Re‐parameterization of a mathematical model of African horse sickness virus using data from a systematic literature search

Abstract African horse sickness (AHS) is a vector‐borne disease transmitted by Culicoides spp., endemic to sub‐Saharan Africa. There have been many examples of historic and recent outbreaks in the Middle East, Asia and Europe. However, not much is known about infection dynamics and outbreak potential in these naive populations. In order to better inform a previously published ordinary differential equation model, we performed a systematic literature search to identify studies documenting experimental infection of naive (control) equids in vaccination trials. Data on the time until the onset of viraemia, clinical signs and death after experimental infection of a naive equid and duration of viraemia were extracted. The time to viraemia was 4.6 days and the time to clinical signs was 4.9 days, longer than the previously estimated latent period of 3.7 days. The infectious periods of animals that died/were euthanized or survived were found to be 3.9 and 8.7 days, whereas previous estimations were 4.4 and 6 days, respectively. The case fatality was also found to be higher than previous estimations. The updated parameter values (along with other more recently published estimates from literature) resulted in an increase in the number of host deaths, decrease in the duration of the outbreak and greater prevalence in vectors.

AHS presents as acute, subacute or subclinical forms (Carpenter et al., 2017). In naive populations of horses, case fatality may exceed 90% in epidemics (Castillo-Olivares, 2021). The acute respiratory form is characterized by a short incubation period (3−5 days), and the animal usually dies from severe hypoxia, congestive heart failure or a combination of both after around 1 week. The subacute or cardiac form of AHS has an incubation period of 1−2 weeks with a short fever followed by the classical clinical sign of AHS and oedema of the supraorbital fossae. The case fatality is around 50% with death usually occurring within 1 week. In most outbreaks, a mixed pulmonary and cardiac form is most commonly seen, which causes fatality of around 80% of susceptible equids (Theiler, 1921). The subclinical form, often referred to as African horse sickness fever, is common in zebras, African donkeys and horses that are partially immune because they have been vaccinated or have recovered from a previous infection (Lu et al., 2020).
The outbreaks of AHSV in Spain in 1987 and Thailand in 2020 were associated with importation of (infected) zebras from Africa (Grewar et al., 2021;Rodriguez et al., 1992). In order to model the risk posed by AHSV if it emerges in countries where equids have no prior exposure, we need data on various parameters such as the length of the latent and infectious periods. It is also important to know whether there is any association between the serotype causing an outbreak and the values of these parameters. In the case of AHSV, parameters such as the latent period are not possible to determine in the field as the exact time of infection is generally not known. Here, a systematic search and data extraction, focusing on studies documenting experimental infection of naive equids in vaccination trials, was performed to inform a model for AHSV previously suggested by Backer and Nodelijk (2011). Overall, 26 studies were used to derive parameters describing the host-virus interactions, compared to the three studies used in the development of the Backer and Nodelijk model (J. A. House et al., 1994;Roy et al., 1996;Scanlen et al., 2002).
Parameters derived from the review were the time until the onset of viraemia, clinical signs and death after experimental infection of a naive equid as well as the duration of viraemia. It is important to consider the role of vectors when modelling AHSV. The parameters for the vectors were updated from literature, similarly to Gubbins et al. (2014); some of this literature was published after the Backer and Nodelijk model.
AHSV is listed as a notifiable disease in disease-free countries by the World Organisation for Animal Health (OIE) (2021). An outbreak can have a severe impact on the welfare of equids and be disruptive for the equine industry (Allison et al., 2009;Clemmons et al., 2021). Policy makers with responsibility for deciding the course of action if an outbreak occurs in a previously disease-free country are heavily reliant on models to predict the likely outcome of outbreaks (Daly et al., 2013;Grassly & Fraser, 2008 with more than one data value. We also performed this statistical analysis to determine whether infection method (either intravenous or subcutaneous inoculation) had an impact on these disease characteristics.
A paired and two-sample t-tests were used to determine if there was a difference between the estimated onset of viraemia between polymerase chain reaction (PCR)-based and virus isolation methods in the equids for which both were compared and all equids for which data for the onset of viraemia were analyzed (including both PCR and virus isolation for equines with both available), respectively.

