Key result
Pulse vaccination models predict hand-foot-mouth disease eradication when R1 is less than 1.
Why the study?
Pulse vaccination is an effective strategy for eliminating infectious diseases, but its impact on hand–foot–mouth disease dynamics with delay and saturation incidence needed analysis.
Mathematical modeling demonstrates that pulse vaccination can lead to an infection-free periodic solution if R1<1, while the disease remains permanent if R2>1.
Model-derived HFMD vaccination thresholds are hypothesis-generating; real-world validation required before clinical use.
In this paper, we have considered a dynamical model of hand–foot–mouth disease (HFMD) with varying total population size, saturation incidence rate and discrete time delay to become infectious. It is assumed that there is a time lag (τ) to account for the fact that an individual infected with virus is not infectious until after some time after exposure. The probability that an individual remains in the latency period (exposed class) at least t time units before becoming infectious is given by a step function with value 1 for 0≤t<τ and value zero for t>τ. The probability that an individual in the latency period has survived is given by e−μ τ, where μ denotes the natural mortality rate in all epidemiological classes. It is reported that the first vaccine to protect children against enterovirus 71, or EV71 has been discovered [Zhu, F. C., Meng, F. Y., Li, J. X., Li, X. L., Mao, A. Y., Tao, H., …, Shen, X. L. (2013, May 29). Efficacy, safety, and immunology of an inactivated alum-adjuvant enterovirus 71 vaccine in children in China: A multicentre, randomised, double-blind, placebo-controlled, phase 3 trial. The Lancet, 381, 2024–2032. doi:10.1016/S0140-6736(13)61049-1]. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination. We have defined two positive numbers R1 and R2. It is proved that there exists an infection-free periodic solution which is globally attractive if R1<1 and the disease is permanent if R2>1. The important mathematical findings for the dynamical behavior of the HFMD model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.
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G. P. Samanta (2014) studied Hand-foot-mouth disease (HFMD). Pulse vaccination was evaluated on Infection-free periodic solution and disease permanence. In a mathematical model of hand-foot-mouth disease with pulse vaccination, an infection-free periodic solution is globally attractive if R1<1 and the disease is permanent if R2>1.
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