A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

The management of venereal disease in New South Wales, 1871 to 1916

Practical techniques to manage the dangers associated with sexually transmitted diseases have varied considerably both cross culturally and historically. Adopting a Foucauldian perspective, this article examines sociohistorical aspects of the governance of venereal disease in New South Wales between 1871 and 1916. Public debates and official documents are analysed to identify strategic shifts in practices associated with venereal disease management , especially in relation to prostitution. Particular attention is paid to the development of contagious disease legislation and its role in the regulation of venereal disease . It is argued that during the period in question, two distinct governmental regimes of disease control can be identified. In the first, medical policing managed venereal disease through the mobilisation of repressive controls, requiring the isolation and detention of polluting bodies. In the second, liberal governance adopted pedagogic practices to train populations perceived as either healthy or unhealthy. It is further argued that as liberal strategies of governance came to dominate the management of venereal disease , the association of prostitution with venereal disease began to weaken. Instead, authorities became increasingly concerned with populations whose behaviour was not traditionally linked with venereal disease , such as the young and the sexually inexperienced.