1. Introduction
Vectorial capacity, defined as the total number of potentially infectious bites that would arise from all the vectors biting a single infectious host on a single day [
1], is a concept used in epidemiology to measure the potential ability of a vector species to transmit a pathogen to a susceptible host population. There are many models for vectorial capacity, each considering different bionomic parameters [
2,
3,
4,
5].
The rate at which vectors complete the gonotrophic cycle, defined as the time required for locating a host, blood feeding, egg maturation and oviposition, has been found to be temperature-dependent [
6,
7,
8,
9,
10]. The extrinsic incubation period (EIP), defined as the time required for a vector to become infectious after consumption of an infected blood meal, is also temperature-dependent [
11,
12]. Multiple models consider how vectorial capacity changes with different climatic conditions [
13,
14,
15,
16,
17,
18,
19,
20,
21]. These are usually used to assess variations in risk geographically and/or for climate change scenarios. Brand and Keeling [
13] suggested a model for vectorial capacity of bluetongue virus (BTV), a
Culicoides-borne orbivirus of veterinary significance, which considered the temperature dependence of the gonotrophic cycle length, vector mortality, and the EIP.
Chitnis et al. [
22] suggested a vectorial capacity model for malaria transmission derived from a discrete-time entomological model of the
Anopheles feeding cycle. Updated versions of this model have been utilised to predict the community-level effect of using a new vector tool on
Plasmodium transmission [
23,
24,
25]. The model considers the effects of vector-control interventions at different stages during the mosquito feeding cycle. Although most of the parameter values of the model are measurable, several, such as the ovary sac proportion (proportion of mosquitoes with uncontracted ovary sacs) require technical time-consuming experiments; therefore, there are limited data available on these parameters. One advantage of this model is that it incorporates host selection, which is influenced by the availability of competent and non-competent hosts and the vector’s preferences for these hosts. This consideration is quantified using the human blood index, defined as the proportion of vectors that have fed on humans relative to the total number of blood-fed vectors analysed.
We suggest an updated version of the Brand and Keeling [
13] model that considers the influence of climate on vectors, as well as features from the Chitnis et al. [
22] model, namely host selection and the impact of vector control tools at various stages of the gonotrophic cycle. This model considers both personal protection through reduction in feeding, as well as community protection through vector mortality and disarming (feeding inhibition due to intoxication). This model is then parameterised for
Culicoides-borne arboviruses of veterinary importance in Europe: BTV, African horse sickness virus (AHSV), Schmallenberg virus (SBV), and epizootic haemorrhagic disease virus (EHDV). This model is then applied to temperature data from the United Kingdom, which has previously seen BTV and SBV outbreaks. The potential reduction in vectorial capacity for AHSV is then calculated for insecticide-treated stable netting, dependent on behaviour of owners.
Feeding multiple times per gonotrophic cycle is observed to occur naturally for some vectors (for example,
Aedes mosquitoes), increasing opportunities for disease transmission [
26]. This behaviour has not been investigated for
Culicoides. In other cases, when vectors are disturbed during a blood meal, they may seek more blood from the same or another host [
1]. This model considers the influence of the average number of blood meals per gonotrophic cycle on the predicted vectorial capacity and the impact of vector-control tools.
4. Discussion
We developed a model for vectorial capacity that considers both climate and host selection behaviour of vectors and vector controls. This model can be applied to more accurately predict vectorial capacity with current, or potential future, vector control strategies. Although temperature was the only climatic effect considered in this study, this model allows for additional climatic variables to be considered. This study focused on the vectorial capacity of Culicoides-borne viruses; however, it can be utilised for other pathogens and vectors.
We calculated the vectorial capacity based on a singular estimate for mean temperature. However, temperature varies according to location. Even within relatively small areas, microclimates can affect the temperature and vectorial capacity [
21,
41,
42]. Previous studies indicate that landscape can significantly influence disease seroprevalence [
43]. However, this variation in disease seroprevalence across different landscapes could also be influenced by the varying abundance of vectors. This, in turn, may depend on the thermal preferences of the vectors [
44].
When considering the mean daily temperature, the number of days above the minimum threshold temperature for virus replication within the vector can be much lower than for the daily maximum temperature, especially for EHDV. Models using the mean temperature may therefore underestimate the vectorial capacity and the potential for pathogen transmission. Future work could explore more nuanced methods to estimate the duration of potential virus transmission, such as accumulated degree days above the threshold temperature, to incorporate within-day temperature variation. However, as finer-scale temperature data are not commonly reported, future studies could focus on developing and validating proxy measures or statistical methods to estimate accumulated degree days from available daily minimum, maximum, and mean temperatures. Such approaches could significantly improve our ability to predict virus transmission potential across varying climatic conditions.
We showed that considering host selection, driven by host availability and preferences of vectors, in models can significantly reduce vectorial capacity predictions. Therefore, the availability and preferences for competent and non-competent hosts, the availability of which varies by location, should be considered when assessing risk and deciding where to implement vector control.
In this study,
was not calculated due to uncertainty of the vector-landscape. Two viruses may have the same vectorial capacity but different values of
due to a different number of vectors per host, which will be variable across location and host type [
43,
45]. Brand and Keeling [
13] used the number of
Culicoides caught in light-traps without hosts present to parameterise the model. However, light-traps have been shown to not be good surrogate hosts for
Culicoides [
45,
46].
