Epidemic Model Incorporating Media Coverage Research Articles

Stationary Distribution and Extinction in a Stochastic SIQR Epidemic Model Incorporating Media Coverage and Markovian Switching

This paper is concerned with the dynamic characteristics of the SIQR model with media coverage and regime switching. Firstly, the existence of the unique positive solution of the proposed system is investigated. Secondly, by constructing a suitable random Lyapunov function, some sufficient conditions for the existence of a stationary distribution is obtained. Meanwhile, the conditions for extinction is also given. Finally, some numerical simulation examples are carried out to demonstrate the effectiveness of theoretical results.

The influence of awareness campaigns on the spread of an infectious disease: a qualitative analysis of a fractional epidemic model.

Mass-media coverage is one of the most widely used government strategies on influencing public opinion in times of crisis. Awareness campaigns are highly influential tools to expand healthy behavior practices among individuals during epidemics and pandemics. Mathematical modeling has become an important tool in analyzing the effects of media awareness on the spread of infectious diseases. In this paper, a fractional-order epidemic model incorporating media coverage is presented and analyzed. The problem is formulated using susceptible, infectious and recovered compartmental model. A long-term memory effect modeled by a Caputo fractional derivative is included in each compartment to describe the evolution related to the individuals’ experiences. The well-posedness of the model is investigated in terms of global existence, positivity, and boundedness of solutions. Moreover, the disease-free equilibrium and the endemic equilibrium points are given alongside their local stabilities. By constructing suitable Lyapunov functions, the global stability of the disease-free and endemic equilibria is proven according to the basic reproduction number R_0. Finally, numerical simulations are performed to support our analytical findings. It was found out that the long-term memory has no effect on the stability of the equilibrium points. However, for increased values of the fractional derivative order parameter, each solution reaches its equilibrium state more rapidly. Furthermore, it was observed that an increase of the media awareness parameter, decreases the magnitude of infected individuals, and consequently, the height of the epidemic peak.

Media effects on the dynamics of a stochastic SIRI epidemic model with relapse and Lévy noise perturbation

In this paper, we study the dynamic properties of an SIRI epidemic model incorporating media coverage, and stochastically perturbed by a Lévy noise. We establish the existence of a unique global positive solution. We investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model depending on the basic reproduction number under some noise excitation. Furthermore, we present some numerical simulations to support the theoretical results.

Global threshold dynamics of a stochastic epidemic model incorporating media coverage

In this paper, we investigate the global threshold dynamics of a stochastic SIS epidemic model incorporating media coverage. We give the basic reproduction number mathcal{R}_{0}^{s} and establish a global threshold theorem by Feller’s test: if mathcal{R}_{0}^{s}leq 1, the disease will die out a.s.; if mathcal{R}_{0}^{s}>1, the disease will persist a.s. In the case of mathcal{R}_{0}^{s}>1, we prove the existence, uniqueness, and global asymptotic stability of the invariant density of the Fokker–Planck equations associated with the stochastic model. Via numerical simulations, we find that the average extinction time decreases with the increase of noise intensity σ, and also find that the increasing σ will be beneficial to control the disease spread. Thus, in order to control the spread of the disease, we must increase the intensity of noise σ.

Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate

This study investigates the disease dynamics of a SIRS epidemic model as affected by environment fluctuations and media coverage. A unique global positive solution for the epidemic model is obtained. The stochastic endemic dynamics of the system is discussed by constructing suitable Lyapunov functions, and the ergodic stationary distribution of the stochastic model is established based on the method of Khasminskii. The extinction of the epidemic disease is also analyzed.

The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model

Media coverage is one of the important measures for controlling infectious diseases, but the effect of media coverage on diseases spreading in a stochastic environment still needs to be further investigated. Here, we present a stochastic susceptible–infected–susceptible (SIS) epidemic model incorporating media coverage and environmental fluctuations. By using Feller’s test and stochastic comparison principle, we establish the stochastic basic reproduction number R0s, which completely determines whether the disease is persistent or not in the population. If R0s≤1, the disease will go to extinction; if R0s=1, the disease will also go to extinction in probability, which has not been reported in the known literatures; and if R0s>1, the disease will be stochastically persistent. In addition, the existence of the stationary distribution of the model and its ergodicity are obtained. Numerical simulations based on real examples support the theoretical results. The interesting findings are that (i) the environmental fluctuation may significantly affect the threshold dynamical behavior of the disease and the fluctuations in different size scale population, and (ii) the media coverage plays an important role in affecting the stationary distribution of disease under a low intensity noise environment.

