To account for population growth constrained by environmental capacity, we formulate a stochastic SIS model with logistic population input and standard incidence to describe disease transmission.Due to the degenerate structure of the stochastic differential equation, we employ the Lyapunov function method and Markov semigroup theory to establish a threshold theorem, including the extinction and ergodicity of the stochastic system.In addition, since the parameters in stochastic models are usually unknown in practice, we study parameter estimation for the proposed model under discrete observations by comparing least squares estimation, pseudo-maximum likelihood estimation (pseudo-MLE), and Bayesian posterior mean estimation. We further investigate how the observation step size, time horizon, and noise intensity affect the widths of confidence intervals and the accuracy of point estimates. Numerical simulations are provided to illustrate the theoretical results and to compare the performance of the three estimation methods.The results complement the dynamical analysis by providing a comparative study of parameter identification for this stochastic SIS model.
Li et al. (Thu,) studied this question.