Threshold behaviour of a stochastic SIR model

Nonlinear stochastic analysis for a stochastic SIS epidemic model

“…Compare with previous study results [4,6,21], the additional condition of σ 2 βµ Λ is unnecessary. Therefore, we improve the main results of previous studies.…”

“…For another, a large number of literatures have used the Lyapunov functions to study the dynamics of infectious diseases and have given many good results [4,6,11,21]. However, this paper applies the Feller's test and canonical probability methods to study the dynamics of system (1.2) and gives some new results.…”

“…The parameters β, α, λ are all nonnegative constants and Λ, µ are positive constants. Recently, authors of [4,6,21] have done much research and have obtained plenty of significant conclusions for system (1.1). They set up the threshold condition R * , which determines disease extinction or permanence under stochastic perturbation, where…”

Computational models and optimal control strategies for emotion contagion in the human population in emergencies

“…In the last decade, researchers have developed several models to investigate emotion contagion based on the assumption that emotion contagion is similar to infectious disease diffusion in the human population, most of which are based on the susceptible-infectious-recovered (SIR) model, an epidemic spread model for describing the dynamics of infectious diseases in the human population [20,21,22,23]. In the SIR model, the human population are divided into three categories: susceptible individuals (S) that have not caught the disease; infected individuals (I) that have been infected and can spread the disease to susceptible individuals; removed individuals (R) that have been infected by the decease, and have been cured and acquired the immunity to the decease currently.…”

The threshold behavior and periodic solution of stochastic SIR epidemic model with saturated incidence

“…However, the idea in [9], [10], [29] to acquire the asymptotic behavior of system (1.2) is unavailable for system (1.4) because the Fokker−Planck equation corresponding to system (1.4) is of degenerate type. In this paper, one of our aims is to study the stationary distribution of system (1.4) by applying Markov semigroup theory ( [13], [14], [16], [17], [23], [24]) which is different from the idea in [8] and [30]. However, perturbations that biological populations suffer often appear periodic phenomena, such as seasonal effect, individual lifecycle and so on.…”