Modelling The Influence Of Naturally Acquired Immunity From Subclinical Infection On Outbreak Dynamics And Persistence Of Rabies in Domestic Dogs Part1
Apr 20, 2023
Abstract
Several mathematical models have been developed for canine rabies to explore dynamics and inform control strategies. A common assumption of these models is that naturally acquired immunity plays no role in rabies dynamics. However, empirical studies have detected rabies-specific antibodies in healthy, unvaccinated domestic dogs, potentially due to immunizing, non-lethal exposure. We developed a stochastic model for canine rabies, parameterized for Laikipia County, Kenya, to explore the implications of different scenarios for naturally acquired immunity to rabies in domestic dogs. Simulating these scenarios using a non-spatial model indicated that low levels of immunity can act to limit rabies incidence and prevent depletion of the domestic dog population, increasing the probability of disease persistence.
However, incorporating spatial structure and human response to high rabies incidence allowed the virus to persist in the absence of immunity. While low levels of immunity, therefore, had limited influence under a more realistic approximation of rabies dynamics, high rates of exposure leading to immunizing non-lethal exposure were required to produce population-level seroprevalences comparable with those reported in empirical studies. False positives and/or spatial variation may contribute to high empirical seroprevalences. However, if high seroprevalences are related to high exposure rates, these findings support the need for high vaccination coverage to effectively control this disease.
High vaccination can improve the body's immunity. Vaccination is to induce the human immune system to generate an immune response against these pathogens by injecting vaccines containing pathogen antigens or parts of pathogens replicated by viruses. This immune response against pathogens protects the body from specific diseases and boosts the body's immunity. Human immunity is also very important in daily life. It is found in the records that Cistanche can be used as a dietary supplement for our daily immunity. The polysaccharides in Cistanche can regulate the immune response of the human immune system and improve immune cells' Stress ability, enhancing the bactericidal effect of immune cells.
Author Summary
Rabies-specific antibodies in unvaccinated domestic dogs have been reported in several studies, in some cases in a substantial proportion of the population. These antibodies may be the result of non-lethal rabies exposure leading to naturally acquired immunity, which could influence rabies transmission and persistence.
In this study, a model was developed to consider a range of scenarios for naturally acquired immunity in a domestic dog population. Model outputs for rabies incidence and seroprevalence, the proportion of the population with rabies antibodies, were compared to estimates from empirical studies. Our results indicate that naturally acquired immunity could contribute to rabies persistence by limiting disease incidence and preventing population extinction.
However, taking into account spatial structure and human response to high rabies incidence showed that rabies could persist without naturally acquired immunity, although immunity may contribute to the low incidence observed for endemic rabies. Assuming higher rates of subclinical exposure led to seroprevalences comparable to the estimates from empirical studies. However, uncertainty remains over the interpretation of rabies antibodies in unvaccinated individuals, and false positives may contribute to the high seroprevalences reported.
Introduction
Rabies is a zoonotic disease, caused by a neurotropic virus in the lyssavirus family. Despite eradication having been achieved in some parts of the world, the disease still presents a significant public health burden, particularly in rural Africa and Asia [1]. All mammalian species are susceptible to rabies, however, only a limited number, primarily bats and carnivores, can maintain the virus within their populations [2]. In Africa, domestic dogs are the primary host of rabies and cause the majority of human cases, therefore controlling the disease in this species is key to preventing human rabies deaths [3].
Several models have been constructed for rabies dynamics in domestic dog populations [4,5]. One assumption commonly used in these models is that immunity only occurs through vaccination, and not as a result of non-lethal exposure (for example [4–7], but see [8]).
While rabies is usually fatal following the appearance of symptoms, Hampson et al. (2009) estimated that 51% of bite exposures in domestic dogs did not lead to clinical infection [9]. Of these exposure incidents, it is unclear whether the virus always fails to establish, and the host remains susceptible, or whether in some cases the virus is cleared by the host’s immune system, with subsequent development of protective immunity. While recovery from clinical rabies is rare, experimental studies have shown that non-lethal rabies exposure can occur, with exposed individuals showing no, or only minor, symptoms [10,11]. Under field conditions, there has been little consideration of seroconversion, the development of a specific antibody response, following rabies exposure.
