Search Advanced

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 1: 95-109. doi: 10.3934/mbe.2017007
Previous Article Next Article
 

Controlling imported malaria cases in the United States of America

  • 1.
    Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
  • 2.
    Department of Mathematics, Howard University, Washington, DC 20059, USA
  • Received: 24 November 2015 Accepted: 02 July 2016 Published: 01 February 2017

  • MSC : 92B05

  • We extend the mathematical malaria epidemic model framework of Dembele et al. and use it to “capture” the 2013 Centers for Disease Control and Prevention (CDC) reported data on the 2011 number of imported malaria cases in the USA. Furthermore, we use our “fitted” malaria models for the top 20 countries of malaria acquisition by USA residents to study the impact of protecting USA residents from malaria infection when they travel to malaria endemic areas, the impact of protecting residents of malaria endemic regions from mosquito bites and the impact of killing mosquitoes in those endemic areas on the CDC number of imported malaria cases in USA. To significantly reduce the number of imported malaria cases in USA, for each top 20 country of malaria acquisition by USA travelers, we compute the optimal proportion of USA international travelers that must be protected against malaria infection and the optimal proportion of mosquitoes that must be killed.

    Citation: Bassidy Dembele, Abdul-Aziz Yakubu. Controlling imported malaria cases in the United States of America[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 95-109. doi: 10.3934/mbe.2017007

    Related Papers:

  • We extend the mathematical malaria epidemic model framework of Dembele et al. and use it to “capture” the 2013 Centers for Disease Control and Prevention (CDC) reported data on the 2011 number of imported malaria cases in the USA. Furthermore, we use our “fitted” malaria models for the top 20 countries of malaria acquisition by USA residents to study the impact of protecting USA residents from malaria infection when they travel to malaria endemic areas, the impact of protecting residents of malaria endemic regions from mosquito bites and the impact of killing mosquitoes in those endemic areas on the CDC number of imported malaria cases in USA. To significantly reduce the number of imported malaria cases in USA, for each top 20 country of malaria acquisition by USA travelers, we compute the optimal proportion of USA international travelers that must be protected against malaria infection and the optimal proportion of mosquitoes that must be killed.


    加载中
    [1] [ P. -L. Alonso, A. Djimde, H. Hughes and S. -A. Ward, A research agenda for malaria eradication: Drugs, DOI: 10.1371/journal.pmed.1000402,January25,2011.
    [2] [ P. Carnevale, J. Mouchet, M. Coosemans, J. Julvez, S. Manguin, R. -D. Lenoble and S. Sircoulou, Biodiversite du Paludisme dans le Monde Editions John Libbey Eurotext, Paris, 2004.
    [3] [ R. -P. Cody and J. -K. Smith, Applied Statistics and the SAS Programming Language Pearson Prentice Hall, Fifth Edition, 2006.
    [4] [ K. -A. Cullen,P. -M. Arguin, Malaria Surveillance-United States, 2011 Centers for Diseases Control and Prevention, null (2013): 1-17.
    [5] [ B. Dembele,A. Friedman,A. -A. Yakubu, Mathematical Model for optimal use of sulfadoxine-pyrimethamine as a temporary vaccine, Bulletin of Mathematical Biology, 72 (2010): 914-930.
    [6] [ B. Dembele,A. -A. Yakubu, Optimal treated mosquito bed nets and insecticides for eradication of malaria in Missira, Discrete and Continuous Dynamical Systems Series B, 17 (2012): 1831-1840.
    [7] [ A. -M. Dondorp,F. Nosten,P. Yi,D. Das,A. -P. Phyo, Artemisinin resistance in Plasmodium falciparum malaria, N Engl J Med, 361 (2009): 455-467.
    [8] [ J. -C. Koella,R. Antia, Epidemiological models for the spread of anti-malaria resistance, Malaria Journal, null (2003): 2-3.
    [9] [ W. -O. Kermack,A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proc. R. Soc A, 115 (1927): 700-721.
    [10] [ A. J. Lokta, Contributions to the analysis of malaria epidemiology, Am. J. Hyg., 3 (1923): 11-21.
    [11] [ G. Macdonald, The analysis of infection rate in diseases in which superinfection occurs, Trop. Dis., 47 (1950): 907-915.
    [12] [ C. -A. Mertler and R. -A. Vannatta, Advanced and Multivariate Statistical Methods: Pratical Application and Interpretation Pyrczak Publishing, Fifth Edition, 2013.
    [13] [ K. O. Okosun,R. Ouifki,N. Marcus, Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity, Biosystems, 106 (2011): 136-145.
    [14] [ C. Y. -J. Peng, Data Analysis Using SAS Sage, 2009.
    [15] [ R. Ross, The Prevention of Malaria $ \ 2^{nd}$ edition, With Addendum on the Theory of Happenings, Murray, London, 1911.
    [16] [ C. H. Sibley,J. E. Hyde,P. F. G. Sims,C. V. Plowe,J. G. Kublin,E. K. Mberu,A. F. Cowman,P. A. Winstanley,W. M. Watkins,A. M. Nzila, Pyrimethamine-sulfadoxine resistance in Plasmodium falciparum: What next?, Trends in Parasitology, 17 (2001): 570-571.
    [17] [ N. Sogoba,S. Doumbia,P. Vounatsou,I. Baber,M. Keita,M. Maiga,S. Toure,G. Dolo,T. Smith,J. M. C. Ribeiro, Monotoring of larval habitats and mosquito densities in the sudan savanna of Mali: Implications of malaria vector control, Am. J. Trop. Med. Hyg., 77 (2007): 82-88.
    [18] [ B. -G. Tabachnick and L. -S. Fidell, Using Multivariate Statistics Pearson, Sixth Edition, 2013.
    [19] [ J. -F. Trape,A. Tall,C. Sokhna,A. -B. Ly,N. Diagne,O. Ndiath,C. Mazenot,V. Richard, The rise and fall of malaria in a West African rural community, Dielmo, Senegal, from 1990 to 2010: A 22 year longitudinal study, The Lancet Infectious Diseases, 14 (2014): 476-488.
    [20] [ http://www.cdc.gov/mmwr/preview/mmwrhtml/ss6205a1.htm. Accessed7/2/2016.
    [21] [ World-Health-Organization, Malaria, Available from: http://www.who.int/mediacentre/factsheets/fs094/en/. Accessed 7/2/2016.
  • Reader Comments
  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(4354) PDF downloads(608) Cited by(4)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(7)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog