Dynamic Analysis of a Stochastic Tuberculosis Model with Incubation Period Detectivity and Exogenous Reinfection
HUANG Song
LIU Zhijun
Abstract：In order to explore the effects of incubation period detectivity,exogenous reinfection and environmental noise disturbance on tuberculosis transmission and control,the dynamics behavior of a tuberculosis model with incubation period detectivity and exogenous reinfection under random perturbations was studied in this paper.Firstly,the existence and uniqueness of the solution was verified by constructing appropriate Lyapunov function and the condition of existence of ergodic stationary distribution was obtained by applying the Has'minskii theory and some inequality techniques.Secondly,the extinction of the disease was proved.Finally,the correctness of the theoretical results was verified through numerical simulations.The results showed that increasing the proportion of incubation period detectivity or reducing the rate of exogenous reinfection could reduce the number of patients who progressed to active tuberculosis.However,the presence of environmental noise led to the complexity of tuberculosis control.The research revealed that the greater noise disturbance could lead to the extinction of tuberculosis and effectively control the epidemic of tuberculosis.
Keywords：stochastic tuberculosis modelincubation period detectivityexogenous reinfectionLyapunov functionHas'minskii theorystationary distributionextinction
Publication Date：2024-03-20
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：9( 111-119 )