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A model for influenza with vaccination and awareness

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  • Baba, Isa Abdullahi
  • Hincal, Evren

Abstract

In this paper we consider three strains of influenza (I1, I2, and I3) where we have vaccine for strain1 (V1) only, and population has enough awareness of strain 2. There is neither vaccine nor awareness for strain 3. Our main aim is to mathematically analyze the effect of the vaccine for strain 1 and awareness of strain 2 on the dynamics of strain 3. It is also in our aim to study the coexistence of these three strains. Six equilibrium points were obtained and their global stability using Lyapunov functions was shown to depend on the magnitude of a threshold quantity, called basic reproduction ratio. It was shown that the coexistence of strain 1 and strain 2 is not possible and the coexistence of the three strains was shown numerically. It can be observed from the numerical simulations that, although vaccine curtail the spread of strain 1, awareness curtail the spread of strain 2, but they both have negative effect on strain 3. This tells the relevant authorities whenever there is influenza epidemic to investigate thoroughly the possibilities of the existence of multiple strains, so as to provide vaccines and enough awareness on all the strains present.

Suggested Citation

  • Baba, Isa Abdullahi & Hincal, Evren, 2018. "A model for influenza with vaccination and awareness," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 49-55.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:49-55
    DOI: 10.1016/j.chaos.2017.11.003
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    1. Lewi Stone & Ronen Olinky & Amit Huppert, 2007. "Seasonal dynamics of recurrent epidemics," Nature, Nature, vol. 446(7135), pages 533-536, March.
    2. Christina E. Mills & James M. Robins & Marc Lipsitch, 2004. "Transmissibility of 1918 pandemic influenza," Nature, Nature, vol. 432(7019), pages 904-906, December.
    3. Steven Riley & Joseph T Wu & Gabriel M Leung, 2007. "Optimizing the Dose of Pre-Pandemic Influenza Vaccines to Reduce the Infection Attack Rate," PLOS Medicine, Public Library of Science, vol. 4(6), pages 1-9, June.
    4. Neil M. Ferguson & Derek A. T. Cummings & Christophe Fraser & James C. Cajka & Philip C. Cooley & Donald S. Burke, 2006. "Strategies for mitigating an influenza pandemic," Nature, Nature, vol. 442(7101), pages 448-452, July.
    5. Xing, Yi & Song, Lipeng & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2017. "Assessing reappearance factors of H7N9 avian influenza in China," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 192-204.
    6. Peter Caley & Niels G Becker & David J Philp, 2007. "The Waiting Time for Inter-Country Spread of Pandemic Influenza," PLOS ONE, Public Library of Science, vol. 2(1), pages 1-8, January.
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    Cited by:

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    3. Şengül, Taylan & Yıldız, Esmanur, 2021. "A dynamical systems approach to the interplay between tobacco smokers, electronic-cigarette smokers and smoking quitters," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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