Stochastic epidemic models with a backward bifurcation

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