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Original Articles
Modeling the Spread of Ebola
Tae Sug Do, Young S. Lee
Osong Public Health Res Perspect. 2016;7(1):43-48.   Published online February 28, 2016
DOI: https://doi.org/10.1016/j.phrp.2015.12.012
  • 1,945 View
  • 17 Download
  • 13 Citations
AbstractAbstract PDF
Objectives
This study aims to create a mathematical model to better understand the spread of Ebola, the mathematical dynamics of the disease, and preventative behaviors.
Methods
An epidemiological model is created with a system of nonlinear differential equations, and the model examines the disease transmission dynamics with isolation through stability analysis. All parameters are approximated, and results are also exploited by simulations. Sensitivity analysis is used to discuss the effect of intervention strategies.
Results
The system has only one equilibrium point, which is the disease-free state (S,L,I,R,D) = (N,0,0,0,0). If traditional burials of Ebola victims are allowed, the possible end state is never stable. Provided that safe burial practices with no traditional rituals are followed, the endemic-free state is stable if the basic reproductive number, R0, is less than 1. Model behaviors correspond to empirical facts. The model simulation agrees with the data of the Nigeria outbreak in 2004: 12 recoveries, eight deaths, Ebola free in about 3 months, and an R0 value of about 2.6 initially, which signifies swift spread of the infection. The best way to reduce R0 is achieving the speedy net effect of intervention strategies. One day's delay in full compliance with building rings around the virus with isolation, close observation, and clear education may double the number of infected cases.
Conclusion
The model can predict the total number of infected cases, number of deaths, and duration of outbreaks among others. The model can be used to better understand the spread of Ebola, educate about prophylactic behaviors, and develop strategies that alter environment to achieve a disease-free state. A future work is to incorporate vaccination in the model when the vaccines are developed and the effects of vaccines are known better.

