Epidemiological models

To demonstrate our approach, we used a simple SI-type compartmental host-vector model framework [36] (described in S2 Text) to simulate the epidemiological dynamics of two important citrus pathogens. We used Southern Gardens Citrus, a commercial citrus plantation in south Florida, as the conceptual setting for our model, and parameterised the models as shown in Tables ​Tables11 and ​and22.

(βκ=(ϕρh)(1-exp(-bκT))), where κ refers to the receiving group. Most estimates are taken from [29, 37] for HLB and [38, 39] for tristeza. The duration of feeding per visit for the HLB model was taken from [40] and for the tristeza model was adjusted according to the total efficiency of CTV transmission described in [41]. All rates (ϕ, b_v, b_h) are per day.

All rates (β, μ, τ) are per day.

The full system of ODEs for the model framework are given in S2 Text, but the ODEs describing the numbers of infected hosts and vectors are as follows:

Linearising around the disease-free steady state, the components of the Jacobian matrix in eq 16 for this system can be calculated:

We used this model framework to create models of two insect-vectored citrus diseases of economic importance to the global citrus industry: huanglongbing (HLB) and tristeza diseases. The epidemiological unit in each model was an individual sweet orange tree (Citrus × sinensis) host, or single insect vector (Asian citrus psyllid, Diaphorina citri Kuwayama, or brown citrus aphid, Toxoptera citricida (Kirkaldy), respectively). Parameter values and sources for the two models are shown in Tables ​Tables11 and ​and2.2. We assume that there is no differential immigration and emigration of infected vectors [42], that the total number of hosts and vectors does not change over time, and that there was no vertical transmission amongst hosts due to certification and testing of budwood source trees [43]. We estimated transmission parameters using the approach described by Jeger and others [42, 44], and selected a suitable number of vectors to achieve an overall R₀ of 100 when the number of hosts is fixed at 250,000 (see S2 Text). Our decision to fix the R₀ for each pathosystem at 100 and use this to calculate the relative densities of hosts and vectors was primarily intended to account for the lack of data on vector abundance, and to allow comparison of different pathogen types [45, 46].

Huanglongbing (also known as citrus greening) is a fatal disease of citrus and related plants caused by phloem-restricted gram negative Alphaproteobacteria of the genus Candidatus Liberibacter [47]. The most common species of Liberibacter worldwide is Ca. L. asiaticus (Las), which is the cause of ‘Asian citrus greening’, and is spread by the phloem-feeding Asian citrus psyllid. Las can be considered a ‘persistently transmitted, circulative pathogen’ [45, 46]. These pathogens enter the haemolymph of the vector and have the potential for transovarial transmission (although this is disputed in the particular case of Las [37, 48]).

Unlike many plant viruses, the citrus tristeza virus (CTV) complex comprises a number of strains which are responsible for a wide range of syndromes in citrus and their relatives [49–51]. Although strains were traditionally differentiated according to disease phenotype [49, 52, 53], this relationship remains unclear [50, 54], and we therefore focus on the spread of an undefined ‘novel’ CTV strain by the brown citrus aphid (considered the most efficient vector of CTV [55]). CTV is considered a ‘semipersistently transmitted, foregut-borne’ pathogen [45, 46], which does not spread systemically and therefore is characterised by rapid acquisition [49, 52, 56] and short persistence [39, 57].