A Modeling Approach for Assessing the Spread of Tuberculosis and Human Immunodeficiency Virus Co-Infections in Thailand

Abstract

Mathematical models were formulated to describe the transmission dynamics of tuberculosis (TB) and human immunodeficiency virus (HIV) and the relationship between them. For TB infections, the population was separated into: 1) a susceptible non-infected group, 2) a latent asymptomatic infected group and 3) an active symptomatic infected group. For HIV infections, it was assumed that each of the three TB groups could be: 1) not infected with HIV or 2) actively infected with HIV. The model was used to study the spread of TB through the non-HIV and HIV groups. Formulas for the basic reproduction numbers and threshold criteria for the spread of TB through the two HIV groups were derived using the next generation method. Using population statistics (number of population, birth rate, and death rate) and health statistics (death by leading cause group, and number of persons affected with tuberculosis and acquired immune deficiency syndrome) reported by the Ministry of Interior, the Ministry of Public Health, and the World Health Organization, parameter values and estimate values were obtained for the basic reproduction numbers for the spread of TB. Numerical simulations confirmed the threshold criteria for the existence of a stable, disease-free equilibrium point and of a stable, endemic equilibrium point.