Abstract
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.
Highlights
Vaccination programs are used as a tool to control the spread of epidemics
In this paper the simulations of the SEIR model with three different vaccination strategies have been conducted using the XPPAUT package and data estimated from the literature
The comparison of the simulation results of our model show that the type of vaccination parameter affecting the pattern of the dynamics of the disease
Summary
The simplest vaccination strategy is to vaccinate all susceptible individuals at a constant rate. This may be combined with vaccination of a fixed fraction of very young children at the smallest possible age where maternal antibodies no longer confound the effect of the vaccine, commonly 9 - 18 months for measles. In this paper we study a general continuous periodic vaccination strategy r t and extend the results of [7]. This is combined with vaccination of a given proportion of newborn individuals. Our results lead us to conjecture that this combined periodic and fixed vaccination strategy is sufficient to eliminate disease from the population exactly when the weighted time-averaged disease-free susceptible population is less than a certain threshold value
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