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.