Dynamical analysis for the impact of asymptomatic infective and infection delay on disease transmission

Abstract

The influence of asymptomatic patients on disease transmission has attracted more and more attention, but the mechanism of some factors affecting disease transmission needs to be studied urgently. Considering the self-healing rate of asymptomatic patients, the cure rate of symptomatic patients, the transformation rate from asymptomatic to symptomatic and the infection delay, a type of infectious disease dynamics model SIsIaS with asymptomatic infection and infection delay is established in this paper. It is found that both the infection delay and the difference size between the cure rate and the self-healing rate not only affect the minimum value of the total number of patients in the persistent state of the disease, but also lead to disease extinction to be controlled by the proportion of symptomatic patients in patients. Moreover, the infection delay can lead to local Hopf bifurcation of periodic solutions. By using the normal form and center manifold theory the direction of Hopf bifurcations and the stability of bifurcated periodic solutions are discussed. At last, sensitivity analysis shows that the infection delay can change the correlation of the proportion of symptomatic patients in patients and the transformation rate to the total number of patients.