The availability of accessible healthcare services for the elderly is an essential requisite for a high quality of urban life (Khalil, 2012; Moroke et al., 2019) . With little evidence that older people today are healthier than the elderly of previous generations (WHO, 2015) , ageing is dominated by poor health, isolation and a strong dependency on medical care. In fact, while aging people get inevitably weaker due to hearing loss, cataracts and refractive errors, back and neck pain and osteoarthritis, chronic obstructive pulmonary disease, diabetes, depression, and dementia that can all contribute to mobility problems (Fredriksen-Goldsen et al., 2011; WHO; de Sousa Faria, 2020) . For instance, some studies have considered older people as a group with substantial healthcare needs by describing the variables of access to medical care provision (Wang et al. ,2020; Du et al., 2020; Koh, Leow, & Wong, 2015) . Other researchers have meanwhile
suggested that the quality of such services -characterised in terms of the number of available beds or physicians or number of square meters -plays a major role in users' behaviour when they have to cope with the choice of being in one healthcare structure rather than another (Bakimchandra et al., 2020; Cabrera-Barona et al., 2018 ).
Hence, a good level of accessibility to essential urban services has significant positive effects on elderly quality of life (Linchuan & Xu, 2020) , and the contribution of people aged 65 and above to society will continue, if not increase, in the future, so long as mobility options are maximised, for example increasing the numbers of buses, improving concessionary tickets for public transport use and the introduction of driverless cars. Some studies (O'Hern & Oxley, 2015) proved that the car continues to be the prime mode of transport for older people, at least in high income countries, including those across America and Europe, but data suggest increase in the prevalence of the numbers killed or seriously injured as a result of frailty: older people are more likely to be injured or killed if involved in a collision (MacLeod et al., 2014; Lee & Lee, 2019; Manning, 2019) . In the light of this, more interventions that help older people move between modes are needed, to try out new modes and new destinations; in addition to support a gradual process of giving-up driving, potentially reducing its negative consequences (Musselwhite & Shergold, 2013; Musselwhite et al., 2015) . In fact, the use of bus or transit, above and beyond walking, keeps people connected to their communities, and essential urban services (Julien, 2015; Shergold, 2015; Manfredini & Di Rosa, 2018) . When dealing with the needs of social and healthcare assistance of elderly people, some studies have conceptualised accessibility of healthcare services by developing an integrated geospatial approach to model medical care use for the elderly supported by transport features, hospitals and clinic proximity, as well as other quality parameters. This approach represents important progress in multidimensionally estimating accessibility to one of the more essential supply systems for the elderly. The limited available data for these parameters could represent a barrier for research in several cities. Thus, as in some previous studies (Wang et al., 2020; Carpentieri et al., 2019; Xu & Yang, 2019) , this study concerns the measure of spatial accessibility to primary healthcare services for the elderly proposing some improvements in modelling the mobility behaviour of these vulnerable users.
Due to the increasing political and scientific interest in the topic, several methods and approaches were generated to compute accessibility to essential services in urban areas; depending on the application context, these measures vary significantly in terms of theoretical basis, operationalisation, interpretability and communicability (Geurs & Van Wee, 2004) . The simplest way to assess healthcare accessibility is to use contour measures (or opportunity measures), define catchment areas by drawing one or more travel time contours around a node, and measure the number of opportunities within each contour (Campbell, et al., 2019; Sahitya, & Prasad, 2020) . This measure is easy to compute and understand but suffers from a poor theoretical basis, since different distances within the same area have no variable evaluating perceived individual and societal benefits -assuming that people select the healthcare alternative with the highest utility. Apart from the strong theoretical basis (Domencich & McFadden, 1975) , it can be difficult to compute and interpret these measures. In the scientific panorama, the two-step floating catchment area (2SFCA) method is one of the most popular approaches for measuring spatial accessibility. The method is a special application of a gravity model, with its main positive aspects proposed for the first time by Radke and Mu (2000) ; since then, the 2SFCA method has been modified and improved several times, and has mostly been used in research on access to healthcare (Hu et al., 2012; Ahn et al., 2014; Ding et al., 2015; Tao et al., 2018) , public transport (Langford et al., 2012; Kanuganti et al., 2016) and green areas (Dony et al., 2015) . In fact, the method evaluates access to a service site in terms of provision (with variables describing the supply side) and need (considering the social features of the demand) -as well as the distance between them -to identify unserved areas. As a result, the method's limitations have yielded several developments and improvements thereof. The following paragraph aims to state some of the main improvements after conducting a systematic literature review.
The 2SFCA method was developed by Luo and Wang (2003) and was first applied in the Chicago area to define the service area of physicians by a travel time threshold while accounting for the availability of physicians by their surrounding demands. The methodology consists of two steps: the first aims to evaluate the balance of supply and demand, quantifying the stress level of services, while the second estimates accessibility as the sum of available services, weighted by their ratios and their distances from users. From its first application, the method was developed differently in order to better overcome its main limits. Tab. 1 below displays some of the studies that were selected because of the improvements they developed for the implementation of the 2SFCA method, which this study sought to adopt and further develop for its age-based 2SFCA method. These improvements are described in the following aspects, after a systematic literature review.
