Applications with Discrete and Continuous Models: Harvesting and Contact Tracing

Harvest plays an important role in management decisions, from fisheries to pest control. Discrete models enable us to explore the importance of timing of management decisions including the order of events of particular actions. We derive novel mechanistic models featuring explicit within season harvest timing and level. Our models feature explicit discrete density independent birth pulses, continuous density dependent mortality, and density independent harvest level at a within season harvest time. We explore optimization of within-season harvest level and timing through optimal control of these population models. With a fixed harvest level, harvest timing is taken as the control. Then with fixed timing, the harvest level is implemented as the control. Finally, both harvest timing and level are used as controls. We maximize an objective functional which includes management goals of maximizing yield, maximizing stock, and minimizing costs associated with both harvest intensity and harvest timing.

The 2014-2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. However, there were many complications and challenges to contact tracing efforts during the 2014-2016 outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leone during the outbreak. Using data on cumulative cases and deaths we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. We explore the role contact tracing played in eventually ending the outbreak and examine the potential impact of improved contact tracing on the death toll.