Abstract
Cholera is an infectious disease that causes severe, watery diarrhea that, if not treated, can lead to dehydration and death. Regardless of medical science advancements and the availability of healthcare services, it has been a global public health concern, affecting both children and adults. In this study, we develop and analyze a nonlinear optimal control problem to investigate the effective control of cholera in a human population. Four control variables were added to an already existing cholera model with vital dynamics: adequate cleanliness, oral vaccine, therapeutic care, and public education. The conditions for the existence of optimal cholera disease control were developed using Pontryagin’s renowned maximal principle. Furthermore, the fourth-order Runge–Kutta forward–backward sweep method was used to simulate the optimality system to demonstrate the effect of various control methods on the spread of cholera within the human population. The findings show that control costs have a direct and plausible impact on the timeliness and robustness of each regulation.
Similar content being viewed by others
Data availability statement
Data sharing does not apply to this article as no datasets were generated or analyzed during the current study.
References
Adebimpe O, Adesina I, Gbadamosi B, Oludoun O, Abiodun O, Adeyemo O (2022) Mathematical modeling of cholera epidemics with vital dynamics. In: Proceedings of sixth international congress on information and communication technology. Springer, pp 591–608
Lemos-Paião AP, Silva CJ, Torres DFM (2018) A cholera mathematical model with vaccination and the biggest outbreak of world’s history. AIMS Math 3(4):448–463
Chayu Y (2020) Mathematical modeling, analysis, and simulation of cholera dynamics. University of Tennessee at Chattanooga S
Elimian K, Musah A, Ochu C, Onwah S, Oyebanji O, Yennan S, Fall I, Yao M, Chukwuji M, Ekeng E, Abok P, Omar L, Balde T, Kankia A, Williams N, Mutbam K, Dhamari N, Okudo I, Alemu W, Ihekweazu C (2020) Identifying and quantifying the factors associated with cholera-related death during the 2018 outbreak in Nigeria. Res Math 37(368):96
Fleming WH, Rishel RW (2012) Deterministic and stochastic optimal control, vol 1. Springer, New York
Hakim LTT, Darti I (2015) Optimal control of a cholera disease model with vaccination. Int J Appl Math Stat 53(4):65–72
Hntsa KH, Kahsay BN (2020) Analysis of cholera epidemic controlling using mathematical modeling. Int J Math Math Sci 2020:96
Hove-Musekwa SD, Nyabadza F, Chiyaka C, Das P, Tripathi A, Mukandavire Z (2011) Modelling and analysis of the effects of malnutrition in the spread of cholera. Math Comput Model 53(9):1583–1595
Jhoana PatriciaRomero-Leiton MO, Hussain T (2021) Optimal control problem for cholera disease and cost-effectiveness analysis. J Math Fund Sci 53(2):200–217
Kahn R, Peak CM, Fernández-Gracia J, Hill A, Jambai A, Ganda L, Castro M, Buckee C (2020) Incubation periods impact the spatial predictability of cholera and ebola outbreaks in sierra leone. Proc Natl Acad Sci USA 117:5067–5073
Njagarah JBH, Nyabadza F (2015) Modelling optimal control of cholera in communities linked by migration. Comput Math Methods Med 1–12
Onuorah MO, Atiku FA, Juuko H, Rogovchenko Y (2022) Mathematical model for prevention and control of cholera transmission in a variable population. Res Math 9(1):96
Ojo MM, Goufo EFD (2022a) Mathematical analysis of a Lassa fever model in Nigeria: optimal control and cost-efficacy. Int J Dyn Control 96:1–22
Ojo MM, Goufo EFD (2022b) Modeling, analyzing and simulating the dynamics of Lassa fever in Nigeria. J Egypt Math Soc 30(1):1–31
Ojo MM, Doungmo Goufo EF (2021a) Assessing the impact of control interventions and awareness on malaria: a mathematical modeling approach. Commun Math Biol Neurosci 2021:Article–ID
Ojo MM, Gbadamosi B, Benson TO, Adebimpe O, Georgina A (2021b) Modeling the dynamics of Lassa fever in Nigeria. J Egypt Math Soc 29(1):1–19
Ojo MM, Benson TO, Peter OJ, Goufo EFD (2022a) Nonlinear optimal control strategies for a mathematical model of covid-19 and influenza co-infection. Physica A Stat Mech Appl 128173
Ojo MM, Benson TO, Shittu AR, Doungmo Goufo EF (2022b) Optimal control and cost-effectiveness analysis for the dynamic modeling of lassa fever. J Math Comput Sci 12:Article–ID
Oludoun O, Adebimpe O, Ndako J, Adeniyi M, Abiodun O, Gbadamosi B (2021) The impact of testing and treatment on the dynamics of hepatitis b virus. F1000research 10:936. https://doi.org/10.12688/f1000research.72865.1
Panja P, Mondal SK, Chattopadhyay J (2017) Dynamical study in fuzzy threshold dynamics of a cholera epidemic model. Fuzzy Inf Eng 9(3):381–401
Peter OJ, Abioye AI, Oguntolu FA, Owolabi TA, Ajisope MO, Zakari AG, Shaba TG (2020) Modelling and optimal control analysis of Lassa fever disease. Inform Med Unlocked 20:100419
Peter OJ, Oguntolu FA, Ojo MM, Oyeniyi AO, Jan R, Khan I (2022a) Fractional order mathematical model of monkeypox transmission dynamics. Physica Scripta 97(8):084005
Peter OJ, Yusuf A, Ojo MM, Kumar S, Kumari N, Oguntolu FA (2022b) A mathematical model analysis of meningitis with treatment and vaccination in fractional derivatives. Int J Appl Comput Math 8(3):1–28
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest Also, no funding was received for conducting this study.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gbadamosi, B., Adebimpe, O., Ojo, M.M. et al. Modeling the impact of optimal control measures on the dynamics of cholera. Model. Earth Syst. Environ. 9, 1387–1400 (2023). https://doi.org/10.1007/s40808-022-01570-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40808-022-01570-9