Citations

Citations to this article as recorded by  
  • Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review
    Sanubari Tansah Tresna, Subiyanto, Sudradjat Supian
    Mathematics.2022; 10(14): 2506.     CrossRef
  • Fractional COVID-19 Modeling and Analysis on Successive Optimal Control Policies
    Mohammed Subhi Hadi, Bülent Bilgehan
    Fractal and Fractional.2022; 6(10): 533.     CrossRef
  • Analysis of a Covid-19 model: Optimal control, stability and simulations
    Seda İğret Araz
    Alexandria Engineering Journal.2021; 60(1): 647.     CrossRef
  • Modeling 2018 Ebola virus disease outbreak with Cholesky decomposition
    Lagès Nadège Mouanguissa, Abdul A. Kamara, Xiangjun Wang
    Mathematical Methods in the Applied Sciences.2021; 44(7): 5739.     CrossRef
  • Mitigation strategies and compliance in the COVID-19 fight; how much compliance is enough?
    Swati Mukerjee, Clifton M. Chow, Mingfei Li, Martin Chtolongo Simuunza
    PLOS ONE.2021; 16(8): e0239352.     CrossRef
  • A Generalized Mechanistic Model for Assessing and Forecasting the Spread of the COVID-19 Pandemic
    Hamdi Friji, Raby Hamadi, Hakim Ghazzai, Hichem Besbes, Yehia Massoud
    IEEE Access.2021; 9: 13266.     CrossRef
  • Analytical solution for post-death transmission model of Ebola epidemics
    Abdul A. Kamara, Xiangjun Wang, Lagès Nadège Mouanguissa
    Applied Mathematics and Computation.2020; 367: 124776.     CrossRef
  • Modelling the daily risk of Ebola in the presence and absence of a potential vaccine
    Stéphanie M.C. Abo, Robert Smith
    Infectious Disease Modelling.2020; 5: 905.     CrossRef
  • Data Fitting and Scenario Analysis of Vaccination in the 2014 Ebola Outbreak in Liberia
    Zhifu Xie
    Osong Public Health and Research Perspectives.2019; 10(3): 187.     CrossRef
  • Effect of sexual transmission on the West Africa Ebola outbreak in 2014: a mathematical modelling study
    Dongmei Luo, Rongjiong Zheng, Duolao Wang, Xueliang Zhang, Yi Yin, Kai Wang, Weiming Wang
    Scientific Reports.2019;[Epub]     CrossRef
  • Mathematical modeling of contact tracing as a control strategy of Ebola virus disease
    T. Berge, A. J. Ouemba Tassé, H. M. Tenkam, J. Lubuma
    International Journal of Biomathematics.2018; 11(07): 1850093.     CrossRef
  • Challenges of Designing and Implementing High Consequence Infectious Disease Response
    Joan M. King, Chetan Tiwari, Armin R. Mikler, Martin O’Neill
    Disaster Medicine and Public Health Preparedness.2018; 12(5): 563.     CrossRef
  • The potential impact of a prophylactic vaccine for Ebola in Sierra Leone
    Erin N. Bodine, Connor Cook, Mikayla Shorten
    Mathematical Biosciences and Engineering.2017; 15(2): 337.     CrossRef
Optimal Implementation of Intervention to Control the Self-harm Epidemic
Byul Nim Kim, M.A. Masud, Yongkuk Kim
Osong Public Health Res Perspect. 2014;5(6):315-323.   Published online December 31, 2014
DOI: https://doi.org/10.1016/j.phrp.2014.10.001
  • 1,869 View
  • 16 Download
  • 3 Citations
AbstractAbstract PDF
Objectives
Deliberate self-harm (DSH) of a young person has been a matter of growing concern to parents and policymakers. Prevention and early eradication are the main interventional techniques among which prevention through reducing peer pressure has a major role in reducing the DSH epidemic. Our aim is to develop an optimal control strategy for minimizing the DSH epidemic and to assess the efficacy of the controls.
Methods
We considered a deterministic compartmental model of the DSH epidemic and two interventional techniques as the control measures. Pontryagin's Maximum Principle was used to mathematically derive the optimal controls. We also simulated the model using the forward-backward sweep method.
Results
Simulation results showed that the controls needed to be used simultaneously to reduce DSH successfully. An optimal control strategy should be adopted, depending on implementation costs for the controls.
Conclusion
The long-term success of the optimum control depends on the implementation cost. If the cost is very high, the control could be used for a short term, even though it fails in the long run. The control strategy, most importantly, should be implemented as early as possible to attack a comparatively fewer number of addicted individuals.

Citations

Citations to this article as recorded by  
  • A review of the use of optimal control in social models
    D. M. G. Comissiong, J. Sooknanan
    International Journal of Dynamics and Control.2018; 6(4): 1841.     CrossRef
  • Adolescent self-harm and risk factors
    Jixiang Zhang, Jianwei Song, Jing Wang
    Asia-Pacific Psychiatry.2016; 8(4): 287.     CrossRef
  • Optimal Intervention Strategies for the Spread of Obesity
    Chunyoung Oh, Masud M A
    Journal of Applied Mathematics.2015; 2015: 1.     CrossRef
Optimal Implementation of Intervention Strategies for Elderly People with Ludomania
Byul Nim Kim, M.A. Masud, Yongkuk Kim
Osong Public Health Res Perspect. 2014;5(5):266-273.   Published online October 31, 2014
DOI: https://doi.org/10.1016/j.phrp.2014.08.006
  • 1,746 View
  • 18 Download
  • 1 Citations
AbstractAbstract PDF
Objectives
Now-a-days gambling is growing especially fast among older adults. To control the gratuitous growth of gambling, well-analyzed scientific strategies are necessary. We tried to analyze the adequacy of the health of society mathematically through immediate treatment of patients with early prevention.
Methods
The model from Lee and Do was modified and control parameters were introduced. Pontryagin's Maximum Principle was used to obtain an optimal control strategy.
Results
Optimal control can be achieved through simultaneous use of the control parameters, though it varies from society to society. The control corresponding to prevention needed to be implemented in full almost all the time for all types of societies. In the case of the other two controls, the scenario was greatly affected depending on the types of societies.
Conclusion
Prevention and treatment for elderly people with ludomania are the main intervention strategies. We found that optimal timely implementation of the intervention strategies was more effective. The optimal control strategy varied with the initial number of gamblers. However, three intervention strategies were considered, among which, preventing people from engaging in all types of gambling proved to be the most crucial.

