An age-structured tuberculosis model with information and immigration: Stability and simulation study

Abstract

This paper establishes an age-structured Tuberculosis (TB) model to investigate the joint impacts of information and immigration of population on the spread of TB disease. Mathematically, we show that the model is point dissipative, and the semi-flow generated by the model has the property of asymptotic smoothness, and then study the existence and global stability of positive steady state by the direct Lyapunov functional. Numerically, by using Matlab software, we verify the theoretical results, and further explore the influence of information (including information coverage and disease-related memory delay) and immigration on the final size of TB disease. The simulation results show that both information coverage and immigration are positive correlated with the final size of disease, and disease-related memory delay can affect the arrival time of positive steady state, which implies us that improving information coverage, enlarging disease-related memory, and reducing the immigration of population (especially latent and infected individuals) can effectively control the progression of TB disease.