BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL FOR TB-DENGUE CO-INFECTION
Authors: Andrawus J, Nwankwo A, *Okuonghae D
Tuberculosis (TB) and Dengue are two diseases that have resulted in high mortality, mostly in developing countries. In this work, we investigate the causes of the backward bifurcation phenomenon in a mathematical model describing the dynamics of Tuberculosis-Dengue co-infection in a population where both diseases are endemic, a phenomenon characterized by the coexistence of a stable disease-free equilibrium with a stable endemic equilibrium, when the associated reproduction number is less than unity. The analyses showed that, for the TB-only model, exogenous reinfection and the reinfection of previously treated individuals are the causes of the backward bifurcation phenomenon, while for the Dengue-only model, disease-induced deaths in infected humans will lead to the backward bifurcation in the system. In co-infection scenarios where tuberculosis is having a larger disease burden than dengue, it is shown that the exogenous reinfection of latently infected TB individuals and the reinfection of previously treated individuals for TB will lead to the backward bifurcation phenomenon. The implication of these results is that for the reproduction numbers of the model to be useful for designing robust public health control measures against both diseases, concerted efforts must be geared towards minimizing the incidences of exogenous reinfection of latently infected TB cases, reinfection of previously treated individuals for TB and disease-induced deaths due to dengue infection.
Affiliations: Department of Mathematics, University of Benin, Benin City, Nigeria
Keywords: Bifurcation, Co-infection, Tuberculosis, Dengue, Stability
Published date: 2017/12/29