However, Cleaveland and Dye (1995) reported that of 17 dogs bitten by two suspected rabid individuals, 12 survived exposure of which four were then seroconverted. As well as subclinical bite exposure, there is also limited evidence that oral exposure, for example from feeding on infected carcasses, can lead to the development of rabies-specific antibodies in carnivores [12,13]. The potential for oral exposure to lead to the development of rabies immunity is also supported by the success of vaccination campaigns using oral vaccines [14,15].
Rabies-specific antibodies have been detected in healthy, unvaccinated individuals across several domestic dog populations in rabies-endemic areas, with a wide range of seroprevalences (the percentage of the population with detectable rabies-specific antibodies) reported [16]. There are several challenges to interpreting serology, including that different studies have used different tests and cut-offs to define seropositive [16,17].
However, given that clinical rabies typically occurs at low prevalence, affecting approximately 1% of dogs annually within populations where rabies is endemic [6,18–20], the high seroprevalences detected in some studies (e.g. 7.4% [21]; 28.0% [22]; 28.8% [23]; 30% [24]) could suggest high rates of non-lethal exposure relative to the rate of exposure leading to clinical infection. While in some cases animals with no history of rabies exposure may test positive due to non-specific neutralization or cross-reactivity, these high estimates of seroprevalence raise the possibility that naturally acquired immunity could play a more significant role in rabies dynamics than previously considered [16].
As a result of the low incidence of rabies in domestic dog populations, rabies seldom leads to substantial depletion of the population [19,25,26]. However, there is evidence that rabies transmission is frequency dependent, with transmission rates remaining relatively constant across a wide range of domestic dog densities [18,27]. Modeling suggests that this form of transmission should lead to high-prevalence outbreaks and substantial population losses [18]. Mechanisms that could limit rabies incidence under real-life conditions include spatial structure (which could lead to local depletion of the susceptible pool without widespread transmission), and human intervention, such as killing and isolation of infectious dogs, following increased incidence [5,9,18,28].
Naturally acquired immunity could potentially also contribute to the low-level persistence of rabies by protecting a proportion of the population, which can then produce new susceptible hosts. Naturally acquired immunity has been considered as a mechanism for the persistence of rabies in vampire bats [29] but is usually not considered in domestic dog models [e.g. 5,7,30].
In this study, we explore the implications of naturally acquired immunity to the rabies virus, resulting from subclinical exposure, for the dynamics of rabies in domestic dogs using a stochastic model parameterized for Laikipia County, Kenya. Rabies is endemic in Laikipia and a seroprevalence of 28% was previously reported in the domestic dog population [22]. A nonspatial model is initially used to explore a wide range of parameter values for naturally acquired immunity in domestic dogs. This model is then extended into a spatial model to consider a subset of potential immunity scenarios. While the spatial model relies on a greater number of assumptions, it allows for consideration of the implications of immunity under a more realistic approximation of rabies dynamics.
Methods
A stochastic model of rabies was developed and parameterized for the domestic dog population in Laikipia County, Kenya. A compartmental structure was used with dogs divided into susceptible (S) individuals who can contract the virus, exposed (E) individuals who are incubating the virus, infectious (I) individuals who can transmit the virus, and individuals with naturally acquired immunity (R) which are immune to re-infection and are assumed to have detectable rabies antibodies. A total population size of 63,434 dogs was simulated and it was assumed that all individuals in the population were unvaccinated. Methods for estimating domestic dog numbers and simulating dog demography are presented in the S1 Text.
