Analysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Study

Collins, Obiora Cornelius; Duffy, Kevin J.

doi:10.1155/2018/2528513

Cited by 11 publications

(11 citation statements)

References 46 publications

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“…Graphically, the value of λ + > 0 stands for the steepness of the increasing fraction curve [4]. is implies that the higher the value of λ + , the more severe the disease outbreak.…”

Section: Theoremmentioning

confidence: 99%

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Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

Onah

Collins

Madueme

et al. 2020

International Journal of Mathematics and Mathematical Sciences

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Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is endemic in parts of West Africa including Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. We formulate a mathematical model for Lassa fever disease transmission under the assumption of a homogeneously mixed population. We highlighted the basic factors influencing the transmission of Lassa fever and also determined and analyzed the important mathematical features of the model. We extended the model by introducing various control intervention measures, like external protection, isolation, treatment, and rodent control. The extended model was analyzed and compared with the basic model by appropriate qualitative analysis and numerical simulation approach. We invoked the optimal control theory so as to determine how to reduce the spread of the disease with minimum cost.

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“…Graphically, the value of λ + > 0 stands for the steepness of the increasing fraction curve [4]. is implies that the higher the value of λ + , the more severe the disease outbreak.…”

Section: Theoremmentioning

confidence: 99%

“…Mathematical model is a powerful tool that has been successfully used to investigate the dynamics of infectious diseases [4][5][6][7][8][9][10][11]. Some of the recent studies on Lassa fever disease dynamics that used mathematical model and other methods are presented below.…”

Section: Introductionmentioning

confidence: 99%

Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

Onah

Collins

Madueme

et al. 2020

International Journal of Mathematics and Mathematical Sciences

Self Cite

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“…Table 8: parameters and their description. Table 9: state variables and their description [23][24][25][26][27]. (Supplementary Materials)…”

Section: Acknowledgmentsmentioning

confidence: 99%

Optimal Control of Shigellosis with Cost-Effective Strategies

Edward

Shaban

Mureithi

2020

Computational and Mathematical Methods in Medicine

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In this paper, we apply optimal control theory to the model for shigellosis. It is assumed that education campaign, sanitation, and treatment are the main controls for this disease. The aim is to minimize the number of infections resulting from contact with careers, infectious population, and contaminated environments while keeping the cost of associated controls minimum. We achieve this aim through the application of Pontryagin’s Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth-order Runge-Kutta schemes. We simulate the model under different strategies to investigate which option could yield the best results. The findings show that the strategy combining all three control efforts (treatment, sanitation, and education campaign) proves to be more beneficial in containing shigellosis than the rest. On the other hand, cost-effectiveness analysis is performed via incremental cost-effectiveness ratio (ICER). The findings from the ICER show that a strategy incorporating all three controls (treatment, sanitation, and education campaign) is the most cost-effective of all strategies considered in the study.

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“…to detect infectious individuals for prompt treatment; conducting active case findings in all of China, prompt isolation and treatment of infectious individuals (WHO, 2020d). Mathematical models have been successfully used in studying the dynamics of infectious disease outbreaks (Hellewell et al, 2020;Balilla, 2020;Li et al, 2020;Kucharski et al, 2020;Mukandavire et al, 2011;Collins & Duffy, 2018;Collins & Govinder, 2014;Tian et al, 2020;Mukandavire, Smith & Morris Jr, 2013;Tuite et al, 2011). For instance, Chen et al (2020) develop a mathematical model for calculating the potential transmission of COVID-19 from the original infection source to human infections.…”

Section: Introductionmentioning

confidence: 99%

Estimating the impact of lock-down, quarantine and sensitization in a COVID-19 outbreak: lessons from the COVID-19 outbreak in China

Collins

Duffy

2020

PeerJ

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In recent history, COVID-19 is one of the worst infectious disease outbreaks currently affecting humanity globally. Using real data on the COVID-19 outbreak from 22 January 2020 to 30 March 2020, we developed a mathematical model to investigate the impact of control measures in reducing the spread of the disease. Analyses of the model were carried out to determine the dynamics. The results of the analyses reveal that, using the data from China, implementing all possible control measures best reduced the rate of secondary infections. However, quarantine (isolation) of infectious individuals is shown to have the most dominant effect. This possibility emphasizes the need for extensive testing due to the possible prevalence of asymptomatic COVID-19 cases.

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Analysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Study

Cited by 11 publications

References 46 publications

Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

Optimal Control of Shigellosis with Cost-Effective Strategies

Estimating the impact of lock-down, quarantine and sensitization in a COVID-19 outbreak: lessons from the COVID-19 outbreak in China

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