Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

Risk analysis for rumor propagation in metropolises based on improved 8-state ICSAR model and dynamic personal activity trajectories

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.

Dynamic analysis of a stochastic rumor propagation model

In this paper, the dynamical behaviors for a five-dimensional virus infection model with diffusion and two delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and a general incidence function are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization methods, the threshold conditions on the global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and antibody and CTL responses, respectively, are established if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion, intracellular delay and production delay are obtained by the numerical simulations.

In this paper, we construct a backward difference scheme for a class of general SIR epidemic model with general incidence function f. We use the step size h &gt; 0, for the discretization. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, under the conditions that function f satisfies some assumptions. The global stabilities of equilibria are obtained. If the basic reproduction number R0&lt;1, the disease-free equilibrium is globally asymptotically stable. If R0&gt;1, the endemic equilibrium is globally asymptotically stable.

Dynamics of a diffusive virus model with general incidence function, cell-to-cell transmission and time delay

Optimal control of a rumor propagation model in online social network by considering influential nodes

This article presents an analysis of deterministic models of computer virus epidemic propagation (SIR models) and their classification. The main areas of research into these models are highlighted. An analysis of existing stochastic models based on the SIR model and their diversity are presented. A method for constructing a stochastic SIR model based on the classical SIR model, represented by a system of Ito stochastic differential equations with a Wiener process, is proposed. The possibility of constructing a stochastic and deterministic model of an information system protected against computer virus infection with probability 1 is demonstrated: a stochastic model, in which infection by viruses occurs continuously, and a deterministic model, in which the virus is present in the information system. A mathematical stochastic model of an information system protected from computer virus outbreaks is constructed as a system of stochastic differential equations whose first integrals are invariants preserved with probability 1. A certain functional relationship between model variables, maintaining a constant value, is considered as the system's security indicator. Introducing a compensator (program control with probability 1 (PCP1)) into the model allows the specified security indicator, described by the model variables, to be maintained with probability 1. Introducing a compensator (program control with probability 1 (PCP1)) into the model allows the specified security indicator, described by the model variables, to be maintained with probability 1. Similarly, based on the proposed algorithm, a deterministic model of an information system protected from computer virus infection is constructed. A control similar to programmed control with probability 1 (PCP1) is introduced into the constructed model, which allows the invariants to be maintained. A distinctive feature of the proposed models is that they preserve invariants associated with the properties that ensure the security of the information system. The behavior of the constructed models is studied using numerical simulation in the MathCad environment. Based on the research results, conclusions were drawn on the possibility of using the proposed method in constructing stochastic models based on other models of epidemic spread, as well as for models of protecting an information system from the spread of a computer virus epidemic.

In the present work, we consider an optimal control for a three-factor stochastic factor model. We assume that one of the factors is not observed and use classical filtering technique to transform the partial observation control problem for stochastic differential equation (SDE) to a full observation control problem for stochastic partial differential equation (SPDE). We then give a sufficient maximum principle for a system of controlled SDEs and degenerate SPDE. We also derive an equivalent stochastic maximum principle. We apply the obtained results to study a pricing and hedging problem of a commodity derivative at a given location, when the convenience yield is not observable.

Rumor propagation in the new media era poses a huge threat to maintaining the normal order of social life. In this context, we put forth a nonlinear dynamics-based stochastic SICR rumor model that integrates media coverage with science education. First, the existence of a unique global positive solution is obtained. Second, sufficient conditions for extinction are constructed on the spread of rumors based on the Lyapunov function methods and Khasminskii’s theory. Finally, the theoretical analysis is verified through numerical simulations. Additionally, it demonstrates how rumor spreading can be hampered by media coverage.

This paper formulates an infected predator-prey model with Beddington-DeAngelis functional response from a classical deterministic framework to a stochastic differential equation (SDE). First, we provide a global analysis including the global positive solution, stochastically ultimate boundedness, the persistence in mean, and extinction of the SDE system by using the technique of a series of inequalities. Second, by using Ito’s formula and Lyapunov methods, we investigate the asymptotic behaviors around the equilibrium points of its deterministic system. The solution of the stochastic model has a unique stationary distribution, it also has the characteristics of ergodicity. Finally, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients to illustrate the performance of the theoretical results. The results show that if the intensity of the disturbance is sufficiently large, the persistence of the SDE model can be destroyed.

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

In this study, a glucose-insulin model with the Michaelis-Menten function as the rate of insulin degradation is analyzed using stochastic differential equations. Further, we solve the stochastic glucose-insulin model using the Milstein method, which is based on truncated Ito-Taylor expansions. Comparison of the approximation solution of a stochastic and deterministic model is illustrated by comparing the approximation solution with the deterministic model. A stochastic model allows random fluctuations in glucose-insulin diseases. Furthermore, the stochastic glucose-insulin model's numerical solution provides insight into its variability. The model predicts glucose-insulin dynamics accurately, which is a powerful tool for managing diabetes. Analytical and simulation results are consistent. Improved treatment strategies and personalized medical interventions could result. Treatments and insulin injections are sensitive to these parameters. Numerical simulation corroborates theoretical results.

The effect of environmental noise on threshold dynamics for a stochastic viral infection model with two modes of transmission and immune impairment

Symmetry in mathematical models often refers to invariance under certain transformations. In stochastic models, symmetry considerations must also account for the probabilistic nature of inter- actions and events. In this paper, a stochastic vector-borne model with plant virus disease resistance and nonlinear incidence is investigated. By constructing suitable stochastic Lyapunov functions, we show that if the related threshold R0s&lt;1, then the disease will be extinct. By using the reproduction number R0, we establish sufficient conditions for the existence of ergodic stationary distribution to the stochastic model. Furthermore, we explore the results graphically in numerical section and find that random fluctuations introduced in the stochastic model can suppress the spread of the disease, except for increasing plant virus disease resistance and decreasing the contact rate between infected plants and susceptible vectors. The results reveal the correlation between symmetry and stochastic vector-borne models and can provide deeper insights into the dynamics of disease spread and control, potentially leading to more effective and efficient management strategies.