First, several studies have focused on distance-decay functions and their parameters. Luo and Qi (2009) Given these limited considerations, this study proposes an age-based 2SFCA method that considers the network characteristics and mobility attitudes of older people to measure spatial accessibility to primary healthcare services. In terms of the pandemic that many cities are facing, the methodology introduces a limiting factor to take into account the restrictions of local authorities of transport and healthcare services.
Hence, this study aims to contribute to the scientific literature on the theme by: introducing three different distancedecay functions, one per age-group (people aged 65-69, 70-74 and 75 and over); developing a multimodal network for time travel analyses comprised of walkable roads and transit (bus and metro) lines; diversifying older people's walking speeds. Moreover, it also aims to support decision-makers in emergency conditions for providing a good level of accessibility to essential services for the elderly, who are the most vulnerable demographic.
In this study, a GIS-based procedure was developed to evaluate the elderly's level of accessibility to primary health services, considering the demographic characteristics of potential users and multimodal transport services (i.e., walking in the street, the frequency of service and the localisation of urban transport stops) (Makarewicz & Németh, 2018; Wang & Cao, 2017) .
The proposed GIS-based procedure is organised in the following three phases: data collection, GIS analysis and, finally, visualisation of results. Methodologically, this approach integrates the use of open data (spatial and alphanumerical) and
organisational capability with an analysis and representation by Geographic Information Systems (GIS) software.
According to the GIS Model Builder tool of the ArcGIS Pro 2.2 software, we defined a geoprocessing workflow to execute operations that organise and analyse the alphanumeric and spatial data ( Fig. 1) . In the procedure's first phase, it was necessary to create a geodatabase using a GIS software that contains different types of data (spatial and alphanumeric). To improve the data output accuracy of the GIS-based procedure, we used a regular spatial grid to divide the area of analysis into small spatial units. The use of a cell grid is very important in experimental and observational science, and also offers the most common framework for spatially explicit models (Jin et al., 2007) . The hexagonal cell -the minimum spatial unit in which the study area is divided -has a hexagonal shape, and each side may have dimensions previously selected by the user based on the area under analysis . In the literature, the use of a hexagonal cell (rather than a square one) is recommended for dealing with areas that have problems related to the connectivity of different space units and the identification of shorter paths for calculating travel distances (Kibambe Lubamba et al., 2013) . For this GIS-based procedure, we used a regular hexagonal cell as the spatial unit with a side length of 50m that provides greater aesthetic attraction -but above all a greater accuracy -in the calculation and visualisation of results. A proportional function was used to assign the census tracking socio-economic data to the hexagonal cells of the grid, taking into account the buildings' footprint located in each cell (Carpentieri & Favo, 2017) .
In the second phase, namely the geoprocessing stage, joint data and network analysis operations elaborated upon the data to evaluate the travel time and accessibility level to urban services for elderly people. In order to evaluate travel times from each hexagonal cell to the main local health buildings, we created a multimodal transport network. We considered the network as the combination of both walkable streets and local public transport lines (bus and metro) in order to better simulate elderly mobility habits. The ArcGIS Network Analysis tool was used to compute the OD travel matrix. We ran three different simulations during morning peak-hour (9:00) for a person aged 65-69, 70-74 and 75 and over respectively, accordingly considering three different walking speeds .
According to the literature review, a modified Two-Step Floating Catchment Area (2SFCA) method was used to measure the accessibility to primary health services. The theoretical basis behind this method is described in greater detail below: the first step is to compute, for each healthcare centre j (Milan Local Health Agency facility), a ratio R j (Equation 1) of supply and demand. The supply of healthcare services is quantified by the number of available surgeons for each building ( ); the demand is the sum of the population, potential users divided into three age ranges in location i, with P i weighted to consider a time-distance-decay function, W ij , which is a function of the total travel time. The travel times between residential locations i and healthcare structures j are estimated by Network Analyst and ArcMap, taking into account both walking and transit routes. Due to the Covid-19 pandemic, policymakers are now facing a further, more urgent challenge unprecedented in recent human history due to its rapid and dangerous expansion. In fact, an emergency such as the present one, with its significant impacts on most urban activities, affects all the components of the urban system (economic productivity, socio-cultural life, communication -up to changing personal relationships),
including the social subsystem (Allam & Jones, 2020; McKibbin & Fernando, 2020) . Hence, in order to consider the limited supply of healthcare services during the spread of Covid-19, a k coefficient was introduced. It varies between 0 and 1, to highlight the variable availability of services for the elderly.
For the second step, A i , the accessibility of each hexagonal cell was obtained (as reported in Equation 2) by summing the supply-demand ratios of the j health centres serving the i cell -multiplied for the impedance function coefficients W ij , to take into account both the spatial distribution of health centres and the population.
The distance-decay function W ij was introduced to reflect elderly people's mobility habits: a Gaussian impedance function, whose values vary between 1 and 0, was used; this function's main characteristic is that it quickly decreases when time travel is close to the maximum availability of minutes that each elderly age category requires (according to their physical capabilities) to access at the health service (Kwan, 1998) .
