Abstract
Nosocomial infections (hospital-acquired) has been an important public health problem, which may make those patients with infections or involved visitors and hospital personnel at higher risk of worse clinical outcomes or infection, and then consume more healthcare resources. Taking into account the stochasticity of the death and discharge rate of patients staying in hospitals, in this paper, we propose a stochastic dynamical model describing the transmission of nosocomial pathogens among patients admitted for hospital stays. The stochastic terms of the model are incorporated to capture the randomness arising from death and discharge processes of patients. Firstly, a sufficient condition is established for the stochastic extinction of disease. It shows that introducing randomness in the model will result in lower potential of nosocomial outbreaks. Further, we establish a threshold criterion on the existence of stationary distribution and ergodicity for any positive solution of the model. Particularly, the spectral radius form of stochastic threshold value is calculated in the special case. Moreover, the numerical simulations are conducted to both validate the theoretical results and investigate the effect of prevention and control strategies on the prevalence of nosocomial infection. We show that enhancing hygiene, targeting colonized and infected patients, improving antibiotic treatment accuracy, shortening treatment periods are all crucial factors to contain nosocomial infections.