Diabetes mellitus and TB co-existence: Clinical implications from a fractional order modelling

Abstract Diabetes mellitus (DM) affects the epidemiology of tuberculosis (TB), being associated with higher risk of treatment failure and TB incidence. DM increase in low- and middle-income countries can impair TB control worldwide. Thus, understanding the mechanisms behind the coexistence of DM and TB infection is useful to devise better health policies. In this paper, we propose a mathematical model of fractional order to analyze the clinical implications of DM in the dynamics of TB transmission. The population is divided in non-diabetics and diabetics. In each sub-population, are included seven TB status, namely: susceptible, fast latent, slow latent, actively TB infection, recovered, fast-latent after reinfection, drug-resistant. The reproduction number of the model is calculated and results concerning the stability of the disease-free and of the endemic equilibria are proved. The numerical results of the model are discussed and conclusions are drawn from a biological point of view.