Mathematical Modelling Approach For Sensitivity and Stability Analyses of Cholera Disease in Aquatic Habitat
Keywords:
Sensitivity, stability, dynamical system, cholera transmission, numerical schemeAbstract
A research is conducted on mathematical modeling approach for sensitivity and stability analyses of cholera disease in aquatic habitat. A deterministic mathematical model is formulated in the analyses of the degree of sensitivity and stability of the dynamical system which aid cholera transmission, spread and control. A numerical approach was adopted using the non-linear (autonomous 1st order) ordinary differential equations (ODE45 numerical scheme) to tackle the problem of sensitivity and stability. Results of sensitivity and stability analyses have significant epidemiological importance in Cholera control. Sensitivity indices of the basic reproduction number are derived, existence and stability of the model steady state based on threshold value were shown. The study further shows that long-term precise predictions of the concentration of infected cells during cholera could be difficult until these key parameters are correctly determined. These results are vital in the ongoing cholera vaccine development. An important parameter to cholera transmission is the contact between susceptible and infected persons, while a crucial parameter to cholera control is the rate of cholera awareness.
References
Blower, S.M. & Dowlatabadi, H. (1994). Sensitivity analysis of complex models of disease transmission: an HIV model as an example. International Statistical Review, 62(2), 229 –243.
Ecohard, R. (2010). Methodology of the sensitivity analysis used for modelling on infection disease. Vaccine, 28, 8132 –8140. doi:10.1016/j.vaccine.2010.09.099
Edward, S. & Nyerere, N. (2015).A mathematical model for the dynamics of cholera with control measures. Application of Computational Mathematics, 4(2), 53 – 63.
Fraser, C. (2012). Mathematical models on infectious disease transmission. National Reservoir Micro Biology, 6, 477 –487.
Gomero, B. (2012). Latin hypercube sampling and partial rank correlation coefficient analysis applied to an optimal control problem. Master’s Thesis, University of Tennessee. https://trace.tennessee.edu/utk_gradthes/1278
Isere A. O., Osemwenkhae J. E. & Okuonghae D. (2014). Optimal control model for the outbreak of cholera in Nigeria. African Journal of Mathematics, Computer Science Research, 7(2), 24
Kadeleka, S. (2011). Assessing the effects of nutrition and treatment in cholera dynamics: The case of Malawi. M.Sc. Dissertation, University of Deres Salaam.
Keeling, M. (2007). Modelling infectious disease in human and animal. Princeton University Press.
Mondal, P. K. & Kar, J. K. (2013). Global dynamics of waterborne disease model with multiple transmission pathways .Applications and Applied Mathematics, 8(1), 75 – 98.
Mosler, J. & Kessely, H. (2015). Factors determining water treatment behaviour for the prevention of cholera treatment in Chad. The American Journal of Tropical Medicine and Hygiene, 93, 57 – 65.
Neilean R. L., Schaefer E., Gaff H., Fister K. R. & Lenhart S. (2010). Modeling optimal intervention strategies for cholera. Bulletin of Mathematical Biology, 72, 4 – 18.
Numfor, E. S. (2010). Mathematical modeling, simulation, and time series analysis of seasonal epidemics. M.Sc. Thesis, East Tennessee State University.
Nwagor, P. & Ekaka-a, E. N. (2017). Sensitivity of a mathematical model of HIV infection with a fractional order characterization. International Journal of Pure and Applied Sciences, Cambridge Research and Publications, 10(1), 86 – 92.
Ochoche, J. M. (2013). A mathematical model for the transmission dynamics of cholera with control strategy. International Journal of Scientific and Technology Research, 2(11), 212 – 217.
Panja, P. (2019). Optimal control analysis of a cholera epidemic model. Biophysical Review and Letters, 14, 27 – 48.
Rodrigues H. S., Monteiro M. T. & Torres D. F. (2013). Sensitivity analysis in a dengue epidemiological model. http://dx.doi.org/10.1155/2013/721406
Stockholm, F. (2006). Methods for uncertainty and sensitivity analysis: Review and recommendations for implementation in ecology. Eysicum, 5, 23 – 29.
Tarantola, S. (2008). Global sensitivity analysis. John Wiley and Sons
Umoh, E.S. (2022). Mathematical Modelling Approach for the Sensitivity and Stability Analyses of Cholera Diseases in Aquatic Environment. M.Sc. Thesis submitted to the Department of Mathematics and Statistics, Ignatius Ajuru University of Education, Port Harcourt, Rivers State.
WHO (2019). Cholera – World Health Organization. https://www.who.int/news-room/fact-sheets/detail/cholera
Wang, J. & Mondak, C. (2011). Modeling cholera dynamics with controls. Canadian Applied Mathematics Quarterly, 19(3), 255 – 273.
Wang, X. & Wang, J. (2014). Analysis of cholera epidemics with bacteria growth and spatial movement. Journal of Biological Dynamics, 2, 23 – 31.
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