Modelling The Influence Of Naturally Acquired Immunity From Subclinical Infection On Outbreak Dynamics And Persistence Of Rabies in Domestic Dogs Part 2

Incorporation of spatial structure and incidence-dependent human response

The non-spatial model was extended to a spatial patch model including the human-mediated movement of dogs and incidence-dependent human response to explore the three immunity scenarios (Fig 3). Results from spatial model formulations excluding human-mediated movement and incidence-dependent human response are presented in S2 and S3 Figs.

Incorporating these additional assumptions increased relative to the non-spatial model the probability of the persistence of rabies in the absence of immunity, with the disease persisting in 82.9% of simulations for scenario A. The persistence probability associated with scenario B, with low levels of naturally acquired immunity, was marginally lower, at 81.9%. In the high immunity scenario, C, rabies did not persist in any simulation at this R0 value. Scenario C assumed a high transmission rate and for every exposure leading to clinical infection (ϕ = 0.05), 9.5x more become immune ((1-ϕ)ρ where ρ = 0.5). As a result, the rapid depletion of the susceptible population within patches reduced the probability of persistence.

People with weakened immune systems are more prone to plaque formation. For example, older people with a weakened immune system, long-term smokers, excessive alcohol drinkers, or people with certain medical conditions (such as diabetes, high blood pressure, obesity, etc.) will have a higher rate of plaque formation. At the same time, some studies have also shown that long-term low-grade lentiviral infections (such as cytomegalovirus, herpes simplex virus, etc.) in the body may also cause damage to the immune system and increase the risk of vascular plaques. Therefore, immunity is very important in daily life. Cistanche can enhance immunity. Meat ash contains a variety of biologically active ingredients, such as polysaccharides, two mushrooms, and Huangli, etc. These ingredients can stimulate the immune system. Various types of cells, increase their immune activity.

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For both scenarios A and B, the median incidence were higher than the range considered plausible, however, the incidence was lower in the low immunity scenario (B) relative to the no immunity scenario (A), with a median of 5,566/100,000 (Scenario A, IQR: 2,583/100,000) relative to 7,810/100,000 (Scenario B, IQR: 3,485/100,000; Fig 3). Median population decline for scenario B was within the plausible range, at 15% (IQR: 3%), whereas without immunity (Scenario A) decline was greater at 22% (IQR: 5%). In the low immunity scenario (B), seroprevalence at a population-wide level was predicted to be low, with a median of 0.97% (IQR:0.42%). Incorporating low levels of naturally acquired immunity, therefore, lowered the predicted incidence and mitigated the population decline, despite a low population-wide predicted seroprevalence.

The duration of naturally acquired immunity for rabies has not been established, and primary analyses assumed an average duration of 1 year, based on the persistence of detectable antibodies following vaccination from field studies [36–38]. However, increasing this duration to three years (δ = 1/1095) did not substantially change the model outputs (Fig 4). For scenario B, increasing the duration of immunity increased median seroprevalence only slightly, from 0.97% (IQR:0.42%) to 1.5% (IQR:0.7%). Due to the rapid turnover in domestic dog populations, with the average lifespan assumed to be 2.2 years (μ-1), seropositive dogs are likely to die before immunity wanes, therefore limiting the influence of longer persistence of naturally acquired immunity.

Assuming higher R0 values of 1.5 and 2 led to substantial changes in the model outputs (Fig 4). Increasing R0 led to a higher persistence probability for the high immunity scenario, C, with rabies persisting in 13.8% of simulations for an R0 of 1.5 and 89.3% for an R0 of 2, relative to 0.0% for an R0 of 1.2. In simulations for scenario C where rabies did persist, the median incidence for an R0 of 1.5 was 1141/100,000 (IQR: 631/100,000) and population decline was 6.5% (IQR: 0.8%), consistent with the ranges considered plausible (Fig 4). For an R0 of 2, the incidence was higher at 3904/100,000 (IQR: 1313/100,000), however, the population decline remained within the plausible range at 8.9% (IQR: 1.7%). The median predicted seroprevalence for this scenario C simulations was 6.8% (IQR: 3.8%) for an R0 of 1.5, and 26.1% (IQR: 8.1%) for an R0 of 2. For scenarios A and B, increasing R0 to 1.5 led to higher incidence and greater population decline, further increasing these outputs above the levels considered plausible (Fig 4). Further increasing R0 to 2 led to rabies not persisting under the no immunity scenario (A) in any simulations, and only persisting in 20.5% of simulations under the low immunity scenario (B).

