3.2 Sensitivity analysis
After visually inspecting the relationship between the input parameters
and the resulting ASF persistence, all of them appeared as clearly
linear, except for the annual hunting rate, whose effect was not. As
shown in Fig. 6, the effect of hunting, expressed as the resulting
lowest wild boar density observed during the 10-year period, could be
broken down into two segments of different slopes. For this reason, we
estimated two different sensitivity values for the hunting rate
parameter, one for the rates corresponding to a minimum wild boar
density < 0.75 individuals / km2, one for
the rates corresponding to a wild boar density > 0.75
individuals / km2.
The global sensitivity analysis revealed than not all the input
parameters had a significant effect on ASF persistence. Of the infection
probabilities related to each of the three transmission pathways, direct
and carcass-mediated transmission exhibited significantly different from
zero sensitivity values (Tab. 3), whereas the sensitivity of
survivor-mediated transmission was not significant. Similarly,
increasing the duration of a carcass infectivity period significantly
increased the ASF persistence, whereas increasing the duration of a
convalescent wild boar infectivity period did not (Tab. 3). ASF
lethality exhibited a significant but negative sensitivity value (Tab.
3), implying that an increase in the proportion of fatal disease
outcomes produced a reduction in virus persistence, because of the
reduced time available for infected wild boars to transmit the disease.
The proportion of reproducing females in the population, on the
contrary, exhibited a positive and significantly different from zero
sensitivity value (Tab. 3), suggesting that an increased reproductive
performance at the population level corresponded to an increased
probability of disease persistence over time.
When analysing the effect of hunting rate in the two different density
segments, the results of the sensitivity analysis exhibited rather
different relationships. The sensitivity of ASF persistence to changes
in hunting rate when wild boar density was higher than 0.75 /
km2 was the highest among all tested parameters,
whereas the same parameter did not exhibit any significant effect on ASF
persistence when wild boar density was lower than 0.75 /
km2 (Tab. 3 and Fig. 6). At 1.5 wild boars /
km2 ASF was expected to persist in the population at
least 10 years, but a reduction of wild boar density to its half
corresponded to an expected persistence of about three years (Fig. 6),
which resulted in a disease fade-out at the end of the first epidemic
wave. On the contrary, further increasing hunting effort to reduce wild
boar density to even lower values did not result in any further
reduction in the expected duration of the epidemic (Fig. 6).
DISCUSSION
Our model captured well both the epidemiological and the demographic
dynamics observed in the affected areas during the first years of the
epidemic, in terms of population size reduction, average prevalence and
seroprevalence, and long-term persistence of the disease at low wild
boar density during the endemic phase. Although we used the
epidemiological data reported for Latvia (Oļševskis et al., 2020) as a
reference for model parameterization, the dynamics emerging from our
study were typical for ASF in wild boar in most of the surveillance data
reported for northern and eastern Europe since the ASF initial outbreak:
ASF reduced infected populations by 70-80% during the first 4-5 years
of the epidemic, as reported in most of the Baltic countries and in
Poland (Depner et al., 2017; Oļševskis et al., 2020; Nielsen et al.,
2021); peaks in the ASF virus prevalence were usually around 5%, with
the average prevalence during the whole period ranging 1-2 % (Depner et
al., 2017; Nurmoja, Schulz et al., 2017); seroprevalence peaked at
values around 10% and then progressively decreased during the endemic
phase, as recently reported for Estonia and Latvia (Nielsen et al.,
2021). Moreover, the additional parameters selected through the
optimization procedure were all in the range of values obtained from
field and laboratory data during these years, even though no a-priori
information was used to select them (Tab. 1, Figs. S1 and S2). The model
exhibited a rather slow dynamic, especially during the initial period
after virus release (years 1-2), when prevalence remained well below 1%
and raised slowly towards a clear first epidemic wave. Besides from
being an intrinsic property of the system, such pattern was determined
by the large area used for simulation, which caused a dilution effect of
the epidemiological parameters during the initial years. Data estimated
exclusively on the initially infected area would have shown higher
prevalence and faster spread of the virus. This should be taken into
account when comparing model dynamics with surveillance data reported
from small affected areas, shortly after the initial virus detection.
