The 2021 Cholera Outbreak in Nigeria, Data and Models Used to Explore Controls and Challenges
DOI:
https://doi.org/10.5614/cbms.2023.6.2.8Keywords:
Basic reproduction number, disease dynamics, model fitting, sensitivity analysisAbstract
Cholera is an acute diarrhoeal illness that affects humanity globally, especially in areas where there is limited access to clean water and adequate sanitation. A Nigerian cholera outbreak from January 2021 to January 2022 resulted in many cases and deaths. A mathematical model that takes into consideration the challenges that affected effective implementation of control measures for this 2021 cholera outbreak is developed. Important epidemiological features of the model such as the basic reproduction number (R0), the disease-free equilibrium, and the endemic equilibrium are determined and analysed. The disease-free equilibrium is shown to be asymptotically stable provided R0 < 1. The model is shown to undergo forward bifurcation at R0 = 1 using the Centre Manifold Theorem. Sensitivity analysis is used to determine the parameters that have the highest influence on transmission. Fitting the model to data from the 2021 Nigerian cholera outbreak, important parameters of the model are estimated. The impact of control measures as well as challenges that affected the effective implementation of these control measures are considered.
References
World Health Organization, https://www.who.int/health-topics/cholera#tab=tab 1, (July 23, 2022).
Centres for Disease Control and Prevention, https://www.cdc.gov/cholera/general/index.html#one, (July 23, 2022).
Nigeria Centre for Disease Control (NCDC). Cholera Situation Report, https://ncdc.gov.ng/diseases/sitreps, (17 July 2022).
Collins, O.C. and Duffy, K.J., Mathematical Analyses on the Effects of Control Measures for a Waterborne Disease Model with Socioeconomic Conditions, Journal of Computational Biology, 28(1), pp.19-32, 2021.
Tien, J.H. and Earn, D.J.D., Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bulletin of Mathematical Biology, 72, pp. 1506-1533, 2010.
Collins, O.C. and Govinder, K.S., Incorporating heterogeneity into the transmission dynamics of a waterborne disease model, Journal of Theoretical Biology, 356, pp. 133-143, 2014.
Robertson, S.L., Eisenberg, M.C. and Tien, J.H., Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source, Journal of Biological Dynamics, 7(1), pp. 254-275, 2013.
Modnak, C., Wang, J. and Mukandavire, Z., Simulating optimal vaccination times during cholera outbreaks, International Journal of Biomathematics, 7(2), p. 1450014, 2014.
Rinaldo, A., Bertuzzo, E., Mari, L., Righetto, L., Blokesch, M., Gatto, M., et al. Reassessment of the 2010-2011 Haiti cholera outbreak and rainfall-driven multiseason projections, Proceedings of the National Academy of Sciences, 109(17), pp. 6602-6607, 2012.
Nyabadza, F., Aduamah, J.M. and Mushanyu, J., Modelling cholera transmission dynamics in the presence of limited resources, BMC Research Notes, 12, pp. 1-8, 2019.
Bertuzzo, E., Azaele, S., Maritan, A., Gatto, M., Rodriguez-Iturbe, I. and Rinaldo, A., On the space-time evolution of a cholera epidemic, Water Resources Research, 44(1), 2008.
Collins, O.C. and Govinder, K.S., Stability analysis and optimal vaccination of a waterborne disease model with multiple water sources, Natural Resource Modeling, 29(3), pp. 426-447, 2016.
Miller Neilan, R.L., Schaefer, E., Gaff, H., Fister, K.R. and Lenhart, S., Modeling optimal intervention strategies for cholera, Bulletin of Mathematical Biology, 72, pp. 2004-2018, 2010.
Collins, O.C. and Duffy, K.J., Optimal Control Intervention Strategies using an n-patch Waterborne Disease Model, Natural Resource Modeling, 29(4), pp. 499-519, 2016.
Mukandavire, Z., Smith, D.L. and Morris, Jr J.G., Cholera in Haiti: reproductive numbers and vaccination coverage estimates, Scientific Reports, 3(1), p. 997, 2013.
