Frequency and Sample Size to Minimize the Cost of a Rapidly Evolving Infectious Animal or Plant Disease

One of the major effects of global change is the spread of animal and plant diseases on farms. Besides the impact on the farms themselves, it is the whole rural world that is affected, through the possible disruption of value chains. Combating these diseases is therefore a crucial but costly problem. So, when faced with an infectious animal or plant pathology, how can we minimize the cost of the disease and of the sampling and analyses testing required to monitor its progress? First, we calculate the imprecision of the results as a function of the sample size and the prevalence of the disease. Then, depending on the desired precision and the prevalence of the disease, we calculate the required sample size. Finally, in the case of iterative sampling, depending on the cost of each sampling and testing event and the costs associated with the spread of the disease, we show on a quantitative example that there is an optimum, i.e. a relationship between the frequency and the sample size (number of samples) that allows the cost of the disease to be minimized. We show the optimum relationship between sample size and frequency, the relationship between minimum total cost and frequency, and finally, we show on a 3-dimensional graph, how the total cost evolves as a function of frequency and sample size.