Stochastic dynamics of an SIS epidemiological model with 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

Two new stochastic epidemic models, a continuous-time Markov chain model and a stochastic differential equation model, are formulated. These are based on a deterministic model that includes vaccination and is applicable to pertussis. For some parameter values, the deterministic model exhibits a backward bifurcation if the vaccine is imperfect. Thus a region of bistability exists in a subset of parameter space. The dynamics of the stochastic epidemic models are investigated in this region of bistability, and compared with those of the deterministic model. In this region the probability distribution associated with the infective population exhibits bimodality with one mode at the disease-free equilibrium and the other at the larger endemic equilibrium. For population sizes N=/>1000, the deterministic and stochastic models agree, but for small population sizes the stochastic models indicate that the backward bifurcation may have little effect on the disease dynamics.

A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold value . That is, when and together with an additional condition, the disease is extinct with probability one, and when , the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, when , the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems.

Comparison of deterministic and stochastic SIS and SIR models in discrete time

A stochastic SIS epidemic model with saturating contact rate

Unraveling pine wilt disease: Comparative study of stochastic and deterministic model using spectral method

Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies

In this paper, we consider a stochastic SIS epidemic model with perturbed disease transmission coefficient. We discuss the threshold behavior in the sense that if \(\mathcal {R}_0^s 1\), the densities of the distributions of the solution can converge in \(L^1\) to an invariant density.

Classification of asymptotic behavior in a stochastic SIS epidemic model with vaccination

A remark on stationary distribution of a stochastic SIR epidemic model with double saturated rates

A stochastic SIRS epidemic model with nonlinear incidence rate

Qualitative study of a stochastic SIS epidemic model with vertical transmission

In this paper, a stochastic SIS epidemic model with birth pulses and pulse treatments is constructed and investigated. By applying Floquet theory and qualitative theory of stochastic differential equations, the existence and stability of trivial solution and infection-free periodic solution are discussed. A special endemic solution and the boundedness of infective individuals are investigated. Numerical results for phase portraits, which are illustrated with two examples, are in good agreement with the theoretical analysis.

The dynamical properties of a stochastic susceptible-infected epidemic model with Logistic growth are investigated in this paper. We show that the stochastic model admits a nonnegative solution by using the Lyapunov function method. We then obtain that the infected individuals are persistent under some simple conditions. As a consequence, a simple sufficient condition that guarantees the extinction of the infected individuals is presented with a couple of illustrative examples.

A stochastic epidemic model with infectivity rate in incubation period and homestead–isolation on the susceptible is developed with the aim of revealing the effect of stochastic white noise on the long time behavior. A good understanding of extinction and strong persistence in the mean of the disease is obtained. Also, we derive sufficient criteria for the existence of a unique ergodic stationary distribution of the model. Our theoretical results show that the suitably large noise can make the disease extinct while the relatively small noise is advantageous for persistence of the disease and stationary distribution.