A method of determining where to target surveillance efforts in heterogeneous epidemiological systems

Abstract

The spread of pathogens into new environments poses a considerable threat to human, animal, and plant health, and by extension, human and animal wellbeing, ecosystem function, and agricultural productivity, worldwide. Early detection through effective surveillance is a key strategy to reduce the risk of their establishment. Whilst it is well established that statistical and economic considerations are of vital importance when planning surveillance efforts, it is also important to consider epidemiological characteristics of the pathogen in question-including heterogeneities within the epidemiological system itself. One of the most pronounced realisations of this heterogeneity is seen in the case of vector-borne pathogens, which spread between 'hosts' and 'vectors'-with each group possessing distinct epidemiological characteristics. As a result, an important question when planning surveillance for emerging vector-borne pathogens is where to place sampling resources in order to detect the pathogen as early as possible. We answer this question by developing a statistical function which describes the probability distributions of the prevalences of infection at first detection in both hosts and vectors. We also show how this method can be adapted in order to maximise the probability of early detection of an emerging pathogen within imposed sample size and/or cost constraints, and demonstrate its application using two simple models of vector-borne citrus pathogens. Under the assumption of a linear cost function, we find that sampling costs are generally minimised when either hosts or vectors, but not both, are sampled.

Fig 1. Effect of varying sampling effort (θ=NΔ) on the mean prevalence at first detection for the HLB model (panels (a) and (b) and the tristeza model (panels (c) and (d).

The estimated prevalence at first detection in hosts is shown in the graphs on the left, and that in vectors is shown in the graphs on the right. The dashed line indicates a host (vertical line) and a vector (horizontal line) sampling effort of 800 samples per 28 days, with the intersection of these dashed lines indicating a theoretical scenario in which a total of 800 hosts and 800 vectors were sampled.

Fig 2. Effect of varying transmission parameters (β) on the suggested group of sampling for the HLB model (panel (a)) and the tristeza model (panel (b)).

We estimate the relative sampling efforts required from vectors compared to that from hosts when using the current model parameters (located at the intersection of the dashed lines) using the ratio $\left[\frac{\left(\frac{{\nu }_h}{{\rho }_h}\right)}{\left(\frac{{\nu }_v}{{\rho }_v}\right)}\right]$, and assume that the relative cost of sampling hosts compared to vectors is equal to this threshold (8 for HLB, 6 for Tristeza)—indicating the ‘equivalence point’ as described in the text. The numbers in the key on the right describe the relative vector sampling effort $\left[\frac{\left(\frac{{\nu }_h}{{\rho }_h}\right)}{\left(\frac{{\nu }_v}{{\rho }_v}\right)}\right]$ for different transmission rates, but the colour gradient relates to the ratio of the relative vector sampling effort to the relative host sampling cost $\left[\frac{{\zeta }_h}{{\zeta }_v}\right]$, and is shown on the log scale in order to better discriminate values less than 1. Regions shown in red have a sampling effort ratio greater than the cost ratio (suggesting that sampling hosts would minimise the total cost) and those in blue have a ratio less than the cost ratio (suggesting that sampling vectors would minimise the total cost). The frontier between these two (indicating a ratio equal to the cost ratio) is shown in white.