Backward bifurcation of an Sir-Si model with vaccination and treatment
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In the presence of treatment, most epidemic models demon- strate behavior of backward bifurcation. This is important in epidemiol- ogy because it provides signi cant information for disease control. How- ever, most models consider only one single population. In this paper, an extended model of two populations in the form SIR-SI involving vaccina- tion and treatment is analyzed. The analysis of local and global stability of equilibria is discussed. By using the center manifold theorem, this model has backward bifurcation behavior when the number of infected people exceeds the treatment capacity. Vaccination decreases the basic reproduction number, but does not a ect the backward bifurcation be- havior. This study also showed that under vaccination and treatment, an endemic equilibrium always occurs when R0 > 1.
Abstract
In the presence of treatment, most epidemic models demon- strate behavior of backward bifurcation. This is important in epidemiol- ogy because it provides signi cant information for disease control. How- ever, most models consider only one single population. In this paper, an extended model of two populations in the form SIR-SI involving vaccina- tion and treatment is analyzed. The analysis of local and global stability of equilibria is discussed. By using the center manifold theorem, this model has backward bifurcation behavior when the number of infected people exceeds the treatment capacity. Vaccination decreases the basic reproduction number, but does not a ect the backward bifurcation be- havior. This study also showed that under vaccination and treatment, an endemic equilibrium always occurs when R0 > 1.
참고문헌 (28)
- R. M. Anderson, "Infectious diseases of humans: dynamics and control" (1992), Oxford University Press
- J. Arino, "Global results for an epidemic model with vaccination that exhibits backward bifurcation", SIAM J. Appl. Math, 64, pp.260~276 (2003)
- Z. Bai, "Existence of multiple periodic solutions for an SIR model with seasonality", Nonlinear Anal.-Theor, 74(11), pp.3548~3555 (2011)
- C. Castillo-Chavez, "Mathematical approaches for emerging and reemerging infection diseases: an introduction", pp.229~250 (2002), Springer
- C. Castillo-Chavez, "Dynamical models of Tuberculosis and their applica-tions", Math. Biosci. Eng, 1, pp.361~404 (2004)
- Y. Dumont, "On a temporal model for the chikungunya disease: modeling, theory and numerics", Math. Biosci, 213(1), pp.80~91 (2008)
- J. C. Eckalbar, "Dynamics of epidemic model with quadratic treat-ment", Nonlinear Anal. Real World Appl, 12(1), pp.320~332 (2011)
- E. S. Nugraha, "Mathematical modeling for control zika transmission", AIP Conf. Proc, 1905, pp.030026~ (2017)
- S. Elkahar, "Stability Anaysis of an SEIR Model with Treatment", Res. Appl. Math, 1, pp.1~16 (2017)
- L. Esteva, "Analysis of a dengue disease transmission model", Math. Biosci, 150(2), pp.131~151 (1998)
- X. Feng, "Backward bifurcation and global stability in epidemic model with treatment and vaccination", Discr. Cont. Dyn. Sys. Ser. B, 19(4), pp.999~1025 (2014)
- A. B. Gumel, "An SVEIR modelfor assessing potential impact of an imperfect anti-SARS vaccine", Math. Biosci. Eng, 3, pp.485~512 (2006)
- J.K. Hale, "Ordinary Differential Equations" (1969), Wiley
- D. Hidayat, "A mathematical model of chagas disease transmission", AIP Conf. Proc, 1937, pp.020008~ (2018)
- Z. Hu, "Analysis of SIR epidemic models with non linear incidence rate and treatment", Math. Biosci, 238(1), pp.12~20 (2012)
- R. M. May, "Transmission dynamics of HIV infection", Nature, 326(6109), pp.137~142 (1987)
- S. M. Moghadas, "Modelling the effect of imperfect vaccines on disease epidemiology", Discr. Cont. Dyn. Syst. Ser. B, 4, pp.999~1012 (2004)
- WO. Kermack, "A contribution to the mathematical theory of epidemics", Proc. R. Soc. B Biol. Sci, 115(772), pp.700~721 (1927)
- J. P. Tian, "Global stability for cholera epidemic models", Math. Biosci, 232(1), pp.31~41 (2011)
- P. Van den Driessche, "Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission", Math. Biosci, 180(1-2), pp.29~48 (2002)
- W. Wang, "Bifurcations in an epidemic model with constant removal rate of the infectives", J. Math. Anal. Appl, 291(2), pp.775~793 (2004)
- W.D. Wang, "Backward bifurcation of an epidemic model with treatment", Math. Biosci, 201(1-2), pp.58~71 (2006)
- J. Y. Yang, "SIV epidemic models with age of infection", Int. J. Biomath, 2(01), pp.61~67 (2009)
- W. Yang, "Global analysis for a general epidemiological model with vaccination and varying population", J. Math. Anal. Appl, 372(1), pp.208~223 (2010)
- J. Zhang, "Backward bifurcation of and epidemic model with saturated treatment function", J. Math. Anal. Appl, 348(1), pp.433~443 (2008)
- J. Zhang, "Analysis of an SEIR epidemic model with saturated incidence and saturated treatment function", Sci. World J, 2014, pp.1~11 (2014)