In terms of mechanistic disease dynamics, our model results indicate
that the two transmission pathways so far considered as the main
infection routes, namely direct and carcass-mediated, are sufficient to
explain and justify the long-term survival of the ASF virus at low wild
boar density and the ongoing geographic expansion of the disease front
in the European continent. The addition of a third transmission
mechanism, mediated by ASF survivors during their convalescent phase,
did not change drastically the disease dynamics, nor substantially
increased the ASF virus persistence probabilities. Three specific
results clearly indicate that survivors play a minor role in virus
persistence: 1) the temporal trend in the main epidemiological
parameters (prevalence and seroprevalence) was similar in the scenarios
with and without the inclusion of survivor-mediated transmission (Tab.
2); 2) persistence probabilities at five and ten years were
substantially the same for the two scenarios (Tab. 2); 3) the
sensitivity values of all the parameters involved in the
survivor-mediated infection were not significantly different from zero
(Tab. 3).
The role of different transmission mechanisms in ASF persistence,
though, is far from being clarified, and several parallel approaches are
being developed to explore the issue. In a recent work, Lange et al.
(2021) proposed a comparison of different alternative ASF persistence
mechanisms, based on the Estonian case study. They estimated a less than
20% persistence probability after 10 years for a scenario involving
only direct and carcass-mediated virus transmission. They also found
that the inclusion of convalescents with up to 4 weeks of transient
infectivity did not increase ASF persistence rates, unless it was
combined with a reduction of disease lethality from 95% to 80% (Lange
et al., 2021). Instead, they reported that a small proportion (0.1 –
1.0 %) of life-long infectious carriers would drastically increase ASF
long-term persistence probabilities. Alternative mechanisms, such as a
shortened protection by maternal antibodies and the possibility of
immunity loss after recovery were not related to an increase in ASF
persistence in their model (Lange et al., 2021). Using a similar
modelling approach and surveillance data for Eastern Poland, Pepin et
al. (2020) obtained results which are more in agreement with our
findings: they estimated 50-60% ASF persistence rates running an
individual-based model which comprised only direct and carcass-mediated
infection, but estimated such persistence on a time horizon of only 2
years, which makes the comparison with our study not optimal. Finally,
O’Neill et al. (2020) presented a different modelling approach to the
study of ASF persistence in wild boar, which made use of a
deterministic, population-based, compartmental model (Keeling and
Rohani, 2008). They reported that the observed epidemiological patterns
of ASF could not be matched when accounting only for infected and
carcass-mediated transmission, and that the inclusion of a re-infection
probability for ASF survivors allowed to obtain long-term disease
persistence and the same epidemiological trends reported in the affected
countries (O’Neill et al., 2020). The apparently contrasting results of
these different modelling exercises confirms the complexity of the
ecological and epidemiological mechanisms on which ASF persistence
relies. In such complexity, our results suggest that the main infection
routes through which ASF can persist at low wild boar density might have
been already unveiled. Although identifying alternative or additional
mechanisms is relevant and needed, the main focus should be kept on the
role of infectious live wild boar and infectious carcasses, which are
likely to explain a large part of the observed dynamics in the affected
countries.
