2.1 Model structure
The model we used resembled the structure of a SEIR (susceptible-exposed-infected-recovered) epidemiological model (Anderson and May, 1992), with the inclusion of a spatially-explicit, stochastic, individual-based structure. It mimics the structure of the model presented in Lange et al. (2018), with a particular focus on the mechanisms of virus transmission. We built it and ran it using the software Netlogo 6.1.1 (Wilensky, 1999).
All processes took place in a grid of 120x120 km (area = 14,400 km2). We divided the grid into 1,600 3x3 km cells, which represented the smaller simulated spatial unit. Such units, covering an area of 9 km2, corresponded to a reasonable estimate of a wild boar’s core home range (Leaper et al., 1999). Each spatial unit was characterized by its local wild boar density, defined as the number of individuals having their home range centred in each cell. This state variable was then used as an input parameter for the reproduction and dispersal processes.
Each wild boar was characterized by a series of state variables, which defined its role and behaviour in the model. First, a wild boar was assigned a sex and classified into one of the three age classes: juveniles (0-1-year-old), yearlings (1-2 years old); adults (older than 2 years). Additional individual state variables were the reproductive state (only for females) and the dispersal state (only for yearlings). Finally, each individual could be classified in one of the eight model compartments: susceptible, exposed, infected, convalescent, immune, infectious carcass, non-infectious carcass, hunted. The “convalescent” compartment included the individuals which survived the acute phase of the disease and were passing through the recovery process. In such phase they were still able to transmit the infection for a limited amount of time, until total recovery. The duration of the infectious period in convalescents was controlled by parameter χ, whose value was determined through a numerical optimization process (see below for details). The “infectious carcass” compartment included the individuals which succumbed ASF and whose decomposing bodies could still transmit the virus. Once a carcass lost its potential infectiousness it was transferred to the absorbing “non-infectious carcass” state. The duration of a carcass infectious period was controlled by parameterΙ, also derived from the optimization process. Such period was by default 50% shorter in summer than in winter.
The analytical framework included two scenarios, one in which disease transmission occurred only through direct contact between susceptible and infected individuals, or between susceptible individuals and infected carcasses, another in which we added a third possible transmission route, which involved the role of ASF convalescents, while keeping the other two transmission mechanisms in place. Transmission routes are shown in Fig. 1.