IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2018y2018i1n2528513.html

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

Author

Listed:
  • Obiora Cornelius Collins
  • Kevin Jan Duffy

Abstract

A mathematical model is formulated that captures the essential dynamics of waterborne disease transmission under the assumption of a homogeneously mixed population. The important mathematical features of the model are determined and analysed. The model is extended by introducing control intervention strategies such as vaccination, treatment, and water purification. Mathematical analyses of the control model are used to determine the possible benefits of these control intervention strategies. Optimal control theory is utilized to determine how to reduce the spread of a disease with minimum cost. The model is validated using a cholera outbreak in Haiti.

Suggested Citation

  • Obiora Cornelius Collins & Kevin Jan Duffy, 2018. "Analysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Study," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnljam:v:2018:y:2018:i:1:n:2528513
    DOI: 10.1155/2018/2528513
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2018/2528513
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/2528513?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Curriero, F.C. & Patz, J.A. & Rose, J.B. & Lele, S., 2001. "The association between extreme precipitation and waterborne disease outbreaks in the United States, 1948-1994," American Journal of Public Health, American Public Health Association, vol. 91(8), pages 1194-1199.
    2. Aaron A. King & Edward L. Ionides & Mercedes Pascual & Menno J. Bouma, 2008. "Inapparent infections and cholera dynamics," Nature, Nature, vol. 454(7206), pages 877-880, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wuxia Bi & Baisha Weng & Zhe Yuan & Yuheng Yang & Ting Xu & Dengming Yan & Jun Ma, 2019. "Evolution of Drought–Flood Abrupt Alternation and Its Impacts on Surface Water Quality from 2020 to 2050 in the Luanhe River Basin," IJERPH, MDPI, vol. 16(5), pages 1-17, February.
    2. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    3. Karel Mulder, 2019. "Future Options for Sewage and Drainage Systems Three Scenarios for Transitions and Continuity," Sustainability, MDPI, vol. 11(5), pages 1-15, March.
    4. Kathleen F. Bush & Cheryl L. Fossani & Shi Li & Bhramar Mukherjee & Carina J. Gronlund & Marie S. O'Neill, 2014. "Extreme Precipitation and Beach Closures in the Great Lakes Region: Evaluating Risk among the Elderly," IJERPH, MDPI, vol. 11(2), pages 1-19, February.
    5. repec:plo:pcbi00:1003312 is not listed on IDEAS
    6. Gina E C Charnley & Sebastian Yennan & Chinwe Ochu & Ilan Kelman & Katy A M Gaythorpe & Kris A Murray, 2022. "The impact of social and environmental extremes on cholera time varying reproduction number in Nigeria," PLOS Global Public Health, Public Library of Science, vol. 2(12), pages 1-20, December.
    7. David R J Pleydell & Samuel Soubeyrand & Sylvie Dallot & Gérard Labonne & Joël Chadœuf & Emmanuel Jacquot & Gaël Thébaud, 2018. "Estimation of the dispersal distances of an aphid-borne virus in a patchy landscape," PLOS Computational Biology, Public Library of Science, vol. 14(4), pages 1-24, April.
    8. Wuxia Bi & Baisha Weng & Zhe Yuan & Mao Ye & Cheng Zhang & Yu Zhao & Dengming Yan & Ting Xu, 2018. "Evolution Characteristics of Surface Water Quality Due to Climate Change and LUCC under Scenario Simulations: A Case Study in the Luanhe River Basin," IJERPH, MDPI, vol. 15(8), pages 1-18, August.
    9. Lindström, Erik, 2013. "Tuned iterated filtering," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2077-2080.
    10. Yohann Moanahere Chiu & Fateh Chebana & Belkacem Abdous & Diane Bélanger & Pierre Gosselin, 2021. "Cardiovascular Health Peaks and Meteorological Conditions: A Quantile Regression Approach," IJERPH, MDPI, vol. 18(24), pages 1-14, December.
    11. Gordon L. Nichols & Yvonne Andersson & Elisabet Lindgren & Isabelle Devaux & Jan C. Semenza, 2014. "European Monitoring Systems and Data for Assessing Environmental and Climate Impacts on Human Infectious Diseases," IJERPH, MDPI, vol. 11(4), pages 1-43, April.
    12. Kathleen A. Alexander & Marcos Carzolio & Douglas Goodin & Eric Vance, 2013. "Climate Change is Likely to Worsen the Public Health Threat of Diarrheal Disease in Botswana," IJERPH, MDPI, vol. 10(4), pages 1-29, March.
    13. Wang, Limin & Kanji, Shireen & Bandyopadhyay, Sushenjit, 2009. "The health impact of extreme weather events in Sub-Saharan Africa," Policy Research Working Paper Series 4979, The World Bank.
    14. Ross Sparks & Tim Keighley & David Muscatello, 2010. "Early warning CUSUM plans for surveillance of negative binomial daily disease counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1911-1929.
    15. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    16. Brian Stone & Jessica L Bullen, 2006. "Urban Form and Watershed Management: How Zoning Influences Residential Stormwater Volumes," Environment and Planning B, , vol. 33(1), pages 21-37, February.
    17. Chris J. Barton & Qingqing Wang & Derrick M. Anderson & Drew A. Callow, 2021. "Synchronizing the Logic of Inquiry with the Logic of Action: The Case of Urban Climate Policy," Sustainability, MDPI, vol. 13(19), pages 1-16, September.
    18. Ianis Delpla & Donald T. Monteith & Chris Freeman & Joris Haftka & Joop Hermens & Timothy G. Jones & Estelle Baurès & Aude-Valérie Jung & Olivier Thomas, 2014. "A Decision Support System for Drinking Water Production Integrating Health Risks Assessment," IJERPH, MDPI, vol. 11(7), pages 1-22, July.
    19. Gabriel Kolaye Guilsou & Moulay-Ahmed Aziz-Alaoui & Raymond Houé Ngouna & Bernard Archimede & Samuel Bowong, 2023. "Gaining Profound Knowledge of Cholera Outbreak: The Significance of the Allee Effect on Bacterial Population Growth and Its Implications for Human-Environment Health," Sustainability, MDPI, vol. 15(13), pages 1-30, June.
    20. Franklin Amuakwa-Mensah & George Marbuah & Mwenya Mubanga, 2016. "Climate variability and infectious diseases nexus: evidence from Sweden," Working Papers 2016.02, FAERE - French Association of Environmental and Resource Economists.
    21. Manisha Shah & Bryce Millett Steinberg, 2017. "Drought of Opportunities: Contemporaneous and Long-Term Impacts of Rainfall Shocks on Human Capital," Journal of Political Economy, University of Chicago Press, vol. 125(2), pages 527-561.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2018:y:2018:i:1:n:2528513. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.