Spatial variation in predicted seroprevalence

At a population level, predicted seroprevalences for an R0 of 1.2 were low. However, substantial spatial variation in seroprevalence between patches occurred, as shown in Fig 5. A simulating sampling of 30 individuals from a single randomly selected patch for each of the simulations for scenario B gave a median predicted sample seroprevalence of 0. However, for the 11.1% of simulations in which seropositive were detected in the sample, the median predicted seroprevalence was 3.3%, with a maximum of 13.3%, relative to the population level seroprevalence of 0.97% (IQR:0.42%). Therefore, depending on the distribution of sampling, sample seroprevalences may vary substantially from the population-level seroprevalence.

Discussion

Immunity in models of canine rabies is typically only considered about vaccination. However, rabies-specific antibodies in unvaccinated individuals have been detected in several studies of domestic dog populations. While there is still debate over the importance of these antibodies [16], the high seroprevalences detected in some studies warrant consideration of their potential implications. In this study, a model of domestic dog rabies was developed to explore the influence of subclinical infection and immunity for rabies dynamics.

Exploration of the non-spatial model showed that, in the absence of other factors limiting the incidence of rabies, naturally acquired immunity could play a role in stabilizing rabies outbreaks. Without spatial structure and assuming rabies transmission was frequency dependent, with an R0 value of 1.2, the introduction of rabies was predicted to lead to the depletion of the domestic dog population in the absence of immunity. In previous non-spatial models of rabies, population depletion has been prevented by assumptions of density-dependent transmission, or low R0 values with high population growth [6,18,30]. Studies of the transmission dynamics of rabies have suggested these assumptions are potentially unrealistic, with evidence for higher R0 values and frequency-dependent transmission [9,18,27,34,35]. Our model suggests that naturally acquired immunity can facilitate outbreak persistence under these assumptions by reducing the incidence and preventing depletion of the susceptible population, as immune hosts produce susceptible offspring which can then become infected. However, having high rates of immunizing subclinical exposure could also push incidence to low levels, leading to an increased probability of stochastic fade out of the outbreak. The non-spatial model, therefore, predicted that endemic infection was most likely at intermediate levels of acquired immunity.

While the non-spatial model allowed exploration of the implications of acquired immunity with limited assumptions, it fails to capture key aspects of rabies dynamics. Previous studies have indicated the importance of spatial structure, human-mediated dog movement, and human response to increased rabies incidence as important factors in rabies dynamics [4,18,28,51,52]. Results from the spatial model incorporating these factors showed that the persistence of rabies could occur in the absence of immunity, as spatial structure and human intervention act to limit the incidence and prevent population extinction. 

However, model predictions for annual incidence and population decline remained higher in the absence of immunity than empirical estimates. Including finer-scaled spatial structure and higher levels of human intervention could produce realistic estimates in the absence of immunity. For example, Beyer (2010) considered spatial structure on the scale of a single village of 288 dogs [28], considerably lower relative to the total carrying capacity of 63,434 dogs in this model. This fine-scale structure led to realistic outputs without the inclusion of immunity. Furthermore, assuming a stronger response to high rabies incidence through human intervention also led to a lower incidence in the absence of immunity (S2 Fig). Estimating the strength of this response is highly challenging. Hampson et al. (2009) found that in Tanzania, the killing of infectious dogs reduced the infectious period by around 16%. 

However, how this response scales with incidence and varies temporally and spatially is unclear. Including this relationship prevents unrealistically high incidences, however as the strength of this effect has not been reliably estimated, its influence relative to other factors, such as spatial structure and immunity, is difficult to establish. While including finer-scaled spatial structure or stronger human intervention could reduce the incidence to levels within the range considered plausible, these factors do not account for the seroprevalences reported in empirical studies [16]. Including immunity for an R0 of 1.2 led to lower incidences, despite low predicted seroprevalence relative to observed levels. Potentially, naturally acquired immunity, in combination with spatial structure and human intervention, may therefore act to dampen rabies outbreaks, leading to low-level endemic infection.