In particular, the temporal trend in the proportion of ASF infections
occurring with each of the two mechanisms (Fig. 4) shows that direct and
carcass—mediated transmissions are likely to play different roles in
different phases of the ASF epidemic. During the initial invasion phase,
which in our model roughly corresponded to the first two years after
virus invasion, almost 70% of the infections occurred directly between
infected and susceptible individuals (Fig. 4a), and in particular within
the same social group (Fig. 4b). This quantification is substantially
different from what reported by Pepin et al. (2020), who estimated that
53-66% of all virus transmission would be due to a contact between a
susceptible wild boar and an infectious carcass. It should be noted,
though, that those quantifications were based on an initial wild boar
density ranging 0.5-2.0 individuals / km2, as opposed
to the 3.0 / km2 used in our model. Accordingly, we
also observed that carcass-mediated ASF transmission became relatively
more frequent and even predominant for decreasing wild boar density
values (Fig. 5), suggesting that carcasses are likely to be the most
important infection route during the endemic phase, when the wild boar
population density has been reduced by 70-80% after the first epidemic
wave. After entering its endemic phase, ASF seems to be maintained
essentially by infected carcasses, which act as a reservoir for the
virus in small pockets, until the wild boar population bounces back to
density levels which re-allow an effective virus transmission through
direct boar-to-boar contacts.
Such prolonged period of endemicity, which some of the affected
countries in north and eastern Europe are experiencing in these years,
is likely to be challenging both for disease surveillance and for the
efforts of its eradication. One of the most challenging results of our
study is the evidence that a long-term disease persistence was
compatible with a very low endemic prevalence, which ranged in average
from 0.2 to 0.3% (Tab. 2). This means that at any given time during the
endemic phase, only 2-3 wild boars out of 1000 in the population were
infected. Moreover, our model reported an average of about 40 infected
carcasses in the whole study area during the endemic phase,
corresponding to a density of about one carcass / 300
km2. In such conditions, the evidence of ASF presence
in a given area can remain substantially invisible to surveillance. In
this phase, both passive and active surveillance are likely to be poorly
effective in detecting the disease, because the likelihood of hunting an
ASF infected wild boar and that of retrieving an infected carcass in the
forest are both rather low. On the other hand, seropositive individuals
represented about 6% of the wild boar population at the beginning of
the endemic period, decreasing to about 1% after three years (Fig. 2),
making much more likely to detect seropositive than virus positive
animals during the endemic phase. Accordingly, in most of the affected
countries the number of virus positive wild boar in hunting bags and the
number of infected carcasses detected in the forest rapidly dropped to
zero after the end of the first epidemic wave, whereas the number of ASF
seropositive cases reported through hunted individuals progressively
increased in subsequent years (Boklund et al., 2018; Nielsen et al.,
2021). In most of the cases, seropositive animals are the sole reported
cases for long periods of time during the endemic phase. Such
epidemiological landscape, in which the probability to detect the virus
in dead wild boar is extremely low, makes the infection status of the
involved wild boar population uncertain.
Our results confirm the possibility for ASF to persist for long times
with a very low endemic prevalence, which ranged in average from 0.2 to
0.3%, and at very low wild boar density (Tab. 2). This means that at
any given time during the endemic phase, only 2-3 wild boars out of 1000
in the population were infected. Moreover, our model reported an average
of about 40 infected carcasses in the whole study area during the
endemic phase, corresponding to a density of about one carcass / 300
km2. In such conditions, the evidence of ASF presence
in a given area can remain substantially invisible to surveillance. In
this phase, both passive and active surveillance are likely to be poorly
effective in detecting the disease, because the likelihood of hunting an
ASF infected wild boar and that of retrieving an infected carcass in the
forest are both rather low. On the other hand, seropositive individuals
represented about 6% of the wild boar population at the beginning of
the endemic period, decreasing to about 1% after three years (Fig. 2),
making much more likely to detect seropositive than virus positive
animals during the endemic phase. Accordingly, in most of the affected
countries the number of virus positive wild boar in hunting bags and the
number of infected carcasses detected in the forest rapidly dropped to
zero after the end of the first epidemic wave, whereas the number of ASF
seropositive cases reported through hunted individuals progressively
increased in subsequent years (Boklund et al., 2018; Nielsen et al.,
2021). In most of the cases, seropositive animals are the sole reported
cases for long periods of time during the endemic phase. Such
epidemiological landscape, in which the probability to detect the virus
in dead wild boar is extremely low, makes the infection status of the
involved wild boar population uncertain.
