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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Analysis of Transmission Dynamics of Cholera: An Optimal Control Strategy

Journal of Applied Nonlinear Dynamics 11(2) (2022) 387--400 | DOI:10.5890/JAND.2022.06.009

Matthew O. Adewole$^{1,2}$, Akindele Onifade$^1$, Ahmad Izani Md Ismail$^2$, Taye Faniran$^3$,\\ Farah A. Abdullah$^2$

$^1$ Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Ogun State, Nigeria

$^2$ School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia

$^3$ Department of Computer Science, Lead City University, Lagos-Ibadan Expressway, Ibadan, Oyo State, Nigeria

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Abstract

Cholera affects populations living with poor sanitary conditions and has caused enormous morbidity and mortality. A mathematical model is presented for the spread of cholera with focus on three human populations; susceptible human, infected human and recovered human. The infected human population was subdivided into two groups - symptomatic individuals and asymptomatic individuals. We obtain the reproductive number and a sensitivity analysis of model parameters is conducted. The sensitivity analysis reveals key parameters which can be used to propose intervention strategies. Our analysis indicates that a single intervention strategy is insufficient for the eradication of the disease. Optimal control strategy is incorporated to find effective solutions for time-dependent controls for eradicating cholera epidemics. We use numerical simulations to explore various optimal control solutions involving single and multiple controls. Our results show that, as in related previous studies, the costs of controls have a direct effect on the duration and strength of each control in an optimal strategy. It is also established that a combination of multiple intervention strategies attains better results than a single-pronged approach since the strength of each control strategy is limited by available resources and social factors.

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