Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation
Ist Teil von
Physica A, 2018-05, Vol.497, p.52-71
Ort / Verlag
Elsevier B.V
Erscheinungsjahr
2018
Link zum Volltext
Quelle
Elsevier ScienceDirect Journals Complete
Beschreibungen/Notizen
We propose and analyze a mathematical model for tuberculosis (TB) transmission to study the role of exogenous reinfection and endogenous reactivation. The model exhibits two equilibria: a disease free and an endemic equilibria. We observe that the TB model exhibits transcritical bifurcation when basic reproduction number R0=1. Our results demonstrate that the disease transmission rate β and exogenous reinfection rate α plays an important role to change the qualitative dynamics of TB. The disease transmission rate β give rises to the possibility of backward bifurcation for R0<1, and hence the existence of multiple endemic equilibria one of which is stable and another one is unstable. Our analysis suggests that R0<1 may not be sufficient to completely eliminate the disease. We also investigate that our TB transmission model undergoes Hopf-bifurcation with respect to the contact rate β and the exogenous reinfection rate α. We conducted some numerical simulations to support our analytical findings.
•A TB transmission model with exogenous reinfection and endogenous reactivation.•Backward bifurcation arises as the exogenous reinfection crosses a critical value.•As the transmission rate exceeds a critical value a bifurcating limit cycle occurs.•Stability of the bifurcating periodic solution is studied.•Simulations covering the breadth of the feasible parameter space are conducted.