A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise

In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model, incorporating media coverage and driven by Lévy noise. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we present some numerical results to support the theoretical work.

Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

ABSTRACTAn susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity. However, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations while the basic reproduction number is greater than unity. Finally, some examples for numerical simulations are included to support the theoretical prediction.

Asymptotic behavior of global positive solution to a stochastic SIR model incorporating media coverage

We study the basic dynamical features of a stochastic SIR epidemic model incorporating media coverage. Firstly, we discuss the positivity and boundedness of solutions of the model within deterministic environment and then investigate the asymptotical stability and global stability of equilibria of deterministic model. Secondly, we show that the stochastic model has a unique global positive solution and that this solution oscillates around the equilibria of the deterministic model under certain conditions. Finally, we give some numerical simulations to illustrate our analytical results.

A stochastic SIS epidemic model incorporating media coverage in a two patch setting

In this paper, we investigate the stochastic disease dynamics of an SIS epidemic model on two patches incorporating media coverage. We give the global existence and positivity of the solutions, and the sufficient conditions for almost surely exponentially stability of the disease-free equilibrium, which means that the disease will be stochastic extinction. Furthermore, we perform some numerical simulations to validate the analytical finding.

An SIRS epidemic model incorporating media coverage with time delay.

An SIRS epidemic model incorporating media coverage with time delay is proposed. The positivity and boundedness are studied firstly. The locally asymptotical stability of the disease-free equilibrium and endemic equilibrium is studied in succession. And then, the conditions on which periodic orbits bifurcate are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number R 0 < 1. However, when R 0 > 1, the stability of the endemic equilibrium will be affected by the time delay; there will be a family of periodic orbits bifurcating from the endemic equilibrium when the time delay increases through a critical value. Finally, some examples for numerical simulations are also included.

A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation

We investigate the complex dynamics of a SIRS epidemic model incorporating media coverage with random perturbation. We first deal with the boundedness and the stability of the disease—free and endemic equilibria of the deterministic model. And for the corresponding stochastic epidemic model, we prove that the endemic equilibrium of the stochastic model is asymptotically stable in the large. Furthermore, we perform some numerical examples to validate the analytical finding, and find that if the conditions of stochastic stability are not satisfied, the solution for the stochastic model will oscillate strongly around the endemic equilibrium.

Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponentialp-stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics.

The Effect of Constant and Mixed Impulsive Vaccination on SIS Epidemic Models Incorporating Media Coverage

A SIS epidemic model incorporating media coverage is presented in this paper. The dynamics of this disease model under constant and pulse vaccination are analyzed. First, stability analysis of the model with constant vaccination shows that the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the endemic equilibrium is globally asymptotically stable if it exists. Second, we consider the impulsive vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic infection-free solution is globally asymptotically stable under some conditions, we also show that the system is permanent. Furthermore, by bifurcation theory we obtain the existence of a positive periodic solution. In order to apply vaccination pulses frequently enough so as to eradicate the disease, the threshold for the period of pulsing, i.e., smax is shown. Our theoretical results are confirmed by numerical simulations. The effectiveness of constant and pulse vaccination policies are compared. 2008 Elsevier B.V. All rights reserved.

The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage

A SIS epidemic model incorporating media coverage is presented in this paper. The dynamics of this disease model under constant and pulse vaccination are analyzed. First, stability analysis of the model with constant vaccination shows that the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the endemic equilibrium is globally asymptotically stable if it exists. Second, we consider the impulsive vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic infection-free solution is globally asymptotically stable under some conditions, we also show that the system is permanent. Furthermore, by bifurcation theory we obtain the existence of a positive periodic solution. In order to apply vaccination pulses frequently enough so as to eradicate the disease, the threshold for the period of pulsing, i.e., τmax is shown. Our theoretical results are confirmed by numerical simulations. The effectiveness of constant and pulse vaccination policies are compared.

A stochastic epidemic model incorporating media coverage

A stochastic epidemic model incorporating media coverage