November  2004, 4(4): 999-1012. doi: 10.3934/dcdsb.2004.4.999

Modelling the effect of imperfect vaccines on disease epidemiology


Institute for Biodiagnostics, National Research Council Canada, Winnipeg, Manitoba, Canada, R3B 1Y6, Canada

Received  March 2003 Revised  February 2004 Published  August 2004

We develop a mathematical model to monitor the effect of imperfect vaccines on the transmission dynamics of infectious diseases. It is assumed that the vaccine efficacy is not $100\%$ and may wane with time. The model will be analyzed using a new technique based on some results related to the Poincaré index of a piecewise smooth Jordan curve defined as the boundary of a positively invariant region for the model. Using global analysis of the model, it is shown that reducing the basic reproductive number ($\mathcal{R}_0$) to values less than one no longer guarantees disease eradication. This analysis is extended to determine the threshold level of vaccination coverage that guarantees disease eradication.
Citation: S.M. Moghadas. Modelling the effect of imperfect vaccines on disease epidemiology. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 999-1012. doi: 10.3934/dcdsb.2004.4.999

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