Re-parameterization of a mathematical model
We will consider a deterministic ordinary differential equation (ODE) model for AHSV suggested by Backer and Nodelijk (2011). In the Backer and Nodelijk model, the vector population adapts to changes in the vector:host ratio. Here, we do not include this in the model. This is due to the assumption that the size of the vector population is dependent on the carrying capacity of midges in the environment surrounding the horses rather than the number of horses present. The total number of vectors therefore does not change. We assume the number of hosts present is likely to reflect the size of the premises. Figure 1 shows

Systematic literature search
A total of 39 articles were found during the PubMed search performed on 20 May 2020. Of these, 11 were excluded during a first screening of their titles for being narrative reviews or a non-equid experimental infection. After reading the full texts of the remaining 28 articles, a further 12 were excluded for being narrative reviews, in vitro experiments, non-equid infection experiments, not challenging equids or not using unvaccinated control animals, all of which mean that no naive equids were experimentally infected. The citations and references of the eligible 16 articles found on PubMed were then screened in order to find more relevant articles. A total of 40 additional full-text articles were then read and 13 were found to be eligible under the same inclusion criteria. During the screening, six titles were identified that qualified for a full text read but could not be accessed; these were not included in the qualitative synthesis. The process of the literature search is described by the PRISMA flow diagram in Figure 2  Altogether, 29 studies were found recording the experimental infection of 61 naive equids; 53 horses, five donkeys and three mules (Alberca et al., 2014;Alexander & Du Toit, 1934;Du Plessis et al., 1998;Dubourget et al., 1992;El Hasnaoui et al., 1998;Guthrie et al., 2009;Hassanain, 1992;C. House et al., 1990;J. A. House et al., 1992J. A. House et al., , 1994Lelli et al., 2013;Lulla et al., 2017;Martínez-Torrecuadrada et al., 1996Minke et al., 2012;Mirchamsy & Taslimi, 1964a, 1964b, 1968Ozawa & Bahrami, 1966;Ozawa et al., 1965Ozawa et al., , 1970Quan et al., 2010;Roy et al., 1996;Scanlen et al., 2002;Stone-Marschat et al., 1996;van Rijn et al., 2018;von Teichman et al., 2010;Whitworth, 1930). These included all serotypes apart from AHSV-7 and two studies where the serotype was unidentified ( Figure 3)   For 11 horses, the time until viraemia and death due to AHSV was recorded. The total infectious period (difference between onset of viraemia and death) of these horses varied between 2 and 7 days with a mean of 3.9 days (Figure 4d). For three horses that survived experimental infection, the time between the start and end of viraemia was recorded using virus isolation. The total infectious periods of these horses were 4, 5 and 5 days, giving a mean of 4.7 days.
The lag between the start of viraemia and onset of clinical signs was reported for 18 horses. This varied between −1 (horse showed clinical signs before viraemia) and 3 days, with a mean of 0.8 days (Figure 4e).

Re-parameterization of a mathematical model
The model parameters updated from the review are given in Table 1.
As well as these host parameters, some vector parameters were also    Table 1 and Table S1 updated from the literature. These were the blood feeding interval (frequency of biting) (Mullens et al., 2004), extrinsic incubation period (latent period of midges) (Carpenter et al., 2011), vector life-span (Gerry & Mullens, 2000) and transmission probability from a host to a vector during a bite (Carpenter et al., 2011). Details of these and other unchanged parameters are given in Supporting Information 1.
We fit a gamma distribution to the quantitative data for the time until viraemia and duration of viraemia to calculate the number of stages in the latent and infectious periods, respectively. The number of stages is equal to the gamma parameter. The number of stages for the latent period and infectious period for dying hosts are 5 (95% CI:3-9) and 11 (95% CI:5-26), respectively. Due to there not being many data points for the infectious period of surviving hosts, the number of stages needed was calculated as 93 (95% CI:19-659). This large value and confidence interval is due to the limited number of data points available. Therefore, due to the limited number of samples, the number of stages for the infectious period of surviving hosts is scaled from the infectious period of the dying hosts. As the mean infectious period of surviving hosts is 1.2 times longer than that of dying hosts, the infectious period of surviving hosts is divided into 13 stages (2 more than the number of stages for the dying horses).  Table 1 and

