Dynamic behaviors of a modified SIR model with nonlinear incidence and recovery rates

Abstract

A complex SIR epidemic dynamical model using nonlinear incidence rate and nonlinear recovery rate is established to consider the impact of available hospital beds and interventions reduction on the spread of infectious disease. Rigorous mathematical results have been established for the model from the point of view of stability and bifurcation. The model has two equilibrium points when the basic reproduction number ; a disease-free equilibrium and a disease endemic equilibrium . We use LaSalle’s invariance principle and Lyapunov’s direct method to prove that is globally asymptotically stable if the basic reproduction number , and is globally asymptotically stable if , under some conditions on the model parameters. The existence and nonexistence of limit cycles are investigated under certain conditions on model parameters. The model exhibits Hopf bifurcation near the disease endemic equilibrium. We further show the occurring of backward bifurcation for the model when there is limited number of hospital beds. Finally, some numerical results are represented to validate the analytical results.

On the Effects of Saturation Terms on A SEIR Epidemic Model with Infected and Susceptible Compartments

“…This section shows several numerical simulation results for second case, which refers to the model equation (20). The results of the simulation are shown in Figure 5, Figure 6, and Figure 7.…”

“…Research on ways of reducing the incidence rate of diseases is still progressing. The dynamical behaviors of a modified SIR model with nonlinear incidence and recovery rates were presented in [20]. Their findings showed that successful treatment of patients at home can lead to minimizing the prevalence of the disease.…”

The Stability Analysis and Transmission Dynamics of the SIR Model with Nonlinear Recovery and Incidence Rates

“…e dynamical system [31] with nonlinear recovery and Monod type equation as incidence rates including three differential equations is given as follows. e total population N(t) is distributed into three classes: susceptible S(t), infected I(t), and recovered R(t) where N(t) � S(t) + I(t) + R(t).…”

“…Continuous compression and impact techniques also make the feedback of the incidence rate more leisurely compared to the standard bilinear structure aSI erefore, it is crucial to take into account the influence of preventive measures as well as preventive steady decline on the transmission of infectious diseases. In order to address the above problems, the author [31] plan to alter the SIR model by taking the nonlinear Monod type equation as incidence rate to study the effect of preventive reduction on the transmission of infectious diseases. e reason behind considering Monod type equation as incidence rate was to explore the effect of intervention decrease on the spread of infectious disease.…”

Estimations and Control of Julia Sets of the SIS Model Perturbed by Noise

“…Liu et al [ 5 ] proposed a mechanism considering the co-evolution between information states and network topology simultaneously. Alshammari and Khan [ 6 ] established a complex SIR epidemic dynamics model based on nonlinear incidence and nonlinear recovery considering the impact of available hospital beds and reduction interventions on the spread of infectious diseases. In recent years, many scholars have focused on the stability and existence of periodic solutions, the equilibrium position of equilibrium points, and the search for bifurcation points.…”