Ecological drivers of African swine fever virus persistence in wild boar populations: Insight for control

Abstract Environmental sources of infection can play a primary role in shaping epidemiological dynamics; however, the relative impact of environmental transmission on host‐pathogen systems is rarely estimated. We developed and fit a spatially explicit model of African swine fever virus (ASFV) in wild boar to estimate what proportion of carcass‐based transmission is contributing to the low‐level persistence of ASFV in Eastern European wild boar. Our model was developed based on ecological insight and data from field studies of ASFV and wild boar in Eastern Poland. We predicted that carcass‐based transmission would play a substantial role in persistence, especially in low‐density host populations where contact rates are low. By fitting the model to outbreak data using approximate Bayesian computation, we inferred that between 53% and 66% of transmission events were carcass‐based that is, transmitted through contact of a live host with a contaminated carcass. Model fitting and sensitivity analyses showed that the frequency of carcass‐based transmission increased with decreasing host density, suggesting that management policies should emphasize the removal of carcasses and consider how reductions in host densities may drive carcass‐based transmission. Sensitivity analyses also demonstrated that carcass‐based transmission is necessary for the autonomous persistence of ASFV under realistic parameters. Autonomous persistence through direct transmission alone required high host densities; otherwise re‐introduction of virus periodically was required for persistence when direct transmission probabilities were moderately high. We quantify the relative role of different persistence mechanisms for a low‐prevalence disease using readily collected ecological data and viral surveillance data. Understanding how the frequency of different transmission mechanisms vary across host densities can help identify optimal management strategies across changing ecological conditions.

We predicted that carcass-based transmission would play a substantial role in persistence, 23 especially in low-density host populations where contact rates are low. By fitting the model to 24 outbreak data using Approximate Bayesian Computation, we inferred that between 53 to 66% of 25 transmission events were carcass-basedi.e., transmitted through contact of a live host with a 26 contaminated carcass. Model fitting and sensitivity analyses showed that the frequency of 27 carcass-based transmission increased with decreasing host density, suggesting that management 28 policies should emphasize the removal of carcasses and consider how reductions in host densities 29 may drive carcass-based transmission. Sensitivity analyses also demonstrated that carcass-based 30 transmission is necessary for the autonomous persistence of ASFV under realistic parameters. 31 Autonomous persistence through direct transmission alone required high host densities; 32 otherwise re-introduction of virus periodically was required for persistence when direct 33 transmission probabilities were moderately high. We quantify the relative role of different 34 persistence mechanisms for a low-prevalence disease using readily collected ecological data and assumed to decay exponentially with distance according to the rate parameter  (Table 1). 168 Additionally because wild boar exhibit heterogeneous contact structure due to family grouping  Specific parameters are listed in Table 1. and infectious disease in live hosts were Poisson random variables (Table 1). We tied viral 184 persistence time in carcasses to carcass decay rates to give uninfected and infected carcasses the 185 same opportunity to be sampled (and we could not find data to suggest otherwise). Therefore, 186 infected carcasses were assumed to remain infectious for the entire duration they persisted in the 187 environment. The infectious period of carcasses were assumed to vary seasonally based on field 188 measures of carcass persistence in Eastern Poland ( can constrain wild boar contact and modulate the spread of infectious diseases (Loehle 1995). 197 We accounted for the effects of social structure as described in Figure S3. Females and 198 immatures occurred in family groups. Members of the same family group had the same home 199 range centroid. Adult males were independent (not part of a group, each having a unique home 200 range centroid). Social structure was dynamicfamily groups that became too large (according 201 to a maximum group size parameter; Table 1), split in half and one group dispersed (Fig. S3 Figure S3). In addition to dispersal due to social structuring, natal dispersal 207 also occurred, but only once at a randomly selected age (Table 1)   The dispersal process (natal or other relocation) was: 1) for each 45 degree angle from 214 the home range centroid, a new possible set of [x,y] coordinates was obtained using the dispersal 215 distance value assigned at random to the group (Table 1; i.e. x = distance x cos(angle) + current 216 x coordinate, y = distance x sin(angle) + current y coordinate). If at least one of these potential 217 locations were valid (i.e., in a grid cell with fewer boars than the carrying capacity or a location 218 off the grid), then a valid potential location was chosen at random and boar(s) were relocated 219 there. Boars that traveled off the grid were lost permanently. If there were no valid locations, the 220 distance value was doubled and the process repeated until a valid location was obtained.

221
Birth and death parameters. Boar conception occurred randomly in reproductively active 222 females based on a seasonally varying conception probability (Table 1; Fig. 2). Pregnant females 223 gave birth to 6 offspring (3 male, 3 female) after a gestation period of 115 days (Table 1).

224
Following birth there was a fixed lag of 3 months before the possibility of conceiving again 225 (Table 1). Thus, the maximum number of litters per year was 2. Net population growth rate was 226 controlled by multiplying the seasonal trends in conception probability by a scaling parameter 227 (Ɵ). The full range of the prior distribution of Ɵ allowed net population growth rates to range 228 between 1.3 and 2.3 for population densities at 10% of the carrying capacity, consistent with Bieber and Ruf [2005]. Conception probability was density dependent such that conception did 230 not occur in individuals in grid cells that were already at carrying capacity. The population-level 231 host demographic dynamics were similar to a logistic model ).

232
Sources of mortality included natural mortality, disease-induced mortality, and hunter 233 harvests (described below). For natural mortality, each individual was assigned a longevity at 234 birth based on wild boar life expectancy (Table 1; Fig. 2).

