An SIQRS Model of Infectious Diseases with Time-Delayed Control Measures

In this paper, we develop a modified SIQRS (susceptible-infected-quarantined-recovered-susceptible) compartmental model of infectious diseases based on the mean field theory of heterogeneous networks to analyze the effect of time-delayed quarantine measures on the transmission of infectious diseases. First, considering the nonlinear infection rate with social network structure, this paper establishes a modified SIQRS compartmental model on heterogeneous network, and introduces two time-delayed parameters into the corresponding ordinary differential equation model. Then, the basic reproduction number R_{0} of this model is obtained by regeneration matrix method, and the threshold conditions of infection outbreak are analyzed. Then, the disease-free equilibrium point (DFE) and the endemic disease equilibrium point (EDE) are obtained when the system is stable under different conditions, and the stability analysis of these two points is performed. Finally, the transmission mechanism of infectious diseases in reality is analyzed by numerical simulation, and the corresponding prevention and control measures are proposed.