Mathematical Study of a Class of Epidemiological Models with Multiple Infectious Stages

Abstract

AbstractThis paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number $\mathcal R_0$ that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever $\mathcal R_0 \leq 1$, while when $\mathcal R_0 \gt 1$, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. A case study for tuberculosis (TB) is considered to numerically support the analytical results.