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

Abstract

• DM fuels the epidemiology of TB. DM is associated with higher risk of treatment failure and TB incidence. • We develop a fractional order model to analyze the clinical implications of DM in the dynamics of TB transmission. • Our model predicts that increasing DM over time in a population induces higher TB incidence and prevalence. • DM also escalates TB multi-drug resistance. • The order of the fractional derivative, α , is associated with more severity of TB and diabetes. 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.