A Risk-Structured Mathematical Model of Buruli Ulcer Disease in Ghana

  • Christina Edholm
  • Benjamin Levy
  • Ash Abebe
  • Theresia Marijani
  • Scott Le Fevre
  • Suzanne LenhartEmail author
  • Abdul-Aziz Yakubu
  • Farai Nyabadza
Part of the Mathematics of Planet Earth book series (MPE, volume 5)


This chapter discusses a mathematical model for the spread of an infectious disease with transmission through a pathogen in an environment, including the effects of human contact with the environment. The model assumes a structured susceptible population consisting of both “low-risk” and “high-risk” individuals. It also includes the effects of shedding the pathogen by the infected population into the environment. The model has a disease-free equilibrium state, and a linear stability analysis shows three possible transmission routes. The model is applied to Buruli ulcer disease, a debilitating disease induced by Mycobacterium ulcerans. There is some uncertainty about the exact transmission path, but the bacteria is known to live in natural water environments. The model parameters are estimated from data on Buruli ulcer disease in Ghana. This chapter includes a sensitivity analysis of the total number of infected individuals to the parameters in the model.


Infectious disease Buruli ulcer disease Pathogen in environment Risk-structured model Ghana 



The authors acknowledge partial support from the National Science Foundation (NSF) under Grant No. 1343651 through the Southern Africa Mathematical Sciences Association (SAMSA) Masamu Program—a program that aims to enhance research in the mathematical sciences by serving as a platform for US–Africa research collaborations. This work was also partially supported by the National Institute for Mathematical and Biological Synthesis (NIMBioS)—one of the several Mathematical Sciences Institutes sponsored by the NSF Division of Mathematical Sciences—through NSF Award DBI-1300426, with additional support from The University of Tennessee, Knoxville. The authors appreciate the support for travel expenses from the Society of Mathematical Biology. They acknowledge an invaluable conversation with Pam Small and Heather Williamson about transmission mechanisms.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Christina Edholm
    • 1
    • 2
  • Benjamin Levy
    • 3
  • Ash Abebe
    • 4
  • Theresia Marijani
    • 5
  • Scott Le Fevre
    • 6
  • Suzanne Lenhart
    • 1
    • 2
    Email author
  • Abdul-Aziz Yakubu
    • 7
  • Farai Nyabadza
    • 8
  1. 1.University of TennesseeKnoxvilleUSA
  2. 2.Department of MathematicsScripps CollegeClaremontUSA
  3. 3.Department of MathematicsFitchburg State UniversityFitchburgUSA
  4. 4.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA
  5. 5.Department of MathematicsUniversity of Dar es SalaamDar es SalaamTanzania
  6. 6.Norwich UniversityNorthfieldUSA
  7. 7.Department of MathematicsHoward UniversityWashingtonUSA
  8. 8.Department of MathematicsUniversity of StellenboschStellenboschSouth Africa

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