To determine R 0 when natural mortality is not equal to zero, (i.e. mw0), we use a non-linear differential equation fitting tool, called the PottersWheel Toolbox [29] . In this fitting technique, the c 2 value of the sum of the squares of the differences between the observed and fitted values is minimized by searching through different parameter values. We set m~0:0004, p~0:0169, b~0:0038, l~0:0037, and fit the free parameters, s,c, and the force of transmission br. We repeat this process 50 times to produce a range of best fits. The basic reproduction number for each run is then calculated using the expression in equation (9) The fitted parameters estimate the basic reproduction number R 0 between 2.08-2.39 with average 2.25. This value is similar to that found from the linear regression fitting. Figure 1c is a plot of the model outcome using the parameters generated from the fitting to the Kitgum outbreak.