Global stability of an SAIRD epidemiological model with negative feedback

In this work, we study the dynamical behavior of a modified SIR epidemiological model by introducing negative feedback and a nonpharmaceutical intervention. The first model to be defined is the Susceptible–Isolated–Infected–Recovered–Dead (SAIRD) epidemics model and then the S-A-I-R-D-Information Index (SAIRDM) model that corresponds to coupling the SAIRD model with the negative feedback. Controlling the information about nonpharmaceutical interventions is considered by the addition of a new variable that measures how the behavioral changes about isolation influence pandemics. An analytic expression of a replacement ratio that depends on the absence of the negative feedback is determined. The results obtained show that the global stability of the disease-free equilibrium is determined by the value of a certain threshold parameter called the basic reproductive number R0 and the local stability of the free disease equilibrium depends on the replacement ratios. A Hopf bifurcation is analytically verified for the delay parameter. The qualitative analysis shows that the feedback information index promotes more changes to the propagation of the disease than other parameters. Finally, the sensitivity analysis and simulations show the efficiency of the infection rate of the information index on an epidemics model with nonpharmaceutical interventions.