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.

SBDiEM: A new mathematical model of infectious disease dynamics

“…Shi et al [49] proposed an HIV model with a saturated reverse function to describe the dynamics of infected cells. Additionally, Bonyah et al [50] developed a SIR model to study the dynamics of buruli ulcer and suggested policy measures to control the disease. Lastly, Zhang et al [51] developed a model with a latent period of the disease wherein the person is not infectious with saturated incidence rates and treatment functions, called SEIR epidemic model.…”

Environmental transmission of Mycobacterium ulcerans drives dynamics of Buruli ulcer in endemic regions of Cameroon

“…Previous studies have linked MU positivity in the environment and water bugs with BU prevalence 8 18 , suggesting that MU positivity in water bugs can differentiate between endemic and non-endemic areas 18 , and that environmental MU positivity may predict BU prevalence spatially 8 . Other studies have explored the theoretical implications of these routes of transmission in mathematical models 31 . However, due to data limitations, no studies have considered the contribution of environmental pathways while controlling for potential water bug transmission or vice versa .…”

A fractional modeling approach of Buruli ulcer in Possum mammals

“…The third most prevalent mycobacterial disease in humans, Mycobacterium ulcerans (MU) infection leads to severe abnormalities and disability [1][2][3][4][5][6][7][8][9]. It is a member of the family of Mycobacteria that can affect both humans and animals with sickness [10,11].…”