Acta Biotheoretica

, Volume 66, Issue 4, pp 279–291 | Cite as

Theoretical Assessment of the Impact of Climatic Factors in a Vibrio Cholerae Model

  • G. KolayeEmail author
  • I. Damakoa
  • S. Bowong
  • R. Houe
  • D. Békollè
Regular Article


A mathematical model for Vibrio Cholerae (V. Cholerae) in a closed environment is considered, with the aim of investigating the impact of climatic factors which exerts a direct influence on the bacterial metabolism and on the bacterial reservoir capacity. We first propose a V. Cholerae mathematical model in a closed environment. A sensitivity analysis using the eFast method was performed to show the most important parameters of the model. After, we extend this V. cholerae model by taking account climatic factors that influence the bacterial reservoir capacity. We present the theoretical analysis of the model. More precisely, we compute equilibria and study their stabilities. The stability of equilibria was investigated using the theory of periodic cooperative systems with a concave nonlinearity. Theoretical results are supported by numerical simulations which further suggest the necessity to implement sanitation campaigns of aquatic environments by using suitable products against the bacteria during the periods of growth of aquatic reservoirs.


Mathematical model V. Cholerae Climatic factors Cooperative systems Stability 


  1. Anguelov R, Dumont Y, Lubuma J (2012) Mathematical modeling of sterile insect technology for control of Anopheles mosquito. Comput Math Appl 64:374–389CrossRefGoogle Scholar
  2. Chitnis N, Hyman JM, Cushing JM (2008) Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol 70:1272–1296CrossRefGoogle Scholar
  3. Codeço CT (2001) Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infect Dis 1:1CrossRefGoogle Scholar
  4. Colwell RR (1996) Global climate and infectious disease: the cholera paradigm. Science 274:2025–2031CrossRefGoogle Scholar
  5. Copasso V, Paveri-Fontana SL (1979) A model for the 1973 cholera epidemic in the european mediterranean region. Rev Epidem Santé Publ 27:121–132Google Scholar
  6. Guillaume et al (2012) République d’Haïti, Ministère de la Santé Publique et de la Population: Direction Nationale de L’Eau Potable et de L’Assainissement. Plan d’élimination du choléra en HaïtiGoogle Scholar
  7. Hartley DM, Morris JG, Smith DL Jr (2005) Hyperinfectivity: a critical element in the ability of V. Cholerae to cause epidemics? Plos Med 3:e1CrossRefGoogle Scholar
  8. Huq A, West PA, Small EB, Huq MI, Colwell RR (1984) Influence of water temperature, salinity, and pH on survival and growth of toxigenic Vibrio Cholerae serovar O1 associated with live copepods in a laboratory microcosms. Appl Environ Microbiol 48:420–424Google Scholar
  9. Islam MS, Rahim Z, Alam MJ, Begum S, Moniruzzaman SM, Umeda A, Amako K, Albert MJ, Sack RB, Huq A, Colwell RR (1999) Association of Vibrio Cholerae O1 with the cyanobacterium, Anabaena sp., elucidated by polymerase chain reaction and transmission electron microscopy. Trans R Soc Trop Med Hyg 93:36–40CrossRefGoogle Scholar
  10. Jifa J (1993) The algebraïc criteria for the asymptotic behavior of cooperative systems with concave nonlinearities. J Syst Sci Complex 6:193–196Google Scholar
  11. Kaper JB, Morris JG (1995) Levine MM cholera. Clin Micro Rev 8:48–86CrossRefGoogle Scholar
  12. Marino S, Hogue IB, Ray CJ, Kirschner DE (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254:178–196CrossRefGoogle Scholar
  13. Mouriño-Pérez RR, Worden AZ, Azam F (2003) Growth of Vibrio Cholerae O1 in Red Tide Waters off California. Appl Environ Microbiol 69:6923–6931CrossRefGoogle Scholar
  14. Mushayabasa S, Bhunu CP (2012) Is HIV infection associated with an increased risk for cholera? Insights from a mathematical model. BioSystems 109:203–213CrossRefGoogle Scholar
  15. Mwasa A, Tchuenche JM (2011) Mathematical analysis of a cholera model with public health interventions. BioSystems 105:190–200CrossRefGoogle Scholar
  16. Pascual M, Bouma MJ, Dobson Andrew P (2002) Cholera and climate: revisiting the quantitative evidence. Microbes Infect 4:237–245CrossRefGoogle Scholar
  17. Reidl J, Karl Klose E (2002) Vibirio Cholerae and cholera: out of the water and into the host. FEMS Microbiol Rev 26:125–139CrossRefGoogle Scholar
  18. Roszak DB, Colwell RR (1987) Survival strategies of bacteria in the natural environment. Microb Ecol 51:365–379Google Scholar
  19. Smith HL (2008) Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. American Mathematical Society, Providence, p 41CrossRefGoogle Scholar
  20. Tudor V, Strati I (1977) Smallpox, cholera. Abacus Press, Tunbridge Wells, p 313pGoogle Scholar
  21. WHO (2017) Cholera. Accessed 15 Aug 2017
  22. Xu H-S (1982) Survival and viability of non-culturable Escherichia coli and Vibrio Cholerae in the estuarine and marine environment. Microb Ecol 8:313–323CrossRefGoogle Scholar
  23. Yibeltal NB (2009) A mathematical analysis of a model of cholera transmission dynamic. AIMS, MuizenbergGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Saint Jerome PolytechnicSaint Jerome Catholic University Institute of DoualaDoualaCameroon
  2. 2.Department of Mathematics and Computer Science, Faculty of ScienceUniversity of NgaoundereNgaoundereCameroon
  3. 3.Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of ScienceUniversity of DoualaDoualaCameroon
  4. 4.University of Toulouse, INPT, LGP-ENIT 47Tarbes CedexFrance
  5. 5.UMI 209 IRD & UPMC UMMISCOBondyFrance
  6. 6.Project team GRIMCAPE-Cameroon, The African Center of Excellence in Information and Communication Technologies (CETIC)University of Yaounde 1YaoundeCameroon

Personalised recommendations