Conclusion

Our findings point to two key areas of future research. First, there is a need to obtain better parameters for our model. While we gathered a number of parameters from the literature the parameters most likely influencing model results (host movement, vector movement, and relative patch size) are not well known. While there has been considerable work on human movement through space (e.g., Hufnagel et al. 2004; Cr6pey and Barth6lemy 2007) there has been very little research on how vectors move through space. To develop optimal control strategies, it will be necessary to gain a better understanding of the range of these parameters.

There are two ways in which this might be accomplished. The first is more direct observational studies of host and vector movement. The second and perhaps more lo-gistically feasible is to employ a pattern-oriented modeling (POM) approach (Grimm et al. 2005). POM provides a strategy to deal with two problems concerning the modeling of large multifaceted systems: complexity and uncertainty. POM leverages the fact that patterns contain "coded" information concerning underlying model processes and structure. Even our relatively simple models indicate that different movement rates lead to readily observed temporal and spatiotemporal differences in the dynamics of epidemics. Thus, the greatest need in terms of empirical data collection may lie in developing detailed spatially explicit databases of disease incidence.

The second key area of future research is to place our optimization in a proper optimal control framework. The theory and methods to optimize systems of coupled ordinary differential equation are well developed (Lenhart and Workman 2007). Using a proper optimal control framework would readily allow us to incorporate a range of costs and benefits of different control strategies and determine how far away our rule of thumb control strategies are from the optimal ones for a given disease system.

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