The peak vectorial capacity summed over the infectious period for AHSV and EHDV were similar to BTV and SBV, respectively. Given that the UK has previously seen outbreaks of BTV and SBV, this study suggests that AHSV and EHDV outbreaks could also be a threat. Recently, in 2024, recommencement of direct horse movements from South Africa to the European Union has been approved [
47]. Our results suggest that an importation of an infected case could lead to further transmission. This study provided evidence that vectorial capacity of the viruses the model was applied to in this study has been increasing in the UK. This highlights the importance of preparedness for the potential emergence of these diseases in the UK and the rest of Europe.
In dividing the vectorial capacity estimates into ten-year blocks and calculating averages for each period, we aimed to observe long-term trends in vectorial capacity. However, this methodological choice introduces the potential for discontinuities between the blocks. Future analyses might benefit from applying smoothing techniques. Despite this, the model predicted that the vectorial capacity of EHDV was only significantly above 0 for the most recent block, ending in 2022. The first reported case of EHDV in Europe was 2022, and outbreaks have continued to occur [
48,
49].
Brand and Keeling [
13] compared three models of vectorial capacity: deterministic, Markovian, and intermediate. The intermediate model requires knowledge of the distribution of the EIP by setting a shape parameter for the gamma distribution (
k). Here, we simulated the Markovian model (by assuming
in Equation (2)), as
k is not known for all viruses in the study. However, the model developed allows the EIP be modelled using the deterministic or intermediate model from Brand and Keeling [
13]. If these other models are used, it is important to consider that the vectorial capacity predictions will generally be lowest for the deterministic model and largest for the Markovian model, with the intermediate model falling in between. Therefore, direct comparisons can not be made between results for different climates/viruses if a different model is used.
This study focused on adulticide vector-control tools. However, other tools, such as larvicide, have been shown to be effective against
Culicoides [
50]. Previously, the killing of larvae has been integrated into models of vectorial capacity by multiplying the vectorial capacity by the coverage of larvicide; however, larvicide does not affect vectorial capacity. By definition, vectorial capacity is the number of cases which arise from a single day of feeding on an infectious host, therefore vectors must have made it to the adult stage to influence vectorial capacity. Instead, larviciding impacts the number of vectors per host, hence reducing
. If the Brand and Keeling [
13] method is used to calculate
from the vectorial capacity, proportionally reducing vectorial capacity or the number of vectors per host by larvicide coverage would yield the same result.
Usage/adherence is sometimes not considered in vector-control studies; however, this study shows that they can be just as important as coverage for reducing vectorial capacity. This is expected, since if a tool is unused, it will not have an effect. A drawback is that this parameter can be hard to quantify. Usage describes a reduction in efficacy due to behaviours such as not stabling the horse every night or whether the horse is outside the stable for some of the time vectors are host seeking. However, vector feeding behaviours are not consistent between nights or over the duration of a night [
51].
The data used to parameterise the stable netting control strategy was gathered using WHO cone bioassays and light-traps within stables. Light traps have been observed to not effectively estimate protective efficacy for spatial repellents [
52]. Considering this, and the relatively small number of vectors caught in the stable (n = 25), the estimation for the reduction in biting may be inaccurate. WHO cone bioassays have also been shown to induce more mortality compared to when the interventions are evaluated in semi-field or experimental-hut conditions [
53,
54]. In this study, we estimate the reduction in vectorial capacity for treated netting that disarms mosquitoes. However, it is important to note that this disarming behaviour was not directly observed during the trials that were used to parameterise the model. Despite these drawbacks, we were able to provide a framework for evaluating the potential implication of transmission for tools with a range of properties. We found that whilst untreated stable netting could need to have high coverage and usage to substantially reduce the vectorial capacity of AHSV in the UK, insecticide treated netting could potentially decrease vectorial capacity, even at low coverage and usage levels.
Other adulticides have been been shown to be effective against
Culicoides for use on host species of relevance to the viruses in this study [
55]. Robin et al. [
56] found that there was no reduction in the percentage of
Culicoides caught in traps which were blood-fed next to a horse treated with topical deltamethrin, compared to an untreated horse. However, the difference in the total number or number of blood-fed
Culicoides was not reported. Killing the vectors before they feed (preprandial killing) would likely increase the percentage of blood-fed vectors caught, while disarming them would decrease it. In contrast, using repellents might not change this percentage, as the insects are still able to escape after encountering the repellent.
This study highlighted the potential added efficacy of vector control tools against mosquitoes that feed multiple times per gonotrophic cycle, compared to those who just feed once. There is evidence that successive blood meals after an infectious blood meal can increase vector competence and shorten the EIP of vectors [
57,
58,
59,
60,
61]. Therefore, this behaviour could increase the infectiousness of vectors, which was not considered in this study. If feeding on multiple hosts were to occur due to disruption when feeding, the size, and therefore viraemic dose, of the blood meal may be less, which may also reduce the probability the vector becomes infectious [
60].
We have established a novel model for vectorial capacity that considers the influence of both climate and vector control at each stage of the vector feeding cycle. We demonstrated how this model can be used to compare the vectorial capacity of viruses. This model was used to assess the potential for outbreaks by comparing the total vectorial capacity during a host’s infectious period between viruses that were previously unobserved in a region and those that had been observed there before. Extensions to this work could include global sensitivity analysis to explore the influence of tools across a range of vector bionomics or temperatures, using methods similar to [
62] to identify target product profiles.
Our research provides valuable insights into how the strategic use of insecticide-treated netting, even at low coverage levels, can substantially reduce the transmission potential of AHSV. This model offers a powerful tool for policymakers and health professionals, aiding in the formulation of more effective vector management strategies that could mitigate the impact of these diseases, especially in the context of changing global climates.