Integrated disease management, optimal effort allocation between prevention and control

Prevention and control are two complementary strategies for disease management. In the absence of disease, prevention could be viewed as wasteful. On the contrary, control requires efforts, only in the presence of the disease. But in some cases, control strategies are implemented a long time after the disease started, when irrevocable damages could be already observed. Deciding how much efforts are dedicated to prevention and control is a difficult problem in practice. In this work, we formulated a simple mathematical model to balance the trade-off between prevention and control efforts, with the expected loss due to disease. We derived an analytical form of the optimal prevention and control efforts and showed that the amount of control and prevention efforts depends on the relative values of the control and prevention efficacy, weighted by the probability of disease occurrence. We illustrated our framework for the management of gastro-intestinal nematodes in small-ruminants. In particular to discuss the use of different common management methods, such as systematic or targeted anthelmintic treatments, and mixed grazing. We proposed simple decision rules that could help designing future management practice and research efforts in this area. For examples, we computed the minimal anthelmintic efficacy for treatment to be economically viable. We also discussed the optimal cost and efficacy of a monitoring method for implementing targeted selective treatment, or the maximal cost of mixed grazing implementation. This framework is particularly useful to discuss the cost of new management strategy, and to ensure that new management designs are economically viable.