title: A theoretical model for the transmission dynamics of the Buruli ulcer with saturated treatment.
abstract: The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.
authors.affiliation: Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
authors.forename: Ebenezer
authors.initials: E
authors.lastname: Bonyah
authors.affiliation: Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
authors.forename: Isaac
authors.initials: I
authors.lastname: Dontwi
authors.affiliation: Department of Mathematical Science, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa.
authors.forename: Farai
authors.identifier: 0000-0001-8607-7372
authors.initials: F
authors.lastname: Nyabadza
mesh_terms: D000349:Africa / Q000453:epidemiology; D050936:Basic Reproduction Number; D054312:Buruli Ulcer / Q000453:epidemiology / Q000276:immunology / Q000382:microbiology / Q000635:transmission*; D003198:Computer Simulation; D017753:Ecosystem; D006801:Humans; D018448:Models, Immunological; D019911:Mycobacterium ulcerans / Q000276:immunology*; D011157:Population Dynamics