Modelling the formation of skin ulcers observed in Buruli ulcer disease

Abstract

Buruli ulcer (BU) is a neglected tropical skin disease caused by infection with Mycobacterium ulcerans. The mode of its transmission into the skin has not been fully clarified, but it is believed to involve mechanical transfer, perhaps by insect bites. M. ulcerans secretes a toxin called mycolactone which causes necrosis of the skin and formation of large skin lesions. Understanding the development of these skin lesions over time is crucial to understand the pathogenesis of BU. We formulate a mathematical model to describe the space-time dynamics of M. ulcerans bacteria, mycolactone and skin cell densities as well as fibrin deposition. We investigate the relative contributions to ulcer formation of direct cytotoxicity of mycolactone and ischaemia following the loss of coagulation control. Our results are consistent with existing biological evidence that higher mycolactone concentrations accelerate cell death. Furthermore, the model indicates that the rate of wound expansion is primarily controlled by the diffusion and net birth rate of bacteria, which sets the overall scaling for the speed of wound expansion, along with two dimensionless constants that define the shape of the trajectory of wound edge position against time, namely the ratio of the mycolactone diffusion coefficient to the bacterial diffusion coefficient, and the ratio of the mycolactone degradation rate to the bacterial net birth rate. When mycolactone diffuses significantly faster than bacteria spread or when mycolactone degrades more slowly than bacteria reproduce, the initial development of the wound is faster. In contrast, the long-term wound expansion speed appears to be relatively unchanged across a wide range of the dimensionless parameters.