Transmission dynamics
For rabies, the majority of transmission is through bite exposure [31]. However, other routes of transmission, such as through oral exposure, may be relevant when considering subclinical infection [13,32,33]. Exposure was therefore defined as any interaction between individuals that could result in a viral transfer. The exposure rate was assumed to be frequency dependent, based on several studies which have indicated that R0 (the basic reproduction number: the average number of secondary cases produced by one case in a completely susceptible population) for rabies is relatively consistent for domestic dogs populations across a range of population densities [27,34,35].
Initial model exploration was conducted using an R0 value of 1.2, which is in the range of one to two typically reported for domestic dog rabies [9,35]. The influence of higher R0 values within this range was also considered using the spatial model. The following equation for R0 was rearranged to calculate the infectious exposure rate (β), the number of individuals exposed per day by an infectious individual:
The product of the exposure rate (β) and the probability of developing a clinical infection following exposure (ϕ) captures the rate of transmission. The basic reproduction number, R0, is found by multiplying this quantity by the average duration of the infectious period (1/ν).
Modeling naturally acquired immunity
Following the exposure of a susceptible individual, we assumed there were three possibilities. Depending on the probability of developing clinical infection (ϕ), a proportion of individuals enter the exposed compartment, from which they progress to becoming clinically infectious at a rate σ per day. Once infectious, the dogs succumb to rabies after 3.1 days (ν-1) on average [9]. The remaining proportion (1-ϕ) are subclinically exposed and either became immune through developing an antibody response (ρ), and enter the R compartment, or remain susceptible (1- ρ). This model structure makes the assumptions that dogs cannot develop symptomatic rabies and then recover and that individuals which are subclinically exposed do not transmit the disease.
In this model, it was assumed that any individuals in the immune (R) compartment had detectable rabies antibodies which confer protective immunity. Therefore, the proportion of individuals in the R compartment was considered to be equal to the predicted seroprevalence. We assumed the dynamics of antibodies developed through natural exposure would be comparable to those from vaccine-derived immunity.
Based on the rate at which antibody titers become undetectable under field conditions following vaccination, for initial model exploration it was assumed individuals would remain in the R compartment for one year on average (δ-1) [36–38]. However, challenge experiments have shown that rabies immunity can persist for longer durations, and dogs may remain protected even where antibody tires have waned below detectable levels [39–41], therefore the influence of a long persistence time of three years was also explored using the spatial model.
The following equations describe the full non-spatial model:
Parameter values are described in Table 1.
Incorporating spatial structure and human intervention
While the non-spatial model allows exploration of rabies dynamics while minimizing the number of assumptions made, it fails to capture key aspects of rabies dynamics. Previous studies developing rabies epidemiological models have shown the importance of rabies dynamics of spatial structure, human-mediated movement of dogs, and human intervention in the case of high rabies incidence [18,43–45]. To consider the implications of naturally acquired immunity under a more realistic scenario, the non-spatial model was extended to incorporate spatial heterogeneity and human intervention.
A patch structure has been used as a form of metapopulation model in which sub-populations represent adjacent parcels of land. In total 154 patches were included, representing a range of land uses, such as individual ranches, villages, and communities that have distinct human communities and are therefore expected to have discrete domestic dog populations (Fig 1).
Infectious dogs were assumed to remain within their patch but could transmit to susceptible individuals in other patches. The force of infection within patch I was therefore assumed to depend on the number of infectious individuals, multiplied by the probability of contact with the patches those infectious individuals were in. Details for calculating contact probabilities are provided in the S1 Text.
While infectious dogs were assumed to remain in their patch, movement of susceptible (S), exposed (E), and immune (R) dogs between patches by the human-mediated movement was simulated using a gravity model (See S1 Text for details). Human intervention in response to high rabies incidence through interventions such as tying up or killing rabid dogs has been suggested to be an important factor in limiting rabies incidence [9,18]. This response was incorporated into the model through an incidence-dependent increase in the mortality rate of infectious dogs, assumed to act at a local level within patches.
Within each patch, it was assumed that if more than 1% of the carrying capacity of the patch died from rabies in the previous month, increased human intervention caused an increase in the death rate of infectious individuals. Further detail on the parameterization of this response is provided in the S1 Text, and results are presented from simulations across a range of levels of intervention to show the influence on model outputs in S1 Fig.