In terms of wild boar population management, our model results confirm
that the effort of eradicating or just controlling ASF is a hard
challenge, but they also indicate that some options are more likely to
be effective than others. In particular, the sensitivity analysis
revealed that the effectiveness of wild boar hunting is limited. Hunting
effects are more apparent during the initial invasion and epidemic
phases, when wild boar density is still at relatively high values (Fig.
6). However, the main effect of hunting is just to shorten the
transition from the epidemic to the endemic condition, through an
initial reduction in population density. High hunting pressure might
also generate unwanted effects, inducing compensatory population growth
rate and accelerated generation time, higher juvenile female
contribution to the reproductive set and earlier reproduction (Morelle
et al., 2020). Moreover, the potentially limited benefits of increased
hunting are likely to be counteracted by several of its side effects,
such as increased wild boar movements, virus contamination risks and
potential human-related long-distance transport of the ASF virus
(Guberti et al., 2019).
Afterwards, when ASF enters its endemic phase, hunting has a negligible
role in increasing the overall probability of virus fade out, because
during that period ASF is mainly transmitted and sustained through
infected carcasses. (Fig. 5). In our modelling conditions, the density
threshold marking such loss of hunting effectiveness was estimated at
0.75 wild boar/km2, but such threshold is likely to be
context dependent and difficult to be estimated with the sole hunting
data. Additionally, it should be noted that modelling hunting as a fixed
proportion of population size, as we did in our model, might reduce
model realism at very low population densities. Hunters’ effectiveness,
in fact, is expected to decrease when a wild boar population is sparser,
making it hard to accomplish the same hunting goals achieved at higher
population densities.
Therefore, if transmission and
persistence mechanisms are different in the different stages of an ASF
epidemic, also management actions should be modulated depending on which
phase a given affected area is experiencing. To this aim, our study
indicates that during the initial years, and especially during the first
epidemic wave, hunting as a management tool should be carefully
evaluated in terms of potential benefits and negative side-effects, and
combined with an intensive effort for the detection and removal of wild
boar carcasses. During the endemic phase, when both virus prevalence and
wild boar density are low, further increasing hunting effort should not
be considered as an effective option. Instead, additional effort should
be dedicated to finding and removing as many wild boar carcasses as
possible. In epidemiological terms, this would correspond to shortening
a carcass’ infectious period, a parameter which exhibited a high
sensitivity value during all phases of the ASF simulated course (Tab.
3).
Finally, the sensitivity analysis revealed a third relevant ASF
persistence mechanism, which offers an additional management
opportunity: ASF persistence probability was significantly and
positively influenced by spring recruitment, expressed in the model as
the proportion of females of all ages giving birth to piglets (Tab. 3).
Newly born wild boar, in fact, provide each year a new input of
susceptible individuals, potentially suitable for infection and virus
transmission, thus allowing the typical increase in ASF prevalence
during summer, observed in several of the affected European countries
(Boklund et al., 2018). Moreover, an increased reproductive performance
also generates a higher population growth rate during the endemic phase
of the ASF epidemic, allowing wild boar density to recover quickly, and
increasing the chances that a second lower epidemic wave might occur.
Ecological theory has long recognized the link between food availability
and recruitment in large herbivorous mammals such as wild boar (Gaillard
et al., 1998). Therefore, management actions such as winter supplemental
feeding, which are a widespread practice in most of the European
countries currently affected by ASF (Guberti et al., 2019), should be
considered as powerful enhancers of ASF persistence and strongly limited
or banned. Other modelling work (O’Neill et al., 2020) has shown that
ASF is more likely to persist in wild boar populations with increased
reproductive performance and increased carrying capacity, which are the
typical demographic and ecological consequences of widespread
supplemental feeding. Such population-level effects of artificial
feeding are likely to be further magnified by the local spatial and
behavioural effect: feeding sites, in fact, increase wild boar spatial
aggregation, favour direct or indirect contact between neighbouring
social groups, and overall are likely to increase virus transmission
rates in the population.