Table 2. Relationship between M. ulcerans in the aquatic environment and Buruli ulcer: summary of results for the best set of fits in the mathematical (temporal) model and for the statistical (spatial) models.
| Mathematical Model | ||||||
|---|---|---|---|---|---|---|
| Variable | Relationship | Time from Exposure to Treatment | Number of models | Mean λMU | Mean λWB | Mean AIC |
| MUconc | Linear | 6 | 26 | 1.27E-04 | 1.86E-06 | 58.52 |
| 7 | 5 | 1.26E-04 | 2.66E-07 | 59.33 | ||
| 9 | 2 | 6.83E-05 | 6.25E-05 | 59.32 | ||
| Power law | 6 | 2 | 1.29E-04 | 1.35E-07 | 59.32 | |
|
Statistical Models | ||||||
| Model | Model Formula 1 | Span (LOESS smoother) | a | b1 | b2 | AIC |
| LM | y=a+b1*MUpos | – | 0.82*** | 5.00* | – | 78.96 |
| y=a+b1*MUpos + b2*WBpos | – | 0.9*** | 5.60* | −1.26 | 79.98 | |
| y=a+b1*MUpos + b2*WBinf | – | 0.74 ** | 4.92* | 0.01 | 80.07 | |
| GAM | y=a+f(MUpos)2 | 1 | 0.82 | 5.00 | – | 79.54 |
| 0.9 | 0.82 | 5.00 | – | 77.52 | ||
| 0.8 | 0.82* | 5.00* | – | 75.55 | ||
| 0.7 | 0.82 | 5.00 | - | 75.92 | ||
*p-value < 0.05 ; ***p-value < 0.001.
Best mathematical and statistical model is represented in bold.
1Response variable (y) is the mean Buruli ulcer incidence in 5km buffers around the sites for the study period.
2The nature of the relationship using GAMs cannot be described with a single equation. See supplementary materials section S8 for a graphical description of the relationship for each value of span.