Efficiency of Different Vaccination Strategies for Childhood Diseases: A Simulation Study


Vaccination strategies are designed and applied to control or eradicate an infection from the population. This paper studies three different vaccination strategies used worldwide for many infectious diseases including childhood diseases. These strategies are the conventional constant vaccination strategy, the periodic step (pulse) vaccination strategy and finally the mixed vaccination strategy of both the constant and the periodic one. Simulation of the different vaccination programs is conducted using three parameter sets of measles, chickenpox and rubella. The Poincaré section is playing as a filter of our simulation results to show a wide range of possible behavior of our model. Critical vaccination level is been estimated from the results to prevent severe epidemics.

Share and Cite:

Moneim, I. (2013) Efficiency of Different Vaccination Strategies for Childhood Diseases: A Simulation Study. Advances in Bioscience and Biotechnology, 4, 193-205. doi: 10.4236/abb.2013.42028.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] London, W.P. and Yorke, J.A. (1973) Recurrent outbreaks of measles, chickenpox and mumps. I. American Journal of Epidemiology, 98, 453-468.
[2] Schwartz, I.B. and Smith, H.L. (1983) Infinite subharmonic bifurcations in an SEIR model. Journal of Mathematical Biology, 18, 233-253. doi:10.1007/BF00276090
[3] Dietz, K. (1976) The incidence of infectious diseases under the influence of seasonal fluctuations. In: Berger, J., Bühler, W., Repges, R. and Tautu, P., Eds., Lecture Notes in Biomathematics, Springer-Verlag, Berlin, 1-15.
[4] Agur, Z., Cojocaru, L., Mazor, G., Anderson, R.M. and Danon, Y. (1993) Pulse mass measles vaccination across age cohorts. Proceedings of the National Academy of Sciences USA, 90, 11698-11702. doi:10.1073/pnas.90.24.11698
[5] Nokes, D. and Swinton, J. (1995) The control of childhood viral infections by pulse vaccination. IMA Journal of Mathematics Applied in Medicine and Biology, 12, 2953. doi:10.1093/imammb/12.1.29
[6] Shulgin, B., Stone, L. and Agur, Z. (1998) Pulse vaccination strategy in the SIR epidemic model. Bulletin of Mathematical Biology, 60, 1123-1148. doi:10.1016/S0092-8240(98)90005-2
[7] Moneim, I.A. (2011) Different vaccination strategies for measles diseases: A simulation study. Journal of Informatics and Mathematical Sciences, 3, 227-236.
[8] Schenzle, D. (1984) An age-structured model of preand post-vaccination measles transmission. IMA Journal of Mathematics Applied in Medicine and Biology, 1, 169191. doi:10.1093/imammb/1.2.169
[9] Anderson, R.M. and May, R.M. (1983) Vaccination against rubella and measles: Quantitative investigations of different policies. The Journal of Hygiene, 90, 259-325. doi:10.1017/S002217240002893X
[10] Anderson, R.M. and May, R.M. (1995) Infectious diseases of humans: Dynamics and control. Oxford University Press, Oxford.
[11] Gao, S., Chen, L. and Teng, Z. (2007) Impulse vaccination of an SEIR epidemic model with time delay and varying total population size. Bulletin of Mathematical Biology, 69, 731-745. doi:10.1007/s11538-006-9149-x
[12] Gao, S., Chen, L., Nieto, J.J. and Torres, A. (2006) Analysis of delayed epidemic model with pulse vaccination and saturation incidence. Vaccine, 24, 6037-6045. doi:10.1016/j.vaccine.2006.05.018
[13] D’Onofrio, A. (2002a) Stability properties of pulse vaccination strategy in SEIR epidemic model. Mathematical Biosciences, 36, 57-72. doi:10.1016/S0025-5564(02)00095-0
[14] D’Onofrio, A. (2002b) Pulse vaccination strategy in the SIR epidemic model: Global asymptotic stable eradication in presence of vaccine failures. Mathematical and Computer Modelling, 36, 473-489. doi:10.1016/S0895-7177(02)00177-2
[15] Zhang, T.L. and Teng, Z.D. (2009) Extinction and permanence for a pulse vaccination delayed SEIR epidemic model. Chaos, Solitons & Fractals, 39, 2411-2425. doi:10.1016/j.chaos.2007.07.012
[16] Zeng, G., Chen, L. and Sun, L. (2006) Existence of periodic solution of order one of planar impulsive autonomous system. Journal of Computational and Applied Mathematics, 186, 466-481. doi:10.1016/j.cam.2005.03.003
[17] Williams, P.J. and Hull, H.F. (1983) Status of measles in the Gambia, 1981. Reviews of Infectious Diseases, 5, 391394. doi:10.1093/clinids/5.3.391
[18] De Quadros, C.A., Andrus J.K. and Olivé, J.M. (1991) Eradication of poliomyelitis: Progress. Pediatric Infectious Disease Journal, 10, 222-229. doi:10.1097/00006454-199103000-00011
[19] Sabin, A.B. (1991) Measles, killer of millions in developing countries: Strategies of elimination and continuing control. European Journal of Epidemiology, 7, 1-22. doi:10.1007/BF00221337
[20] Iooss, G. and Joseph, D. (1980) Elementary stablility and bifurcation theory. Springer-Verlag, New York. doi:10.1007/978-1-4684-9336-8
[21] Aron, J.L. (1990) Multiple attractors in the response to a vaccination program. Theoretical Population Biology, 38, 58-67. doi:10.1016/0040-5809(90)90003-E
[22] Moneim, I.A. (2005) Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate. Mathematical Bioscience and Engineering, 2, 591-611. doi:10.3934/mbe.2005.2.591
[23] Burton, T.A. (1985) Stablility and periodic solutions of ordinary and functional differential equations. Academic Press, New York.
[24] Moneim, I.A. (2007a) Seasonally varying epidemics with and without latent period: A comparative simulation study. Mathematical Medicine and Biology, A Journal of the IMA, 24, 1-15.
[25] Hethcote, H.W. (1989) Three basic epidemiological models. In: Gross, L., Hallam, T.G. and Levin, S.A., Eds., Applied Mathematical Ecology, Springer-Verlag, New York, 119-144. doi:10.1007/978-3-642-61317-3_5
[26] Duncan, C.J., Duncan S.R. and Scott, R. (1997) The dynamics of measles epidemics. Theoretical Population Biology, 52, 155-163. doi:10.1006/tpbi.1997.1326
[27] Greenhalgh, D. (1990) Deterministic models for common childhood diseases. International Journal of Systems Science, 21, 1-20. doi:10.1080/00207729008910344
[28] Moneim, I.A. (2007b) The effect of using different types of contact rate. Computers in Biology and Medicine, 2, 591-611.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.