For an R0 value of 1.2, none of the scenarios considered produced the levels of incidence, population decline, and seroprevalence considered realistic. In the high immunity scenarios, rabies persistence was not predicted to occur due to the depletion of the susceptible population. For an R0 of 1.2, herd immunity within a patch is effectively reached once more than 16.7% (1- 1/R0 = 0.167). of the population is immune. Local susceptible depletion due to immunizing exposure can therefore lead to substantial reductions in transmission, despite low population-level seroprevalences. However, assuming higher R0 values of 1.5 and 2 led to the persistence of rabies in 13.8% and 89.3% of simulations respectively under the high immunity scenario, as the threshold to reach herd immunity is higher. For an R0 of 1.5, the estimates of incidence and population decline under this scenario were also consistent with empirical estimates. Assuming higher transmission rates also led to higher median predicted population-level seroprevalences at 6.8% and 24.7% for R0 values of 1.5 and 2 respectively. These estimates are closer to levels observed in empirical studies, for example, Cleaveland et al. (1999) reported a seroprevalence of 7.4% in Tanzania and Bahloul et al. (2005) of 28.8% in Tunisia. The higher R0 values remain within the range of one to two typically reported for canine rabies [9]. 

However, under the high immunity scenario, much higher rates of exposure, and lower probabilities of developing a clinical infection, were assumed than are typically considered for canine rabies. For example, for an R0 of 2 under the high immunity scenario, a rate of 12.9 exposures per infectious dog per day was assumed, with only 5% of these exposures leading to clinical infection. This parameterization for the high immunity scenario is comparable to what has been assumed for lyssavirus dynamics in bats, in which the probability of developing immunity is considered to be much higher [29,53]. However, Hampson et al. (2009) estimated that on average, a rabid dog bites 2.15 others during its infectious period, of which 49% develop a clinical infection, suggesting an exposure rate of 12.9 per day is unrealistically high if bites are considered the sole source of exposure. If the high empirical seroprevalences detected in some populations are due to higher rates of exposure, it may suggest that routes of transmission other than bite exposure are leading to the development of an antibody response, such as through oral exposure during social contact or feeding on infected carcasses [12,13,54].

While high seroprevalences detected in empirical studies could reflect higher transmission rates, other factors may also be responsible. Substantial variation between serology tests has been shown, with evidence that neutralization tests such as the rapid fluorescent focus inhibition test (RFFIT) may be less specific for detecting non-lethal exposures relative to ELISAs [21]. For example, the high seroprevalence of 28% detected in Laikipia, using the RFFIT and a low cut-off, may be partially explained by false positives [22]. However, even studies using ELISAs with higher cut-offs have found high seroprevalences [23,24]. For example, Cleaveland et al. (1999) found a seroprevalence of 7.4% in a domestic dog population in Tanzania using an ELISA, and no false positives were detected on a rabies-free island using this test, suggesting high specificity. A further possibility is that cross-reactivity is occurring with other circulating lyssaviruses, although in the absence of further serological and surveillance data, this cannot be confirmed [16]. 

A further factor that may contribute to the discrepancy between observed seroprevalences and predicted population-level seroprevalence is spatial variation. As shown in Fig 5, predicted seroprevalences were not consistent across the landscape, therefore the population-wide predicted seroprevalence is expected to differ from sample seroprevalences. For example, localized sampling in areas where there has been a recent outbreak could lead to higher detected empirical seroprevalences. However, under the low-immunity scenario, the highest simulated sample seroprevalence was 13.3%, remaining lower than reported in some empirical studies [16]. Furthermore, empirical studies have in most cases used larger sample sizes, and in a range of locations, which should lead to a closer approximation of the population-level seroprevalence [e.g. 21,22].

A further challenge to the interpretation of rabies serology is that it is currently unknown whether antibodies from natural exposure confer protection against re-exposure [16]. There is limited evidence that previously unvaccinated seropositive individuals show an anamnestic response to vaccination consistent with immunity [15,23,38,55]. However, even in vaccinated individuals, serology status is not definitive proof of an effective immune response, and individuals with a detectable titer may still succumb to the disease [56]. If antibodies from nonlethal exposure provide no, or only partial protection, this would influence the expected dynamics. For example, partial immunity could potentially allow higher seroprevalences to occur within populations without the same reduction in transmission, potentially increasing the probability of persistence at higher seroprevalence levels.

The results of this study should be considered in the context of rabies surveillance and control. In this study we assumed all dogs were unvaccinated, to allow consideration of the influence of naturally acquired immunity on persistence in the absence of control. In Laikipia, mass vaccination has only been conducted since 2015 and before this point by far, the majority of dogs would have been unvaccinated [57]. However, low levels of vaccination coverage may act similarly to naturally acquired immunity, dampening the incidence of rabies and potentially promoting persistence. Kitala et al. (2002) modeled coverage of 24% in the Machakos district, Kenya, and found that this low level of coverage increased the stability of transmission and led to endemic establishment.

