A modified SIR model is used to explain the transmission of Mycobacterium ulcerans (MU) and its dependence on arsenic (As) environments. Some studies have suggested that As plays a major role in the spread and prevalence of buruli ulcer (BU). In addition, it has been hypothesized that a vector in the form of a water-bug plays a key role in the epidemiology of BU. We develop an epidemiological model based on these assumptions for the dynamics and prevalence of BU and show that As positively induces the growth and spread of MU.

In order to evaluate the feasibility of a combined evolutionary algorithm-information theoretic approach to select the best model from a set of candidate invasive species models in ecology, and/ or to evolve the most parsimonious model from a suite of competing models by comparing their relative performance, it is prudent to use a unified model that covers a myriad of situations. Using Schnute's postulates as a starting point, we present a single, unified model for growth that can be successfully utilized for model selection in evolutionary computations. Depending on the parameter settings, the unified equation can describe several growth mechanisms. Such a generalized model mechanism, which encompasses a suite of competing models, can be successfully implemented in evolutionary computational algorithms to evolve the most parsimonious model that best fits ground truth data. We have done exactly this by testing the effectiveness of our reaction-diffusion-advection (RDA) model in an evolutionary computation model selection algorithm. The algorithm was validated (with success) against field data sets of the Zebra mussel invasion of Lake Champlain in the United States.

We use a reaction diffusion equation, together with a genetic algorithm approach for model selection to develop a general modeling framework for biological invasions. The diffusion component of the reaction diffusion model is generalized to include dispersal and advection. The reaction component is generalized to include both linear and non-linear density dependence, and Allee effect. A combination of the reaction diffusion and genetic algorithm is able to evolve the most parsimonious model for invasive species spread. Zebra mussel data obtained from Lake Champlain, which demarcates the states of New York and Vermont, is used to test the appropriateness of the model. We estimate the minimum wave spread rate of Zebra mussels to be 22.5 km/year. In particular, the evolved models predict an average northward advection rate of 60.6 km/year (SD ± 1.9), which compares very well with the rate calculated from the known hydrologic residence time of 60 km/year. A combination of a reaction diffusion model and a genetic algorithm is, therefore, able to adequately describe some of the hydrodynamic features of Lake Champlain and the spread of a typical invasive species--Zebra mussels within the lake.