Absolute values of the predicted densities depend strongly on the assumed relationship between dragging data and actual densities. Therefore, more emphasis should be put on the relative values than on the absolute values. Our model indicated a strong influence of woodland fragmentation on Lyme disease risk. Increasing fragmentation by decreasing coverage of woodland and decreasing size of blocks lead to (i) an increase of the NIP and DIN in woodlands adjacent to non-vegetated areas, and to (ii) a decrease of the NIP and DIN in woodlands adjacent to grasslands. The reason why grassland made such differences can be inferred from the parameters and transition rules utilised in the model. With lower tick survival and lower reproduction hosts availability, grasslands act as a sink for ticks. Lower survival of infectious ticks can contribute to lower infection prevalence in reservoir hosts in grassland. When questing larvae were picked up in grassland, the probability of getting infected would be lower. As a result, such larvae dropped off in woodland could dilute infection in woodland. Consistent with the negative association found by Guerra et al. 
between grassland and I. scapularis
ticks, our results emphasise the presence of grassland as a way of reducing the density and infection prevalence of I. ricinus
tick in highly fragmented woodlands. It can therefore be hypothesised that strategies like burning or mowing the grassland, which can reduce tick abundance, may also amplify the Lyme disease risks in adjacent woodland. The important role of reproduction hosts on sustaining the local tick population can be highlighted as well. In situation II, DON was higher in landscapes with greater woodland covers, where reproduction host abundances at landscape level were higher. Similar positive relations were also found between questing I. ricinus
abundances and deer densities in various habitat types 
. Our findings can provide important directions for future empirical studies, such as including the effects of adjacent land cover types, as previous analyses mostly focused on woodlands 
. In this study, we only examined fragmented woodland with two extreme situations of adjacent land covers: entirely grassland or entirely non-vegetated areas. In reality, woodland are often adjacent to mixed areas, consisting of non-vegetated areas and grassland, for example suburban residential (houses and gardens) and agricultural areas (pastures/croplands). Further insight could be gained by investing the effect of varying their relative proportion.
By further analysing the simulation results, we found significant impacts of landscape configuration metrics on Lyme disease risks. Based on these findings, two consequences of woodland fragmentation on host movement can be highlighted. First, movement of reproduction hosts between isolated forested patches favour pathogen transmission. Movements between forest patches were only possible when patches were closer than the movement capacity of the host. Thus, a higher patch density and a lower aggregation level can result in higher between-patch movement rates. In situation I, this led to higher nymphal infection prevalence in woodland. Theoretical studies have paid increasing attention to the effects of between-patch host movement on the invasion and persistence of disease 
. Population groups in small forest patches can be exposed to considerable risk of direct disease transmission if between-patch movement of reservoir host is sufficiently high. In line with Watts et al 
, our model expands such conclusion to the field of vector-borne diseases, suggesting reproduction host movement between isolated forest patches could also favour and maintain disease transmission.
Second, movements of hosts between different land cover types shape the local patterns of nymphal abundance and infection prevalence. In the sensitivity analysis, higher movements of reproduction hosts out of their habitat could lead to lower woodland DON. Simulation results by Gaff and Gross 
and Hoch et al. 
showed a similar decrease of tick density in forests when considering an increased deer movement to adjacent grassland. It can indicate the role of reproduction hosts in transporting ticks between land cover types. In situation II, movements of hosts between land cover types were related to the length of forest edge, which is a function of landscape shape index. Decreased movements of both reservoir and reproduction hosts to non-vegetated areas (associated to lower landscape shape index value) were related to an increase in woodland NIP. This would provide crucial hypotheses for future empirical studies: controlling the movements of reproduction host between different land cover types is unlikely to reduce the pathogen transmission. For instance, fencing the woodland may not be useful. Fencing has already been reported to be less useful to remove ticks in the forest or to control tick infestation in adjacent moorlands 
. A possible reason can be that the local absence of a reproduction host may increase tick feeding on reservoir hosts 
. This may lead to an increase of pathogen transmission.
Common processes related to changes in forest area or structure include forest harvesting and forest conversion. Our findings suggest possible impacts of forest management practices: if forest is exploited by removing (i) large clumps rather than a number of small blocks, (ii) regular shapes like square and round that minimize forest edge and (iii) those adjacent to areas that are already deforested, then the risk of Lyme disease may be lowered. Similar suggestions for forest harvesting have been proposed by 
. Although this can lead to slower forest recovery, payoff may be found in the context of risk of tick-borne diseases.