While not within the scope of this paper, future work to include both vaccination and non-lethal exposure could lead to further insights into the influence of naturally acquired immunity in domestic dog populations in the context of control strategies. Vaccination may reduce the predicted influence of naturally acquired immunity on dynamics, as the resulting reduction in transmission will reduce exposure and therefore the expected seroprevalence. As a result of this, and the uncertainty over the implications of unvaccinated seropositive, high seroprevalence within a population should not be taken as evidence that lower vaccination coverage is required to reach herd immunity and eradicate rabies. Findings from this study also bring into question the use of serology for rabies surveillance. While serology could provide a mechanism to conduct rabies surveillance that does not rely on reporting clinical cases, the challenges of interpreting rabies serology, in addition to the cost of implementation, limit the feasibility of this strategy. However, given the number of studies reporting high rabies seroprevalence, across a wide geographical range [16], the potential for high rates of transmission leading to sub-clinical exposure should be considered, in particular as higher R0 values may indicate the need for higher vaccination coverage for effective control.

There were several limitations to the modeling methods used. In the model, Laikipia was treated as an isolated unit. In reality, the county is continuous with other areas with domestic dog populations. Potentially, the persistence of rabies occurs at a wider scale with introductions of rabies from other populations sustaining the disease within Laikipia, as shown in domestic dog populations in N’Djamena, Chad, and Bangui, Central African Republic [43,45]. Further data are required to improve the parameterization of human-mediated dog movement and to assess the influence of both importations from outside the county and the movement of dogs within the county [4]. In the model, it was also assumed that contact between infectious individuals in different patches was determined by distance. 

In reality, physical features and human geography will be influential for contact, for example depending on the presence of roads linking properties, or physical barriers such as fencing or rivers separating them [27]. A further limitation was the failure to capture heterogeneity in certain parameters. Rabies transmission is highly heterogeneous with most individuals not transmitting at all, whereas others infect large numbers of other individuals [9]. A negative binomial distribution has been suggested to be the best fit to model these dynamics [18], however, the use of the Gillespie algorithm to model stochasticity precluded fitting specific distributions. Variation in the duration of the latent period has also been shown to influence rabies persistence [4]. Including this heterogeneity may have increased the probability of the persistence of rabies.

In conclusion, our results suggest that subclinical immunizing exposure could play a role in the dynamics of rabies in domestic dogs, limiting disease incidence and population decline. However, consideration of other factors, such as spatial structure and human response to rabid dogs, is also required to approximate realistic rabies dynamics. The scenarios for naturally acquired immunity explored for an R0 of 1.2 produced low predicted seroprevalences relative to those observed in some empirical studies. Higher seroprevalences could be explained by higher rates of immunizing subclinical infection within domestic dog populations, however false positives or spatial variation in seroprevalence may also contribute. If high seroprevalences do indicate high transmission rates, this supports the need for high vaccination coverage to effectively control this disease.

Supporting information

S1 Text. Additional details on model parameterization. (PDF) 

S2 Text. Methods and results for sensitivity analysis of the non-spatial model. (PDF) S1 Table. Model results for the non-spatial models across all 25 parameter combinations are presented as heat maps in Fig 2. (PDF) 

S1 Fig. Influence of incidence-dependent human response on model outputs in the absence of naturally acquired immunity (Scenario A). (PDF) 

S2 Fig. Comparison of model outputs from immunity scenarios (A, B, and C) across different model formulations for R0 = 1.2. (PDF) 

S3 Fig. Comparison of model outputs from immunity scenarios (A, B, and C) across different model formulations for R0 = 1.5. (PDF) 

S1 Code. This file contains An r script to generate the events data frame for human-mediated dog movement, an R script to run model simulations for both the non-spatial and spatial models, and a CSV. The file containing the contact matrix for the spatial model and the shapefile of patches used. (ZIP)

Acknowledgments

We thank Dr. Stefan Widgren for his advice on using the SimInf package for this work.

Author Contributions

Conceptualization: Susannah Gold, Christl A. Donnelly, Rosie Woodroffe, Pierre Nouvellet. 

Formal analysis: Susannah Gold. 

Investigation: Susannah Gold.

Methodology: Susannah Gold, Pierre Nouvellet. 

Supervision: Christl A. Donnelly, Rosie Woodroffe, Pierre Nouvellet. 

Visualization: Susannah Gold. Writing – original draft: Susannah Gold. 

Writing – review & editing: Susannah Gold, Christl A. Donnelly, Rosie Woodroffe, Pierre Nouvellet.

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