time series plots of the models show that the graph of the asymptomatic class settled at the higher endemic point than that of the symptomatic. Hence, we conclude that the asymptomatic class is more dangerous than the symptomatic class, so health workers and the government should be on the watch-out for that silent source of COVID-19 transmission.