Immunity scenarios
The parameters of key interest for the model are the proportion of exposures leading to clinical infection (ϕ) and, of subclinical exposures (1-ϕ), the proportion which develops immunity (ρ). Of bite exposures, Hampson et al. (2009) estimated that 0.49 led to clinical infection. However, other routes of exposure, such as feeding on infected carcasses, or saliva transfer during social contact, may be less likely to lead to clinical infection relative to bite exposure [31,33]. Compared to considering only bite exposures, incorporating other forms of exposure could therefore lead to a higher exposure rate (β) but a lower probability of developing clinical infection (ϕ).
Using the non-spatial model, to explore the implications of different probabilities of nonlethal rabies exposure, we varied ϕ at five levels between 0.05 (very few exposures lead to clinical infection) and 0.95 (almost all exposures lead to clinical infection) but fixed R0 at 1.2. As a result, when ϕ was higher, the exposure rate (β) was lowered according to the relationship R0 = β ϕ/ν, to produce the same number of secondary clinical infections. This relationship gave a range for β from 0.37–7.06 exposures per infectious individual per day for an R0 of 1.2. For each level of ϕ, we ran the model across five levels of ρ, the probability of developing immunity, from 0 (no subclinical exposures lead to immunity) to 1 (all subclinical exposures lead to immunity) to give 25 parameter combinations in total. In addition, a sensitivity analysis of the non-spatial model is presented in the S2 Text.
Following the exploration of the full range of parameter values, three-parameter combinations were considered in detail, representing three potential scenarios (Table 1). The first scenario (A) assumed no development of naturally acquired immunity. In this scenario, it was assumed transmission only occurred through bite exposures and 50% of bites led to clinical infection (Based on an estimate of 0.49 from Hampson et al. (2009), ϕ = 0.5) with those individuals not developing clinical infection remaining susceptible (ρ = 0). The second scenario (B) assumed immunity could be acquired following non-lethal bite exposure.
The probability of clinical infection was equal to the first scenario (ϕ = 0.5) but of bite exposures that did not lead to clinical infection, it was assumed that 25% developed immunity (ρ = 0.25). The third scenario (C) represents the least conservative scenario for naturally acquired immunity. It was assumed that, in addition, to biting exposure, other forms of exposure also occurred, such as oral exposure through social contact, which increased the exposure rate, but a lower proportion of exposures developed a clinical infection (ϕ = 0.05 and β = 7.7). Of subclinical exposures, we assumed 50% developed immunity (ρ = 0.5).
Running model and outputs extracted
The model was implemented using the SimInf package in R [48]. Infection dynamics were implemented as continuous-time Markov chains using the Gillespie stochastic algorithm. The model was run with a daily time step with outputs extracted at weekly intervals. For each simulation of the spatial model, the model was initiated with a prevalence of 0.5% (24 dogs) in the patch with the largest population size. In the non-spatial model, 24 individuals were also introduced. For each parameter combination, 1000 simulations were run for 30 years.
The probability of rabies persistence was measured as the percentage of simulations in which infectious individuals remained present in the population at 30 years post-introduction. For simulations in which rabies remained present, the annual incidence per 100,000 dogs for the final year, and the immune proportion in the final time step across the population were extracted. In addition, to consider spatial variation in predicted seroprevalence between patches in the spatial model, serology sampling within patches was simulated. For each simulation, a patch was randomly selected, and a sampling of 30 individuals was simulated. The proportion of these individuals in the R compartment was taken as the within-patch predicted seroprevalence.
Empirical estimates for rabies incidence, population decline, and seroprevalence
To consider the plausibility of different parameter combinations for non-lethal exposure and naturally acquired immunity, we compared model outputs for rabies incidence, population decline, and predicted seroprevalence to empirical estimates extracted from the literature. For Laikipia County, there is currently no estimate of annual rabies incidence in the domestic dog population. Therefore, in the absence of location-specific data, we extracted plausible ranges from other free-ranging domestic dog populations (see Table 2). We extracted these data from studies conducting active surveillance, as passive surveillance is likely to significantly underestimate incidence [26]. Based on these studies, we assumed an upper limit for annual rabies incidence of 1,500/100,000 (Table 2).
