Transmission dynamics and optimal control of measles epidemics

Liuyong Pang, Shigui Ruan, Sanhong Liu, Zhong Zhao, Xinan Zhang

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Based on the mechanism and characteristics of measles transmission, we propose a susceptible-exposed-infectious-recovered (SEIR) measles epidemic model with vaccination and investigate the effect of vaccination in controlling the spread of measles. We obtain two critical threshold values, μc1 and μc2, of the vaccine coverage ratio. Measles will be extinct when the vaccination ratio μ > μc1, endemic when μc2 < μ < μc1, and outbreak periodically when μ < μc2. In addition, we apply the optimal control theory to obtain an optimal vaccination strategy μ∗ (t) and give some numerical simulations for those theoretical findings. Finally, we use our model to simulate the data of measles cases in the U.S. from 1951 to 1962 and design a control strategy.

Original languageEnglish (US)
Pages (from-to)131-147
Number of pages17
JournalApplied Mathematics and Computation
Volume256
DOIs
StatePublished - Apr 1 2015

Fingerprint

Vaccination
Dynamic Control
Optimal Control
Vaccines
Control theory
Critical Threshold
Optimal Control Theory
Vaccine
Computer simulation
Epidemic Model
Threshold Value
Control Strategy
Coverage
Numerical Simulation
Model

Keywords

  • Endemic
  • Epidemic cycles
  • Measles
  • Optimal control
  • Vaccination strategy

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Transmission dynamics and optimal control of measles epidemics. / Pang, Liuyong; Ruan, Shigui; Liu, Sanhong; Zhao, Zhong; Zhang, Xinan.

In: Applied Mathematics and Computation, Vol. 256, 01.04.2015, p. 131-147.

Research output: Contribution to journalArticle

Pang, Liuyong ; Ruan, Shigui ; Liu, Sanhong ; Zhao, Zhong ; Zhang, Xinan. / Transmission dynamics and optimal control of measles epidemics. In: Applied Mathematics and Computation. 2015 ; Vol. 256. pp. 131-147.
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