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Abubakar, Sani Fakai; Ibrahim, M. O.

Optimal control analysis of treatment strategies of the dynamics of cholera. (English) Zbl 07659719

J. Optim. 2022, Article ID 2314104, 26 p. (2022).

MSC:

92-XX Biology and other natural sciences
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References:

[1] Ganesan, D.; Gupta, S. S.; Legros, D., Cholera surveillance and estimation of burden of cholera, Vaccine, 38 (2020) · doi:10.1016/j.vaccine.2019.07.036
[2] Idoga, P. E.; Toycan, M.; Zayyad, M. A., Analysis of factors contributing to the spread of cholera in developing countries, The Eurasian Journal of Medicine, 51, 2, 121-127 (2019) · doi:10.5152/eurasianjmed.2019.18334
[3] Llanes, R.; Somarriba, L.; Hernández, G.; Bardají, Y.; Aguila, A.; Mazumder, R. N., Low detection of vibrio cholerae carriage in healthcare workers returning to 12 Latin american countries from Haiti, Epidemiology and Infection, 143, 5, 1016-1019 (2015) · doi:10.1017/s0950268814001782
[4] Momba, M.; Azab El-Liethy, M., Vibrio cholerae and Cholera Biotypes (2018), Pretoria, South Africa: Global Water Pathogen Project, Pretoria, South Africa
[5] Hattaf, K.; Rachik, M.; Saadi, S.; Tabit, Y.; Yousfi, N., Optimal control of tuberculosis with exogenous reinfection, Applied Mathematical Sciences, 3, 5, 231-240 (2009) · Zbl 1172.92023
[6] Miller Neilan, R. L.; Schaefer, E.; Gaff, H.; Fister, K. R.; Lenhart, S., Modeling optimal intervention strategies for cholera, Bulletin of Mathematical Biology, 72, 8, 2004-2018 (2010) · Zbl 1201.92045 · doi:10.1007/s11538-010-9521-8
[7] Namawejje, H.; Obuya, E.; Luboobi, L. S., Modeling optimal control of cholera disease under the interventions of vaccination, treatment and education awareness, Journal of Mathematics Research, 10, 5 (2018) · doi:10.5539/jmr.v10n5p137
[8] Panja, P., Optimal control analysis of a cholera epidemic model, Biophysical Reviews and Letters, 14, 01, 27-48 (2019) · doi:10.1142/s1793048019500024
[9] Javidi, M.; Ahmad, B., A study of a fractional-order cholera model, Applied Mathematics & Information Sciences, 8, 5, 2195-2206 (2014) · doi:10.12785/amis/080513
[10] Lamond, E.; Kinyanjui, J., Cholera Outbreak Guidelines: Preparedness, Prevention and Control (2012), Oxford, United Kingdom: Oxfam GB, Oxford, United Kingdom
[11] Ochoche, M. J.; Madubueze, E. C.; Akaabo, T. B., A mathematical model on the control of cholera: hygiene consciousness as a strategy, The Journal of Mathematics and Computer Science, 5, 2, 172-187 (2015)
[12] Wu, J.; Dhingra, R.; Gambhir, M.; Remais, J. V., Sensitivity analysis of infectious disease models: methods, advances and their application, Journal of The Royal Society Interface, 10, 86 (2013) · doi:10.1098/rsif.2012.1018
[13] Isere, A. O.; Osemwenkhae, J. E.; Okuonghae, D., Optimal control model for the outbreak of cholera in Nigeria, African Journal of Mathematics and Computer Science Research, 7, 2, 24-30 (2014) · doi:10.5897/ajmcsr2013.0527
[14] Edward, S.; Nyerere, N., A mathematical model for the dynamics of cholera with control measures, Applied and Computational Mathematics, 4, 2, 53 (2015) · doi:10.11648/j.acm.20150402.14
[15] Elhia, M.; Laaroussi, A.; Rachik, M.; Rachik, Z.; Labriji, E., Global stability of a susceptible-infected-recovered (sir) epidemic model with two infectious stages and treatment, International Journal of Science and Research, 3, 5, 114-121 (2014)
[16] Liao, S.; Yang, W., On the dynamics of a vaccination model with multiple transmission ways, International Journal of Applied Mathematics and Computer Science, 23, 4, 761-772 (2013) · Zbl 1285.93043 · doi:10.2478/amcs-2013-0057
[17] Gronwall, T. H., Note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Annals of Mathematics, 20, 4 (1919) · JFM 47.0399.02 · doi:10.2307/1967124
[18] Mafuta, P.; Mushanyu, J.; Nhawu, G., Invariant region, endemic equilibria and stability analysis, IOSR Journal of Mathematics, 10, 2, 118-120 (2014) · doi:10.9790/5728-1022118120
[19] Van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 1-2, 29-48 (2002) · Zbl 1015.92036 · doi:10.1016/s0025-5564(02)00108-6
[20] Diekmann, O.; Heesterbeek, J. A. P.; Metz, J. A., On the definition and the computation of the basic reproduction ratio r 0 in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28, 4, 365-382 (1990) · Zbl 0726.92018 · doi:10.1007/bf00178324
[21] Hincapié-Palacio, D.; Ospina, J.; Torres, D. F. M., Approximated analytical solution to an ebola optimal control problem, International Journal for Computational Methods in Engineering Science and Mechanics, 17, 5-6, 382-390 (2016) · Zbl 07871441 · doi:10.1080/15502287.2016.1231236
[22] Birkhoff, G.; Rota, G. C., Ordinary Differential Equations (1989), Boston: Ginn, Boston · Zbl 0183.35601
[23] Elhia, M.; Rachik, M.; Benlahmar, E., Optimal control of an sir model with delay in state and control variables, International Scholarly Research Notices, 2013 (2013), 403549 · Zbl 1300.92097 · doi:10.1155/2013/403549
[24] Fleming, W. H.; Rishel, R. W., Deterministic and stochastic optimal control, Springer Science & Business Media, 1 (2012)
[25] Isaac Oke, S.; Matadi, M. B.; Xulu, S. S., Optimal control analysis of a mathematical model for breast cancer, Mathematical and Computational Applications, 23, 2 (2018) · doi:10.3390/mca23020021
[26] Lenhart, S.; Workman, J. T., Optimal Control Applied to Biological Models (2007), London, UK: Chapman and Hall/CRC, London, UK · Zbl 1291.92010
[27] Gumel, A.; Shivakumar, P.; Sahai, B., A mathematical model for the dynamics of hiv-1 during the typical course of infection, Nonlinear Analysis: Theory, Methods & Applications, 47, 3, 1773-1783 (2001) · Zbl 1042.92512 · doi:10.1016/s0362-546x(01)00309-1
[28] Karrakchou, J.; Rachik, M.; Gourari, S., Optimal control and infectiology: application to an hiv/aids model, Applied Mathematics and Computation, 177, 2, 807-818 (2006) · Zbl 1096.92031 · doi:10.1016/j.amc.2005.11.092
[29] Lemos-Paião, A. P.; Silva, C. J.; Torres, D. F. M.; Venturino, E., Optimal control of aquatic diseases: a case study of Yemen’s cholera outbreak, Journal of Optimization Theory and Applications, 185, 3, 1008-1030 (2020) · Zbl 1444.92118 · doi:10.1007/s10957-020-01668-z
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