Due to the low incidence of rabies, substantial population decline is not expected to result from endemic rabies, although populations may fluctuate in size. For example, in dog populations with endemic rabies in Indonesia and South Africa, Morters et al. (2014) report a variation in population size of up to 22% from the mean over the study period. In South Africa, Conan et al. (2015) report annual changes in population size from +18.6% to -24.5%. In this study, we assumed that once endemic, taken 30 years post-introduction, rabies would not cause a population declines greater than 20% relative to the carrying capacity.
We also considered the seroprevalence predicted by the model relative to empirical estimates. In Laikipia, Prager et al. (2012) reported a seroprevalence of 28% in 75 domestic dogs tested using a rapid fluorescent focus inhibition test (RFFIT; 95% CI: 18.2–39.6%). However, this study used a low cut-off of 0.05 IU/mL which increases the probability of false positives. There is also evidence that enzyme-linked immunosorbent assays (ELISAs) are more specific for detecting non-lethal exposure relative to neutralization tests [21]. Studies using ELISAs have also detected high seroprevalences. Laurenson et al. (1997) found a seroprevalence of 30.0% in Namibia [24], Bahloul et al. (2005) of 28.8% in Tunisia [23], and Cleaveland et al. (1999) of 7.4% in Tanzania [21]. We, therefore, considered a range of 7–30% for seroprevalence in domestic dogs [16].
Results
Non-spatial model
Assuming an R0 of 1.2, with no spatial structure and no incidence-dependent human response, rabies was not predicted to persist in the absence of any naturally acquired immunity (ρ = 0) or with a low probability of sub-clinical exposure (ϕ = 0.95) (Fig 2A). Allowing a proportion of dogs to develop immunity (ρ>0) increased the probability of rabies persistence, with the highest persistence probabilities at intermediate probabilities of acquired immunity. For example, assuming 50% of exposures led to clinical infection, with 25% of sub-clinically exposed individuals developing immunity (Scenario B- ϕ = 0.5, ρ = 0.25), rabies remained endemic in 94% of the simulations. The median annual incidence under this scenario was high at 61,820/ 100,000 (Interquartile range (IQR): 19,139/100,000), with a high population decline relative to the carrying capacity (Median: 96.0%, IQR: 2.0%). Assuming higher probabilities of acquired immunity led to lower persistence, due to reduced incidence and an increased probability of stochastic extinction.
For example, under scenario C, with a low probability of an individual developing clinical infection (ϕ = 0.05), and a high probability of developing immunity (ρ = 0.5), incidence was reduced to 2,207/100,000 (IQR: 1181) with rabies persisting in 87% of simulations. No parameter combination in the homogenous model led to median outputs for both incidence and population decline in the range considered plausible (Table 3). However, of the parameter combinations in which rabies was predicted to persist in the majority of simulations, Scenario C (the high immunity scenario, Table 2) had an incidence closest to the plausible range and a low median population decline of 3.6% (IQR: 1.1%) (Fig 2).
Of the full set of 25 parameter combinations considered, the combination which generated the highest median predicted seroprevalence, of 16.0% (IQR: 3.5%), was a probability of an individual developing clinical infection (ϕ) of 0.05 and a probability of developing immunity (ρ) of 0.25. This predicted seroprevalence is close to the threshold for herd immunity for an R0 of 1.2 (1-1/R0 = 0.167). At this threshold each infectious individual infects on average one other, leading to stable endemic infection. For the subset of three immunity scenarios considered, predicted seroprevalences using the non-spatial model were 0.0% (IQR: 0.0%), 11.1% (IQR: 5.2%), and 14.9% (IQR: 6.1%) for scenarios A, B, and C respectively.
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