Narrow Results

In this paper, we develop an epidemic model with a nonlinear function that describes the saturated digital contact tracing. The model is theoretically and numerically analyzed based on its dynamics. The model equilibria points and the basic reproduction number are obtained. However, the proposed model reveals both backward and forward bifurcation, and backward bifurcation occurs when the digital contact tracing saturation parameter is larger than a specific threshold. Real data are used to fit the model and estimate the parameter values. Sensitivity analysis reveals that interventions such as reducing the infection rate, enhancing quarantine efforts, and accelerating vaccination can effectively reduce the basic reproduction number, $R_0$. Simulations show that improving tracing accuracy and encouraging greater participation in providing personal track information can effectively reduce the peak of undetected exposed individuals. Moreover, we analyze the expression for the specific threshold and determine that the increasing hospital resources and strengthening patient quarantine can reduce the potential occurrence of backward bifurcation. The analysis and simulations presented in this paper provide valuable suggestions for the prevention and control of the epidemic.