Dynamics of Vaccination Model with Holling Type II Functional Response
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We propose a mathematical model with Holling type II functional response, to study the dynamics of vaccination. In order to make our model more realistic, we have incorporated the recruitment of infected individuals as a continuous process. We have assumed that vaccination cannot be perfect and there is always a possibility of re-infection. We have obtained the existence of a disease free and endemic equilibrium point, when the recruitment of infective is not considered and also obtained the existence of at least one endemic equilibrium point when recruitment of infective is considered. We have proved that if Rv < 1, disease free equilibrium is locally asymptotically stable, which leads to the elimination of the disease from the population. The persistence of the model has also been established. Numerical simulations have been done to establish the results obtained.
Abstract
We propose a mathematical model with Holling type II functional response, to study the dynamics of vaccination. In order to make our model more realistic, we have incorporated the recruitment of infected individuals as a continuous process. We have assumed that vaccination cannot be perfect and there is always a possibility of re-infection. We have obtained the existence of a disease free and endemic equilibrium point, when the recruitment of infective is not considered and also obtained the existence of at least one endemic equilibrium point when recruitment of infective is considered. We have proved that if Rv < 1, disease free equilibrium is locally asymptotically stable, which leads to the elimination of the disease from the population. The persistence of the model has also been established. Numerical simulations have been done to establish the results obtained.
참고문헌 (18)
- M. E. Alexander, "A vaccination model for transmission dynamics of influenza", SIAM J. Appl. Dyn. Syst, 3, pp.503~524 (2004)
- R. M. Anderson, "Infectious diseases of humans" (1991), Oxford University Press
- B. Buonomo, "On the dynamics of an SEIR epidemic model with a convex incidence rate", Ric Mat, 57(2), pp.261~281 (2008)
- L. Cai, "Global stability of a stage-structured epidemic model with a nonlinear incidence", Appl. Math. Comput, 214(1), pp.73~82 (2009)
- L. Cai, "Global dynamics of a mathematical model for HTLV-I infection of CD4+ T-cells", Appl. Math. Model, 35(7), pp.3587~3595 (2011)
- V. Capasso, "A generalization of the Kermack–Mckendrick deterministic epidemic model", Math. Biosci, 42, pp.43~61 (1978)
- P. van den Driessche, "Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission", Math. Biosci, 180, pp.29~48 (2002)
- A. Fonda, "Uniformly persistent semidynamical systems", Proc. Amer. Math. Soc, 104(1), pp.111~116 (1988)
- M. Gomes, "Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence", J. Math. Biol, 51(4), pp.414~430 (2005)
- H. W. Hethcote, "The mathematics of infectious diseases", SIAM Rev, 42, pp.599~653 (2000)
- M. J. Keeling, "Modeling infectious diseases in humans and animals" (2008), Princeton University Press
- X. Liu, "SVIR epidemic models with vaccination strategies", J. Theoret. Biol, 253, pp.1~11 (2008)
- S. M. Moghadas, "Modelling the effect of imperfect vaccines on disease epidemiology Discrete Contin", Dyn. Syst.Ser. B, 4, pp.999~1012 (2004)
- L. Perko, "Differential equations and dynamical systems" (1996), Springer-Verlag
- G. P. Sahu, "Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate", Appl. Math. Model, 36, pp.908~923 (2012)
- A. Scherer, "Mathematical models of vaccination", Brit. Med. Bull, 62, pp.187~199 (2002)
- W. J. Wang, "Global analysis of an epidemic model with latent period and partial immunity", Math. Pract. Theory, 39(17), pp.98~103 (2009)
- X. Zhou, "Analysis of an influenza A(H1N1)epidemic model with vaccination", Arab. J. Math, 1, pp.267~282 (2012)