Optimal control policies for a non-eruptive population of rodents—The relevance of migration

Abstract

In the Azores, as in many other places around the world, rodents are responsible for economic losses, environmental problems, and several health problems such as fatal cases of Leptospirosis.We apply a population model of rodents to understand what are the relevant biological and economical parameters that dictate the best control strategy. The model is constructed in discrete time and it includes the effect of poison mortality and rodent migration. The optimal control solutions are obtained minimising the total adult rodent population together with the cost of control, for different migration rates and different costs of control.We find that for very small or no migration the optimal solution exhibits a phase transition as the cost of control increases. It changes from applying a large amount of poison that drives rodents close to extinction, to no poison applied. This phase transition is robust to changes in the parameters and details of the model.Increasing the rate of migration, the phase transition disappears and the total amount of poison in the optimal solution decreases towards zero as its cost increases. In the presence of migration and for very low cost, the optimal is obtained concentrating the control during the period of large population increase but for more significant costs the optimal is obtained concentrating the control in the months preceding this increase. Also, as the migration of rodents into the field under control increases, the optimal control is concentrated in a few months around the start of the high reproduction season.We conclude that the appropriate optimal control policy is strongly dependent on the balance between the cost of control and the cost resulting from rodent damage, as well as the level of migration into the field under control.