A mathematical modeling proposal applied to the prevention of possible cholera outbreaks
DOI:
https://doi.org/10.14393/BEJOM-v1-n1-2020-50097Keywords:
SIS models; Qualitative Analysis of Nonlinear Systems; Cholera; Basic Reproduction Number; Deterministic models.Abstract
This article intends to present a mathematical modeling in order to characterize and determine possible prevention of cholera outbreaks, that is, to determine the causative factors of this disease and to search for results that show ways of controlling and irradiating them in Mathematics at the Faculty of Science and Technology of the University of Coimbra in partnership with the Pontal Institute of Exact and Natural Sciences, the main objective of this paper is to expose a deterministic mathematical model of cholera that was developed by Codeço (2001) and Fakai, Ibrahim and Danbaba (2013). Initially, a study was conducted on Susceptible - Infected - Susceptible (SIS) models in order to understand and delineate how to represent a mathematical model for possible prevention of cholera outbreaks. It is noteworthy that in this model among the results achieved, we highlight those related to the basic reproduction number (R0) and the critical number or threshold (Sc), which are used to predict and estimate the occurrence of the cholera outbreak. When R0 < 1, the disease-free steady state is asymptotically stable, that is, cases will shrink and disappear. If R0 > 1 the stability of the disease-free balance is unstable, that is, the cholera outbreak will occur in the community of interest. As for (Sc), if the number of susceptible people in the population is greater than the critical number (Sc), a cholera outbreak will occur.
Downloads
References
CODEÇO, T. C. Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infect Dis 1,1. 2001. doi:10.1186/1471-2334-1-1 Disponível em:≪https://bmcinfectdis.biomedcentral.com/articles/10.1186/1471-2334-1-1#citeas≫. Acesso em: 01/05/2019.
FAKAI, S. A.; IBRAHIM, M. O.; DANBABA, A. Deterministic Mathematical Model Of Cholera, Predicting Chances Of Its Outbreak. International Journal of Scientific Technology Research. Vol. 2. 2013. Disponível em: ≪http://www.ijstr.org/final-print/apr2013/Deterministic-Mathematical-Model-Of-Cholera-Predicting-Chances-Of-Its-Outbreak.pdf≫. Acesso em: 26/05/2019.
FRASER, C.; RILEY, S.; ADERSON, R. M.; FERGUSON, N. M. Factors thatmake an Infectious Disease Outbreak Controllable. Proceedings of the National Academy of Sciences of the USA. 2004.
GLOBO, Jornal da. Moçambique confirma novos casos de cólera após passagem do ciclone Idai. Disponível em: ≪https://g1.globo.com/mundo/noticia≫ Acesso em 30/03/2019.
≪mocambique-confirma-novos-casos-de-colera-apos-passagem-de-ciclone.ghtml≫. Acesso em: 01/05/2019.
LEITE,M. F. S.; PETRONILHO,J. C. S. Notas de Equações Diferenciais e Modelação. Departamento de Matemática da Universidade de Coimbra (FCTUC). 2019.
MINISTÉRIO DA SAÚDE. Cólera: causas, sintomas, transmissão, tratamento ediagnóstico. Disponível em: ≪http://portalms.saude.gov.br/saude-de-a-z/colera≫ 2018. Acesso em: 01/05/2019.
PARRY, M. L.; CANZIANI, O. F.; PALUTIKOF, J. P.; Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press. Cambridge, UK. 2007. Disponível em: ≪https://www.ipcc.ch/report/ar4/wg2/≫ Acesso em: 03/06/2019.
Downloads
Published
Issue
Section
License
Copyright (c) 2020 Maria de Fátima da Silva Leite, Bertrand Luiz Corrêa Lima
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
- Articles published from 2025 onwards are licensed under the CC BY 4.0 license. By submitting material for publication, authors automatically agree to the journal’s editorial guidelines and affirm that the text has been properly reviewed. Simultaneous submission of articles to other journals is prohibited, as is the translation of articles published in this journal into another language without proper authorization.
- Articles published prior to 2025 are licensed under the CC BY-NC 4.0 license.