Biological process models for tick-borne zoonoses are very few in numbers whilst the published empirical works are numerous. The situation indicates that a formal framework to understand and control the transmission of tick-borne zoonotic diseases has not been achieved. Models for tick population dynamics 
are quite detailed in tick biology but none have explicitly stated landscape heterogeneity. Models for pathogen dynamics 
adopted representations of landscape but assumed single-host processes or completely ignored the life stages of tick. This study, however, helps to bridge the gap. The present model for the dynamics of both tick and pathogen accommodates a multi-host structure and tick post-egg life stages onto a cell-based representation of the landscape. Cell-based representation of the landscape is strongly associated to remotely sensed data, which are abundant and provide detailed information on the landscape (e.g. spatial relationships, attributes etc.). Such data format may be more convenient to model complex and dynamic systems 
than the patch-based approach.
In our model, several simplifying assumptions were made that may have influenced the results. These could be adapted in future developments to better represent reality. Firstly, the host preference of ticks could be more flexible. The present model simplifies tick feeding by assuming larvae only feed on reservoir host and adult tick only on reproduction hosts. Evidence that larvae also feed on reproduction hosts 
and that adults feed on reservoir hosts 
has been published recently. Moreover, in some instances, host-finding rates could be affected by density-dependent competition between ticks 
. Secondly, movement patterns of host could be more detailed. The stochastic movement rules adopted in our model were only a first step. The trigger and completion of the movement may be multi-factorial, for example dependent on local host density, the phase of movement (i.e. home-ranging and dispersive) and geographical connectivity 
. Thirdly, the influence of climate and seasonal weather patterns could be included. In tick-borne zoonoses transmission systems, the temporal dynamics of either pathogen or populations of tick and their hosts have been studied extensively 
. These temporal dynamics result from environmental factors such as seasonal changes of climate and host abundance 
. Some key tick behaviours have been regarded to be particularly sensitive to season, for example host-finding activity, diapause and maturation. Fourthly, biodiversity, which can be influenced by landscape fragmentation 
, may need to be considered. A very simple species assemblage of two generic hosts was adopted because the field data of species richness, distribution and abundance are largely missing in Belgium, and large uncertainties remain on reservoir capacity of various host species, as well as their tendency to pick up ticks. However, the changing diversity and composition of host community can in theory significantly affect the zoonotic dynamics 
. When data for more species are available, more land cover types (for example, ecotones) need to be included as different species may prefer different types of the land cover 
in which ticks also suffer from different mortality rates 
. Finally, tick feeding behaviours could be better specified. In the model, we assumed fixed durations for tick feeding. However, it has been reported that the duration of feeding can vary, for example larvae sometimes feed for almost one week 
. For computational reasons, a time step of one week was used, which affected the opportunities for larvae to spread. It may be important to explore the effect of this assumption, as well as whether or not the drop-off rhythms of ticks (i.e. the maximum drop-off of engorged ticks may occur during a specific period in a day) exists for I. ricinus
and responses to temperature and land cover 
Cellular automata allow for a certain degree of flexibility in the theoretical study of complex ecosystems. For example in the tick-borne disease model at hand, applying a set of simplifying assumptions allowed to explore the effect of landscape structure. Beyond the immediate results brought by testing a range of scenarios, the model also allowed to outline a number of interesting areas of further empirical investigation. In this regard, the virtual setting of the model is an excellent complement to empirical work when field data are insufficient for direct comparisons 
, or, as is the case for ticks, extremely costly and challenging to collect. Still, further challenges will be encountered when applying the model to scenarios based on real-world situations. It is clear that, when transposing this model to real-world cases, more challenges may emerge, and require case-specific modifications.
In conclusion, the model developed in this study incorporated a cell-based representation of the environment to explore the effects of forest fragmentation on the risks of Lyme disease in a spatially-explicit manner. It can be combined with either real world landscapes or artificial representations. Assuming no impacts of biodiversity, our simulations have shown a strong influence of configuration of habitat patterns, i.e. the density, shape and aggregation level of woodland patches, on density and B. burgdorferi infection prevalence of I. ricinus ticks. These results suggest that, via altering the patterns of local host population interactions, landscape fragmentation can significantly affect the landscape-level dynamics of Lyme disease risk.