Effect of mixed infection on TB dynamics

Abstract

Poor living conditions, overcrowding and strain diversity are some of the factors that influence mixed infection in Tuberculosis (TB) at the population level. We formulate a mathematical model for mixed infection in TB using nonlinear ordinary differential equations where such factors were represented as probabilities of acquiring mixed infection. A qualitative analysis of the model shows that it exhibits multiple endemic equilibria and backward bifurcation for certain parameter values. The reactivation rate and transmission rate of individuals with mixed infection were of importance as well as the probabilities for latent individuals to acquire mixed infection. We calculate the prevalence of mixed infection from the model and the effect of mixed infection on TB incidence, TB prevalence and Mycobacterium tuberculosis (MTB) infection rate. Numerical simulations show that mixed infection may explain high TB incidences in areas which have a high strain diversity, poor living conditions and are overcrowded even without HIV.