235
Initial conditions and demographic burn-in. Populations were initialized as follows. A 236 matrix with the number of rows equivalent to the desired population size was created. Each 237 individual (row) was assigned attributes at random (Table 1). For males whose age was beyond 238 dispersal age, dispersal status was recorded as completed. All females and males less than 239 dispersal age were divided into group sizes that were ¼ of the maximum sounder size (plus one  boar/km 2 , locally ranging from 0.5-1 boar/km 2 to 3-5 boar/km 2 (Regional Directorate of State 251 Forests, Białystok, Poland). However, because we had no data on how the absolute number of boar sampled related to the underlying density, we added parameters h and c to scale the 253 absolute numbers of boar sampled up or down (Table 1). First we calculated the relative number 254 of boar sampled daily by each surveillance method (number sampled on day t/maximum ever 255 sampled on any given day) to produce seasonal trends in the proportion of the population 256 sampled ( Fig. 2; Fig. S4). Next, we multiplied the seasonal trend data for each surveillance 257 method by the scaling factors (h and c, Table 1; Fig. S4) to determine the daily proportion of 258 boar that would be sampled by hunter harvesting or dead carcasses. The product of the trend data 259 and the scaling factor can be thought of as a daily detection probability. We assumed that boar < 260 6 months of age would not be hunted (typically not targeted by hunters) and that boar < 3 months 261 of age would not be sampled by the dead carcass method (because they are unlikely to be found). 262 We recorded the disease status for all boar that were sampled and then immediately removed 263 them from the landscape permanently.     283 We estimated the unknown parameters using ABC with rejection sampling. Estimated 284 parameters are indicated in Table 1.

285
Approximate Bayesian computation selects parameter sets for the posterior distribution   Despite high uncertainty in several estimated parameters, the models captured the general 367 trends in the surveillance data well (Fig. 3). All models captured monthly cases better than 368 monthly maximum distance from the border (Table 2, Fig. 3). Relative to the observed data, the the first year, which included a period of abnormally low surveillance) (Fig. 3a, Fig. S4). The average prevalence observed through surveillance in the model tracked the magnitude of true 373 sample prevalence for both hunter-harvest and carcass surveillance samples (Fig. S5). Models fit 374 on homogenous landscapes of host density did not capture spatial spreading rates as well as the 375 patchy landscapes that included high-density patches (2 boar / km 2 ; average 1 boar / km 2 ; Table   376 2).

377
Rejection rates for the proposed parameter sets were high for all four models, such that 378 posterior distributions ranged between 6-53 values (0.00031%-0.0027% model acceptance rate) 379 (Table 2), and uncertainty in parameter estimates were large (See Fig. S6). Due to the high 380 amount of stochasticity in model processes and uncertainty in parameter estimates, the model fit 381 the data on average (i.e., R 2 for the median trajectory of stochastic runs relative to observed data; 382 Fig. 3c, d) better than the observed data relative to any one trajectory (i.e., median of R 2 's for 383 each stochastic run; Fig. 3a, b). R 2 for the full data (including out-of-sample predictions) were 384 lower than those for the in-sample predictions ( Table 2, Fig. 3a, b), indicating that the model

390
The models predicted a substantial amount of carcass-based transmission (monthly 391 average between 53 and 66% during 2014-2015 depending on the landscape; Fig. 4) and a much 392 higher prevalence of ASF in sampled carcasses versus hunter harvested samples (Fig. S5a). The 393 best model (patchy landscape) also predicted a slow decline of the wild boar population over 394 time (Fig. S5b), which corresponded to proportionately more transmission events originating from carcass-based transmission over time (Fig. 4), especially in the patchy and low-density 396 homogenous landscapes.

| Host density effects on ASF persistence
398 Sensitivity analyses showed that densities higher than 1 boar / km 2 were important for 399 autonomous persistence (Fig. 5 a,d,g). Without carcass-based transmission, persistence required 400 re-introduction 10 or more times per year at lower host densities (Fig. 5b,e). However, with only 401 carcass-based transmission, persistence occurred across some narrow range of carcass-based 402 transmission probabilities even at low host densities (Fig. 5c,f) with few to no re-introductions.

403
In contrast, high host density (4 boar / km 2 ) allowed for autonomous persistence when carcass-404 based transmission was absent (Fig. 5g,h,i) over some narrow range of transmission probabilities 405 for either transmission mechanism on its own.   analyses also demonstrated that decreasing host density could have unexpected consequences. 472 We found that while high host densities allowed autonomous persistence by direct transmission, the chance of increased long-distance movement due to social structure disruptions. 487 We assumed that ASF was 100% lethal in wild boar, which is an oversimplification of (dark grey -"infected zone" in the text, light grey -"buffer zone"). and a transmission probability given contact,  (d for direct and c for carcass-based).

776
Persistence of carcasses on the landscape varied seasonally (to reflect weather-based differences 777 in degradation rates) but were the same regardless of the mechanism of death, such that carcasses 778 by all mortality mechanisms had equal probability of being sampled. Seasonal trends in 779 conception probability, carcass persistence, and sampling modes were all multiplied by scaling 780 parameters (θ, p, h, c) which were estimated. We also allowed for exposed individuals to be introduced along the eastern border at frequency f. realistic values: h  0.05, c  0.025, p  , q  2,   .5 other parameters were as in Table 1.  were used for prediction out-of-sample.