Righetto, L, Casagrandi, R., Bertuzzo, E., Mari, L., Gatto, M., Rodriguez-Iturbe, I. and Rinaldo, A., The role of aquatic reservoir fluctuations in long-term cholera patterns, Epidemics, 4(1), pp. 33-42, 2012.
Wang, J. and Liao, S., A generalized cholera model and epidemic-endemic analysis, Journal of Biological Dynamics, 6(2), pp. 568-589, 2012.
Onuorah, M.O., Atiku, F.A. and Juuko, H., Mathematical model for prevention and control of cholera transmission in a variable population, Research in Mathematics, 9(1), p. 2018779, 2022.
Mukandavire, Z., Liao, S., Wang, J., Gaff, H., Smith, D.L. and Morris Jr JG., Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe, Proceedings of the National Academy of Sciences, 108(21), pp. 8767-8772, 2011.
United Nations International Children?s Emergency Fund (UNICEF), https://www.unicef.org/nigeria/press-releases/19-million-children-internally-displaced-conflict-and-violence-2019-highest-number, (July 23, 2022).
van den Driessche, P. and Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180(1-2), pp. 29-48, 2002.
Collins, O.C. and Duffy, K.J., Estimating the impact of lock-down, quarantine and sensitization in a COVID-19 outbreak: lessons from the COVID-19 outbreak in China, PeerJ, 8, p. e9933, 2020.
Sanches, R.P., Ferreira, C.P., Kraenkel, R.A., The role of immunity and seasonality in cholera epidemics, Bulletin of Mathematical Biology, 73, pp. 2916-2931, 2011.
Herdicho, F.F., Chukwu, W. and Tasman, H., An optimal control of malaria transmission model with mosquito seasonal factor. Results in Physics, 25, p. 104238, 2021.
Ibrahim, M.A. and Denes, A., A mathematical model for Lassa fever transmission dynamics in a seasonal environment with a view to the 2017-20 epidemic in Nigeria, Nonlinear Analysis: Real World Applications, 60, p. 103310, 2021.
Mukandavire, Z. and Garira, W., HIV/AIDS model for assessing the effects of prophylactic sterilizing vaccines, condoms and treatment with amelioration, Journal of Biological Systems, 14(3), pp. 323-355, 2006.
Codeco, C.T., Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir, BMC Infectious Diseases, 1(1), pp. 1-14, 2001.
Mukandavire, Z., Tripathi, A., Chiyaka, C., Musuka, G., Nyabadza, F. and Mwambi, H.G., Modelling and analysis of the intrinsic dynamics of cholera, Differential Equations and Dynamical Systems, 19, pp. 253-265, 2011.
Hartley, D.M., Morris, Jr J.G. and Smith, D.L., Hyperinfectivity: a critical element in the ability of V. cholerae to cause epidemics?, PLoS Medicine, 3(1), p. e7, 2006.
Date, K.A., Vicari, A., Hyde, T.B., Mintz, E., Danovaro-Holliday, M.C., Henry, A., et al. Considerations for oral cholera vaccine use during outbreak after earthquake in Haiti, 2010-2011, Emerg. Emerging Infectious Diseases, 17(11), p. 2105, 2011.
Sepulveda, J., Gomez-Dantes, H. and Bronfman, M., Cholera in the Americas: an overview, Infection, 20, pp. 243-248, 1992.
Mwasa, A. and Tchuenche, J.M., Mathematical analysis of a cholera model with public health interventions, Biosystems, 105(3), pp. 190-200, 2011.
Chitnis, N., Hyman, J.M., and Cushing, J.M., Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology, 70, pp. 1272-1296, 2008.
Taylor, R., Interpretation of the correlation coefficient: a basic review, Journal of Diagnostic Medical Sonography, 6(1), pp. 35-39, 1990.
World Health Organization, https://www.who.int/news-room/fact-sheets/detail/cholera#:?:text=Currently%20there%20are%20three%20WHO,150%20ml%20of%20clean%20water, (July 17, 2022).
Mahalanabis, D., Molla, A.M. and Sack, D.A., Clinical management of cholera, In Cholera, pp. 253-283 Springer, Boston, MA, 1992.
Castillo-Chavez, C. and Song, B., Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1(2), pp. 361-404, 2004.
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