Dynamical behavior of a stochastic SICR rumor model incorporating media coverage

Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching

Stability analysis and optimal control of rumor spreading model under media coverage considering time delay and pulse vaccination

Modeling and dynamic analysis of a stochastic mutualism model with distributed delays

In daily lives, when emergencies occur, rumors will spread widely on the internet. However, it is quite difficult for the netizens to distinguish the truth of the information. The main reasons are the uncertainty of netizens’ behavior and attitude, which make the transmission rates of these information among social network groups be not fixed. In this paper, we propose a stochastic rumor propagation model with general incidence function. The model can be described by a stochastic differential equation. Applying the Khasminskii method via a suitable construction of Lyapunov function, we first prove the existence of a unique solution for the stochastic model with probability one. Then we show the existence of a unique ergodic stationary distribution of the rumor model, which exhibits the ergodicity. We also provide some numerical simulations to support our theoretical results. The numerical results give us some possible methods to control rumor propagation. Firstly, increasing noise intensity can effectively reduce rumor propagation when . That is, after rumors spread widely on social network platforms, government intervention and authoritative media coverage will interfere with netizens’ opinions, thus reducing the degree of rumor propagation. Secondly, speed up the rumor refutation, intensify efforts to refute rumors, and improve the scientific quality of netizen (i.e., increase the value of β and decrease the value of α and γ), which can effectively curb the rumor propagation.

With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R 0 is obtained. When R 0 < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R 0 > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.

Rumor propagation has become a major area of social network research. There are some existing models that combine rumor propagation and trust network, but the trust degree is constant in these models without considering the influence of rumor propagation on trust degree among nodes. This paper put forward a rumor propagation model (DTM) which is based on two-level-mixing SIR epidemic model [1] and trust network, taking the interaction between trust network and rumor propagation into account. The probability of people believing the rumor from rumormongers is computed by the trust degree and the trust degree used in next step is modified according to the results of previous rumor propagation. The simulation results reveal that trust plays an important role in rumor spreading and vice versa. In comparison with the traditional rumor propagation models, the rumor spreading with DTM will be accelerated as the increasing of trust degree.

In our life there are various infectious diseases which lead to negative effects on the economy. Therefore, it is highly important to develop mathematical models to describe the spread of the pandemic. In this study, we first develop a deterministic SEI1I2R epidemic model incorporating double epidemic hypothesis. We first verify that there exists a unique global positive solution of the system with any positive initial value, then we investigate the local and global asymptotical stability of the equilibria. Following that, we incorporate the inherent stochasticity of the virus spread by reinterpreting the previous SEIR-type epidemic model of infectious diseases as stochastic systems modelled via the log-normal standard Ornstein–Uhlenbeck process. After that we study the stochastic dynamics of the model in detail. More precisely, we first analyze the existence and uniqueness of the global solution of the system. Then by using the Markov semigroup theory, we establish sufficient criteria for the existence and uniqueness of an invariant probability measure of the system, which implies the persistence of the disease in a community. Especially, under the same conditions as the local asymptotical stability of the endemic equilibrium, we get the specific form of the local probability density function around the quasi-endemic equilibrium of the stochastic system. Meanwhile, we also verify that the invariant global probability density function can be approximated by the local probability density function as the noise intensity tends to zero. In addition, we give some sufficient conditions for elimination of the disease. Finally, numerical simulations are carried out to demonstrate the validity of the derived results and the availability of the proposed models by using MATLAB. This work can improve our insight into epidemic dynamics and help us implement interventions to regulate the disease dynamics.

