Stationary distribution and probability density function of a stochastic waterborne pathogen model with logistic growth  

作　　者：Yue Liu Jize Wei 

机构地区：[1]Department of Mathematics City University of Hong Kong,Tat Chee Avenue Kowloon,Hong Kong,P.R.China [2]Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom,Kowloon,Hong Kong,P.R.China

出　　处：《International Journal of Biomathematics》2023年第8期191-229,共39页生物数学学报（英文版）

摘　　要：Waterborne disease threatens public health globally.Previous studies mainly consider that the birth of pathogens in water sources arises solely by the shedding of infected individuals,However,for free-living pathogens,intrinsic growth without the presence of hosts in environment could be possible.In this paper,a stochastic waterborne disease model with a logistic growth of pathogens is investigated.We obtain the sufficient conditions for the extinction of disease and also the existence and uniqueness of an ergodic stationary distribution if the threshold R_(0)^(s)>1.By solving the Fokker-Planck equation,an exact expression of probability density function near the quasi-endemic equilibrium is obtained.Results suggest that the intrinsic growth in bacteria population induces a large reproduction number to determine the disease dynamics.Finally,theoretical results are validated by numerical examples.

关 键 词：Waterborne pathogen logistic growth stochastic perturbation Fokker-Planck equation density function 

分 类 号：O175[理学—数学]