Abstract
AbstractThe phenomenon of bifurcation in disease transmission models has been observed in a number of epidemiological models. The consequence of bifurcation is that the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, for disease elimination. This paper addresses the problem of finding the causes of bifurcation in standard deterministic models for the spread of HBV diseases with non-Cytolytic cure processes on infected liver and blood cells. The model contains logistic growth of healthy liver and blood cells and non -Cytolytic cure processes of infected cells. I have got that the model exhibits back ward and forward bifurcations with some conditions. The existence of a backward bifurcation is an interesting artifact since this means that the disease cannot be eradicated by simply reducing the value of the basic reproduction number$${R}_{0}$$R0below 1.This can have important implications on drug therapy protocols, since it sheds light on possible control mechanisms for disease eradication.
Publisher
Springer Science and Business Media LLC
Reference19 articles.
1. Anderson, R. M. & May, R. M. Infectious Diseases in Humans: Dynamics and Control (Oxford University Press, 1991).
2. Brauer, F. et al. (eds) Mathematical Epidemiology, Lecture Notes in Mathematics, Mathematical Biosciences Subseries Vol. 1945 (Springer, 2008).
3. Capasso, V. Mathematical Structures of Epidemic Systems, Lecture Notes in Biomathematics Vol. 97 (Springer-Verlag, 1993).
4. Hethcote, H. W. The mathematics of infectious diseases. SIAM Rev. 42, 599–653 (2000).
5. Buonomo, B. & Lacitignola, D. On the backward bifurcation of a vaccination model with nonlinear incidence. Nonlinear Anal. Modell. Control 16(1), 30–46 (2011).