Citations

Citations to this article as recorded by  
  • Roll the Dice
    Hae-Wol Cho, Chaeshin Chu
    Osong Public Health and Research Perspectives.2014; 5(5): 243.     CrossRef
Articles
Optimal Control Strategy of Plasmodium vivax Malaria Transmission in Korea
Byul Nim Kim, Kyeongah Nah, Chaeshin Chu, Sang Uk Ryu, Yong Han Kang, Yongkuk Kim
Osong Public Health Res Perspect. 2012;3(3):128-136.   Published online June 30, 2012
DOI: https://doi.org/10.1016/j.phrp.2012.07.005
  • 1,934 View
  • 15 Download
  • 10 Citations
AbstractAbstract PDF
Objective To investigate the optimal control strategy for Plasmodium vivax malaria transmission in Korea.
Methods
A Plasmodium vivax malaria transmission model with optimal control terms using a deterministic system of differential equations is presented, and analyzed mathematically and numerically.
Results
If the cost of reducing the reproduction rate of the mosquito population is more than that of prevention measures to minimize mosquito-human contacts, the control of mosquito-human contacts needs to be taken for a longer time, comparing the other situations. More knowledge about the actual effectiveness and costs of control intervention measures would give more realistic control strategies.
Conclusion
Mathematical model and numerical simulations suggest that the use of mosquito-reduction strategies is more effective than personal protection in some cases but not always.

Citations

Citations to this article as recorded by  
  • Optimal control analysis of hepatocytic-erythrocytic dynamics of Plasmodium falciparum malaria
    Titus Okello Orwa, Rachel Waema Mbogo, Livingstone Serwadda Luboobi
    Infectious Disease Modelling.2022; 7(1): 82.     CrossRef
  • Effects of climate change on Plasmodium vivax malaria transmission dynamics: A mathematical modeling approach
    Jung Eun Kim, Yongin Choi, Chang Hyeong Lee
    Applied Mathematics and Computation.2019; 347: 616.     CrossRef
  • Optimal bed net use for a dengue disease model with mosquito seasonal pattern
    Bruno Buonomo, Rossella Della Marca
    Mathematical Methods in the Applied Sciences.2017;[Epub]     CrossRef
  • Optimal control in epidemiology
    Oluwaseun Sharomi, Tufail Malik
    Annals of Operations Research.2017; 251(1-2): 55.     CrossRef
  • A new analysis of infection dynamics: multi-regions discrete epidemic model with an extended optimal control approach
    Omar Zakary, Mostafa Rachik, Ilias Elmouki
    International Journal of Dynamics and Control.2017; 5(4): 1010.     CrossRef
  • On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach
    Omar Zakary, Mostafa Rachik, Ilias Elmouki
    International Journal of Dynamics and Control.2017; 5(3): 917.     CrossRef
  • Bifurcation and Sensitivity Analysis of Malaria–Schistosomiasis Co-infection Model
    E. A. Bakare, C. R. Nwozo
    International Journal of Applied and Computational.2017; 3(S1): 971.     CrossRef
  • Effect of awareness programs and travel-blocking operations in the control of HIV/AIDS outbreaks: a multi-domains SIR model
    Omar Zakary, Abdelilah Larrache, Mostafa Rachik, Ilias Elmouki
    Advances in Difference Equations.2016;[Epub]     CrossRef
  • Transmission Dynamics and Optimal Control of Malaria in Kenya
    Gabriel Otieno, Joseph K. Koske, John M. Mutiso
    Discrete Dynamics in Nature and Society.2016; 2016: 1.     CrossRef
  • Years of Epidemics (2009–2011): Pandemic Influenza and Foot-and-Mouth Disease Epidemic in Korea
    Hae-Wol Cho, Chaeshin Chu
    Osong Public Health and Research Perspectives.2013; 4(3): 125.     CrossRef

PHRP : Osong Public Health and Research Perspectives