DISCUSSION
In order to better inform the host parameters used in the ODE model developed by Backer and Nodelijk (2011), data were extracted from 26 studies, representing 43 experimentally infected naive equids. Since this analysis, further naive experimental infection studies for AHSV have been published (van Rijn et al., 2020). These data did not conflict with the findings of this study. Overall, the updated model parameters suggest more hosts on the premises would die and the outbreak on each premises would be shorter than previously predicted. More vectors would also become infected, which may increase the probability of transmission between premises.
Many of the studies in this systematic search use different volumes and titres of virus for experimental infection. Experimental infection through needle injection is not a natural route of infection. How well this mimics natural infection by midges is not known (Coetzee et al., 2014;Darpel et al., 2012). It is therefore unclear whether this route of infection or the titre/volume of virus inoculated affects the time taken to become viraemic or show clinical signs. Bluetongue virus experimental infections have shown that infection via the intradermal route in sheep reduced the time until clinical signs and increased their severity compared to the intravenous route (Umeshappa et al., 2011). It was also found that subcutaneous inoculation appears to mimic the natural route of infection more closely than the intravenous inoculation route, in respect to the dissemination of the virus from the skin to secondary target organs as has been observed following natural infection (Coetzee et al., 2014;Umeshappa et al., 2011). In this review, we found no difference in the time until viraemia, clinical signs or death between intravenous and subcutaneous routes of infection.
Variation in VP2 is a mechanism for escape from pre-existing neutralizing antibodies that block viral attachment to the host cell (Burrage et al., 1993;Jewell & Mecham, 1994). These variations may impact the infectivity of the virus for the cells of hosts or vectors, but viral pathogenicity is typically determined by more than one viral protein and is therefore not necessarily serotype dependent. For example, van Rijn et al. (2018) reported that introducing a deletion in the NS3/NS3a protein of AHSV renders the virus avirulent. Lulla et al. (2016) reported that an AHSV-1 isolate was more virulent than an AHSV-4 isolate in mice, but whether this difference was determined by VP2 or indeed consistent between different isolates of the respective serotypes was not addressed by that study. No differences in time until viraemia, clinical signs or death were found between serotypes in this study. Studies of bluetongue virus (BTV) (the type species of the Reoviridae family) indicate that more recently identified serotypes  show adaptations involving VP2 (as well as VP1, VP3 and VP7) that support direct-contact transmission, rather than by vector insects. These changes also influence the virulence of these serotypes for different ruminant hosts (Guimerà Busquets et al., 2021;Pullinger et al., 2016), but there is no evidence for similar variations in AHSV.
Articles analyzed to parameterize this model dated back as far as 1930, that is, before PCR-based techniques were available. In one study, the reverse transcription-PCR (RT-PCR) assay and virus isolation methods were found to be equally sensitive for detection of virus in blood samples from horses experimentally infected with AHSV-4.
However, viraemia was detected more consistently by RT-PCR than by virus isolation from horses infected with AHSV-9 except from one animal for which virus was detected only by virus isolation (Sailleau et al., 1997). Other studies have shown that RT-quantitative PCR has higher sensitivity than virus isolation (Guthrie et al., 2013;Quan et al., 2010). Three articles, with a total of six experimental infections of naive equids from which data were extracted in this study, compared the detection of viraemia by PCR and virus isolation methods. Of these, two studies (involving a total of four equids) (Alberca et al., 2014;Guthrie et al., 2009) did not find a difference in the first day of detection of viraemia, whereas one found that viraemia was detected one day earlier by PCR than by virus isolation in both animals involved (Lelli et al., 2013). Further analysis showed no significant differences between virus detection methods and estimated onset of viraema.
However, caution is needed when interpreting RT-PCR results in relation to the duration of viraemia. For example, in BTV infection, nucleic acid can be detected in blood of hosts after infectious virus has been cleared (MacLachlan, 1994;MacLachlan et al., 1994;Mayo et al., 2021).
Consequently, a long duration of viraemia detected by PCR is not a reliable guide to infectivity, or the ability of the host to act as a source of virus to infect feeding insects.  (2000), based on trap data, also has its limitations. A recent study found that biting rate per day (per cow) was expected to be approximately 50% of a 24-h trap collection (Möhlmann et al., 2021). Another study found that on average 2.2 times more Culicoides were found on a cow than on a Shetland pony (Elbers & Meiswinkel, 2015 Robin et al., 2015). Vaccination to prevent the horse from becoming infected reduces (to 0 in a perfect vaccine) the transmission probability from vector to host (p V ). The transmission probability from hosts to vectors (p H ) would also likely be reduced if a partially immune animal became infected due to lower levels of viraemia (Scanlen et al., 2002).
Euthanasia of infected horses for ethical reasons affects our ability to assess the case fatality. However, as mentioned previously, during an outbreak it is likely that equids with severe clinical signs that are unlikely to survive would be euthanized. Therefore, including these euthanized hosts when considering those that do not survive would not be unrealistic in the model. The longer infectious period of surviving hosts may also be informative for policy makers when deciding if culling should be used as a control strategy. The rapid onset of death in AHSV-infected naive horses is itself thought to limit virus spread. The persistence (long term) of AHSV in the field is thought to be heavily dependent on the availability and distribution of alternative, possibly asymptomatic hosts, such as zebras or potentially donkeys or mules.
Therefore, it is important to consider secondary hosts and their ability to aid spread of AHSV between premises, even if they are not specifically included in the model. preventing Culicoides blood-feeding on horses may be key in AHSV control.