Mixed vaccination strategy for the control of tuberculosis: A case study in China

Siyu Liu; Yong Li; Yingjie Bi; Qingdao Huang; Siyu Liu; Yong Li; Yingjie Bi; Qingdao Huang

doi:10.3934/mbe.2017039

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 3: 695-708. doi: 10.3934/mbe.2017039

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Mixed vaccination strategy for the control of tuberculosis: A case study in China

. College of Mathematics, Jilin University, Changchun 130012, China

Received: 13 May 2016 Accepted: 09 October 2016 Published: 01 June 2017
MSC : Primary: 92D30, 37N25; Secondary: 34K13

This study first presents a mathematical model of TB transmission considering BCG vaccination compartment to investigate the transmission dynamics nowadays. Based on data reported by the National Bureau of Statistics of China, the basic reproduction number is estimated approximately as $\mathcal{R}_{0}=1.1892$. To reach the new End TB goal raised by WHO in 2015, considering the health system in China, we design a mixed vaccination strategy. Theoretical analysis indicates that the infectious population asymptotically tends to zero with the new vaccination strategy which is the combination of constant vaccination and pulse vaccination. We obtain that the control of TB is quicker to achieve with the mixed vaccination. The new strategy can make the best of current constant vaccination, and the periodic routine health examination provides an operable environment for implementing pulse vaccination in China. Numerical simulations are provided to illustrate the theoretical results and help to design the final mixed vaccination strategy once the new vaccine comes out.
- Tuberculosis,
- mixed vaccination strategy,
- basic reproduction number,
- epidemic model
Citation: Siyu Liu, Yong Li, Yingjie Bi, Qingdao Huang. Mixed vaccination strategy for the control of tuberculosis: A case study in China[J]. Mathematical Biosciences and Engineering, 2017, 14(3): 695-708. doi: 10.3934/mbe.2017039

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Abstract

This study first presents a mathematical model of TB transmission considering BCG vaccination compartment to investigate the transmission dynamics nowadays. Based on data reported by the National Bureau of Statistics of China, the basic reproduction number is estimated approximately as $\mathcal{R}_{0}=1.1892$. To reach the new End TB goal raised by WHO in 2015, considering the health system in China, we design a mixed vaccination strategy. Theoretical analysis indicates that the infectious population asymptotically tends to zero with the new vaccination strategy which is the combination of constant vaccination and pulse vaccination. We obtain that the control of TB is quicker to achieve with the mixed vaccination. The new strategy can make the best of current constant vaccination, and the periodic routine health examination provides an operable environment for implementing pulse vaccination in China. Numerical simulations are provided to illustrate the theoretical results and help to design the final mixed vaccination strategy once the new vaccine comes out.

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