论文信息 - Backward Bifurcation in SIVS Model with Immigration of Non-Infectives

Backward Bifurcation in SIVS Model with Immigration of Non-Infectives

This paper investigates a simple SIVS (susceptible-infected-vaccinated-susceptible) disease transmission model with immigration of susceptible and vaccinated individuals. We show global stability results for the model, and give an explicit condition for the existence of backward bifurcation and multiple endemic equilibria. We examine in details how the structure of the bifurcation diagram depends on the immigration.

Diána H. Knipl | Gergely Röst | G. Röst | D. Knipl | Diána Knipl

[1] Points singuliers des équations différentielles , 1934 .

[2] L. Markus,et al. II. ASYMPTOTICALLY AUTONOMOUS DIFFERENTIAL SYSTEMS , 1956 .

[3] C. Kribs-Zaleta. Center manifolds and normal forms in epidemic models , 2002 .

[4] J. Velasco-Hernández,et al. A simple vaccination model with multiple endemic states. , 2000, Mathematical biosciences.

[5] Fred Brauer,et al. Backward bifurcations in simple vaccination/treatment models , 2011 .

[6] Carlos Castillo-Chavez,et al. Backwards bifurcations and catastrophe in simple models of fatal diseases , 1998, Journal of mathematical biology.

[7] Leah Edelstein-Keshet,et al. Mathematical models in biology , 2005, Classics in applied mathematics.

[8] Abba B. Gumel,et al. Causes of backward bifurcations in some epidemiological models , 2012 .

[9] Horst R. Thieme,et al. Asymptotically Autonomous Differential Equations in the Plane , 1993 .

[10] P van den Driessche,et al. Backward bifurcation in epidemic control. , 1997, Mathematical biosciences.

[11] C. Castillo-Chavez,et al. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction , 2002 .

[12] Carlos Castillo-Chavez,et al. Asymptotically Autonomous Epidemic Models , 1994 .

[13] Fred Brauer,et al. Backward bifurcations in simple vaccination models , 2004 .

[14] K. Hadeler,et al. A core group model for disease transmission. , 1995, Mathematical biosciences.