Global Dynamics of an Age-Structured Tuberculosis Model with Vaccine Failure and Nonlinear Infection Force

Abstract

China bears a heavy burden due to tuberculosis (TB) with hundreds of thousands of people falling ill with the disease every year. Therefore, it is necessary to understand the effectiveness of current control measures in China. In this paper, we first present a TB model that incorporates both vaccination and treatment. Additionally, the model considers TB transmission characteristics such as relapse and variable latency. We then define the basic reproduction number R0 of the proposed model and indicate that the disease-free equilibrium state is globally asymptotically stable if R0<1, and the endemic equilibrium state is globally asymptotically stable if R0>1. We then apply the Grey Wolf Optimizer algorithm to obtain the parameters and initial values of the model by combining TB data collected in China from 2007 to 2020. Through the partial rank correlation coefficient method, we identify the parameters that are most sensitive to R0. Based on the analysis results of the model, we propose some suggestions for TB control measures in the conclusion section.