As one of the most important aspects of spreading dynamics on networks, propagation of rumor, which includes the process of rumor diffusing and elimination, plays an important role in the understanding of information dissemination within social networks. However, the current understanding of rumor propagation within networks is far from clear, especially the full analysis of the process of rumor diffusing and elimination is lacking. Here, with the rumor elimination process supplemented to the susceptible-infective-refractory (SIR) rumor spreading model, a modified rumor spreading model is established and defined as spreader-ignorant-eliminater-Rstifler-Estifler (SIERsEs) model. The developed mean-field equations of SIERsEs model, with the diffussing and elimination thresholds calculated, could describe the theory of steady-state dynamics of the rumor propagation. Simulation analysis is performed to assess the interaction between the diffussing and elimination process, and estimate the influences of diffusing rate, estimation rate, and averaged degree of the network, on the rumor spreading. The results show whether low or high value of average network degree would accompany a low level of the influence of rumor propagation. In addition, the shortcomings of the traditional immunization strategies, such as targeted immunization and acquaintances immunization, are pointed out. Based on this understanding, we propose two optimized immunization strategies, defined as active immunization and passive immunization, and we further evaluate how different parameters (forgetting rate of spreader, forgetting rate of eliminater and the starting time of immunization) affect the suppression effectiveness of the newly developed active and passive immunization strategies. Importantly, some so-called rumor-inhibition strategies actually could not inhibit but enhance the rumor propagation instead. These obtained findings in the present study could not only elaborate our understandings in spreading dynamics within network, but also provide an insight into the developing effective strategies of inhibiting rumor propagation.

This paper introduces a rumor propagation model with saturation incidence, based on hypergraph theory. Hypergraphs can capture the higher-order interactions between nodes in a social network, where the node degree is substituted with hyperdegree. First, the threshold for rumor spreading model is obtained, the global asymptotically stable of the rumor-free equilibrium, and the global attractive and global asymptotically stable of the rumor-prevailing equilibrium are proved. Then, we incorporate impulsive vaccination into the model to represent the guided effect, simulating the periodic educational activities organized by official institutions to counteract rumor dissemination. By employing the comparison theorem, the paper demonstrates the global attractiveness of the rumor-free periodic solution and the persistence of the model. Finally, through numerical simulations, the paper compares the effects of higher-order and pairwise interactions on rumor spreading, validating the theoretical conclusions. The results indicate that higher-order interactions can promote rumor spreading, while impulsive vaccination can effectively decrease the scale of rumor spreading.

In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô[Formula: see text] formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria.

&lt;abstract&gt;&lt;p&gt;The spread of infectious diseases are inevitably affected by natural and social factors, and their evolution presents oscillations and other uncertainties. Therefore, it is of practical significance to consider stochastic noise interference in the studies of infectious disease models. In this paper, a stochastic SIR model with nonlinear incidence and recovery rate is studied. First, a unique global positive solution for any initial value of the system is proved. Second, we provide the sufficient conditions for disease extinction or persistence, and the influence of threshold $ \tilde{R_{0}} $ of the stochastic SIR model on disease state transition is analyzed. Additionally, we prove that the system has a stationary distribution under some given parameter conditions by building an appropriate stochastic Lyapunov function as well as using the equivalent condition of the Hasminskii theorem. Finally, the correctness of these theoretical results are validated by numerical simulations.&lt;/p&gt;&lt;/abstract&gt;

The hepatitis C virus is hitherto a tremendous threat to human beings, but many researchers have analyzed mathematical models for hepatitis C virus transmission dynamics only in the deterministic case. Stochasticity plays an immense role in pathology and epidemiology. Hence, the main theme of this article is to investigate a stochastic epidemic hepatitis C virus model with five states of epidemiological classification: susceptible, acutely infected, chronically infected, recovered or removed and chronically infected, and treated. The stochastic hepatitis C virus model in epidemiology is established based on the environmental influence on individuals, is manifested by stochastic perturbations, and is proportional to each state. We assert that the stochastic HCV model has a unique global positive solution and attains sufficient conditions for the extinction of the hepatotropic RNA virus. Furthermore, by constructing a suitable Lyapunov function, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the solutions to the stochastic HCV model. Moreover, this article confirms that using numerical simulations, the six parameters of the stochastic HCV model can have a high impact over the disease transmission dynamics, specifically the disease transmission rate, the rate of chronically infected population, the rate of progression to chronic infection, the treatment failure rate of chronically infected population, the recovery rate from chronic infection and the treatment rate of the chronically infected population. Eventually, numerical simulations validate the effectiveness of our theoretical conclusions.

An evolutionary game model for analysis of rumor propagation and control in social networks

Dynamic analysis and control measures of rumor propagation model considering true individuals and public opinion individuals

Stationary distribution of a stochastic cholera model between communities linked by migration