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A cholera mathematical model with vaccination and the biggest outbreak of world’s history

Center for Research and Development in Mathematics and Applications (CIDMA), Department ofMathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Topical Section: Mathematical modeling

We propose and analyse a mathematical model for cholera considering vaccination. Weshow that the model is epidemiologically and mathematically well posed and prove the existenceand uniqueness of disease-free and endemic equilibrium points. The basic reproduction number isdetermined and the local asymptotic stability of equilibria is studied. The biggest cholera outbreak ofworld’s history began on 27th April 2017, in Yemen. Between 27th April 2017 and 15th April 2018there were 2 275 deaths due to this epidemic. A vaccination campaign began on 6th May 2018 andended on 15th May 2018. We show that our model is able to describe well this outbreak. Moreover, weprove that the number of infected individuals would have been much lower provided the vaccinationcampaign had begun earlier.
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Keywords mathematical modeling; SITRVB cholera model; local asymptotic stability; vaccinationtreatment; Yemen cholera outbreak

Citation: Ana P. Lemos-Paião, Cristiana J. Silva, Delfim F. M. Torres. A cholera mathematical model with vaccination and the biggest outbreak of world’s history. AIMS Mathematics, 2018, 3(4): 448-463. doi: 10.3934/Math.2018.4.448

References

  • 1. Asian Scientist: Math in a time of cholera, 30th August 2017. Available from:https://www.asianscientist.com/2017/08/health/mathematical-model-yemen-cholera-outbreak/.
  • 2. V. Capasso and S. L. Paveri-Fontana, A mathematical model for the 1973 cholera epidemic in the European Mediterranean region, Rev. Épidémiol. Santé Pub., 27 (1979), 121–132.
  • 3. F. Capone, V. De Cataldis and R. De Luca, Influence of diffusion on the stability of equilibria in a reaction-diffusion system modeling cholera dynamic, J. Math. Biol., 71 (2015), 1107–1131.
  • 4. J. Carr, Applications of Centre Manifold Theory, Springer-Verlag: New York, 1981.
  • 5. C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361–404.
  • 6. N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, B. Math. Biol., 70 (2008), 1272–1296.
  • 7. Cholera vaccine, 06th June 2018. Available from: https://en.wikipedia.org/wiki/Cholera_vaccine.
  • 8. C. T. Codeço, Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir, BMC Infect. Dis., 1 (2001), 1–14.
  • 9. D. M. Hartley, J. G. Morris and D. L. Smith, Hyperinfectivity: a critical element in the ability of V. cholerae to cause epidemics? Plos Med., 3 (2006), e7.
  • 10. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599–653.
  • 11. S. D. Hove-Musekwa, F. Nyabadza, C. Chiyaka, et al. Modelling and analysis of the effects of malnutrition in the spread of cholera, Math. Comput. Model., 53 (2011), 1583–1595.
  • 12. Index Mundi, Birth rate of Yemen, 06th June 2018. Available from: https://www.indexmundi.com/g/g.aspx?c=ym&v=25.
  • 13. Index Mundi, Death rate of Yemen, 06th June 2018. Available from: https://www.indexmundi.com/g/g.aspx?c=ym&v=26.
  • 14. R. I. Joh, H. Wang, H. Weiss, et al. Dynamics of indirectly transmitted infectious diseases with immunological threshold, B. Math. Biol., 71 (2009), 845–862.
  • 15. Q. Kong, Z. Qiu, Z. Sang, et al. Optimal control of a vector-host epidemics model, Math. Control Relat. Fields, 1 (2011), 493–508.
  • 16. A. P. Lemos-Paião, C. J. Silva and D. F. M. Torres, An epidemic model for cholera with optimal control treatment, J. Comput. Appl. Math., 318 (2017), 168–180.
  • 17. Z. Mukandavire, F. K. Mutasa, S. D. Hove-Musekwa, et al. Mathematical analysis of a cholera model with carriers and assessing the effects of treatment, In: Wilson, L.B. (Ed.), Mathematical Biology Research Trends. Nova Science Publishers, (2008), 1–37.
  • 18. A. Mwasa and J. M. Tchuenche, Mathematical analysis of a cholera model with public health interventions, Biosystems, 105 (2011), 190–200.
  • 19. R. L. M. Neilan, E. Schaefer, H. Gaff, et al. Modeling optimal intervention strategies for cholera, B. Math. Biol., 72 (2010), 2004–2018.
  • 20. H. Nishiura, S. Tsuzuki, B. Yuan, et al. Transmission dynamics of cholera in Yemen, 2017: a real time forecasting, Theor. Biol. Med. Model., 14 (2017), 14.
  • 21. G. J. Olsder and J. W. van der Woude, Mathematical Systems Theory, VSSD: Delft, 2005.
  • 22. M. Pascual, L. F. Chaves, B. Cash, et al. Predicting endemic cholera: the role of climate variability and disease dynamics, Clim. Res., 36 (2008), 131–140.
  • 23. Reuters, Cholera vaccination campaign starts in Yemen after year delay: WHO, 07th May 2018. Available from: https://www.reuters.com/article/us-health-cholera/cholera-vaccination-campaign-starts-in-yemen-after-year-delay-who-idUSKBN1I8162.
  • 24. Z. Shuai, J. H. Tien and P. van den Driessche, Cholera models with hyperinfectivity and temporary immunity, B. Math. Biol., 74 (2012), 2423–2445.
  • 25. C. J. Silva and D. F. M. Torres, Optimal control for a tuberculosis model with reinfection and post-exposure interventions, Math. Biosci., 244 (2013), 154–164.
  • 26. The Telegraph News, 'Race against time' to curb cholera outbreak in Yemen, 09th May 2018. Available from: https://www.telegraph.co.uk/news/0/race-against-time-curb-cholera-outbreak-yemen/.
  • 27. P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
  • 28. Wikipedia, 2016–2018 Yemen Cholera Outbreak, 08th June 2018. Available from: http://en.m.wikipedia.org/wiki/2016-18_Yemen_cholera_outbreak.
  • 29. World Health Organization, Yemen cholera situation report no. 4, 19th July 2017. Available from: http://www.emro.who.int/images/stories/20170719_WHO_cholera_SitRep_4_v2.pdf?ua=1.
  • 30. World Health Organization, Yemen crisis, Fighting the world's largest cholera outbreak: oral cholera vaccination campaign begins in Yemen, 06th June 2018. Available from: http://www.emro.who.int/pdf/yem/yemen-news/oral-cholera-vaccination-campaign-in-yemen-begins.pdf?ua=1.
  • 31. World Health Organization, Yemen: Weekly Cholera Bulletins, 21st May 2018. Available from: http://www.emro.who.int/yem/yemeninfocus/situation-reports.html.
  • 32. World Health Organization, Yemen: Weekly Epidemiological Bulletin W15 2018, 21st May 2018. Available from: http://www.emro.who.int/images/stories/yemen/week_15.pdf?ua=1.
  • 33. X. Yang, L. Chen and J. Chen, Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models, Comput. Math. Appl., 32 (1996), 109–116.
  • 34. Yemen population, 06th June 2018. Available from: http://www.worldometers.info/world-population/yemen-population/.

 

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