The coefficient β was set equal to 180 for people aged between 65-69, 160 for those between 70-74 and 140 for those aged 75 and over, in order to best represent mobility attitudes of different elderly age categories according to outcomes in the scientific literature (Bauer & Groneberg, 2016) . Fig.2 below shows the Gaussian impedance functions used in our application. The coefficient k was introduced to consider the variation of the number of available services in different scenarios: it represents the ratio between the available services S j during emergency scenarios, instances when the supply of healthcare services could be reduced, and the number of services functioning ordinarily.
Since the main objective of this methodology is to focus on both under and overly-served areas in order to identify possible measures for improvement -such as the spatial relocation of existing resources or physical improvements to reduce access to primary health centres -in the third phase, maps and tables were produced to visualise and quantify the results of the GIS-based procedure and hence support the planning process of policymakers, even in the face of emergency scenarios, in assuring essential services for the elderly.
Tab. 2 provides the list of alphanumeric and spatial data (vector and raster) requests for the application of the GISbased procedure. 
The proposed GIS-based procedure was applied to the city of Milan to evaluate urban accessibility to primary public health services for the elderly. Milan was selected as the case study for the developed methodology because, according contracted services: they respectively share 50% of the full demand for healthcare assistance. Considering the regional scenario, the supply from the public side is greater than the contract facilities of a private nature. More particularly, in 2017, according to the Lombardy region's statistics, the ATS of the Metropolitan City of Milan recorded 54.5% of access to private healthcare services, regardless of the number of available beds or the category of medical service provided.
Since the methodology described in the previous paragraph was applied to the Milan Municipality District, we considered all of those services -both public and private -dedicated to elderly healthcare within the city boundaries. Fig. 3 above indicates that healthcare centres managed by ATS Milan are spread across the whole city's territory and offer the following primary services to the elderly: cardiology, diabetology, neurology, ophthalmology, orthopaedics, otolaryngology, pulmonology, urology, rehabilitation, dermatology and gynaecology. Tab. 3 shows the number of available surgeries within each structure; it also highlights whether the healthcare structure is public or private.
For this application, we evaluated the accessibility to primary health services for the elderly before (base scenario) and
during the Covid-19 pandemic emergency (Covid-19 scenario). For the first scenario, we considered the supply of J o u r n a l P r e -p r o o f As soon as the first Covid-19 infection in the Milan area was confirmed, the ATM created a dedicated team that developed an action plan, scheduled on different levels and times, in order to promptly react during the emergency phase, on one hand guaranteeing a certain level of service, and to consequently get ready for the ongoing coexistence phase of the virus (Phase 2). In fact, during the lockdown weeks, the ATM maintained a level equal to 75% of ordinary operativity for those who needed to move for work or health needs -even though in Milan, as in every European city, the usage of public transport declined up to 90%, as shown in the following chart (Fig. 5) . The data shown in Fig. 5 below refers to the period between 15 January 2020 (more than a month before the first Covid-19 infection was confirmed in Italy) and 4 May 2020, the first day of Phase 2. To encourage people's mobility in urban areas, the ATM worked to ensure a significant level of activity of public transport, as well as an intense and capillary cleaning of each vehicle. Among these safety measures, the company also provided travel tickets for people aged 65 and over for direct delivery to their residences (ATM, 2020). These polices show that, although people reduced their movements, transport companies continued to provide a satisfactory level of service, especially for those whose demand for certain services and needs -such as for health facilities -is unchangeable and inflexible. On the other hand, the elderly could be seriously discouraged from using public transport due to the particularity of the present health emergency; as such, our methodology takes into account this aspect through its distance-decay functions, which are different per age group, in order to limit people's mobility capitals.
In terms of the supply side, in order to apply the methodology to the Milan area case study, a multimodal transport network of the city was created using ArcGIS tools to add roads shapefile and GTFS (General Transit Feed Specification) data to a network dataset and to evaluate travel times. Firstly, OpenStreetMap data was used to create the pedestrian network, taking into account only walkable roads and their gradient. Then, GTFS data from the ATM was used to add bus and railway routes and stops in the transport network. Since public transport is not a continuous service in space and time, additional modelling operations were needed to connect the pedestrian system to the public transit system (Rossetti et al., 2020; Zecca et al., 2020) . Once the multimodal network was ready, the ArcGIS Network Analyst tool was used to compute an OD (Origin and Destination) matrix, containing in each cell the total travel time to get from a generic hexagonal cell to a certain healthcare centre. Fig. 5 shows the structure of the multimodal network of the city of Milan. The variation of transport costs was not considered when computing generalised costs since these are flat within the Milan municipality, as travel fares do not depend on physical distances and public transport modality.
The numerical values in Tab J o u r n a l P r e -p r o o f the Lombardy region and the city of Milan during March 2020. It is worth highlighting that the Covid-19 scenario, for the application of the methodology, takes into account the moment immediately following the pandemic's outbreak. Fig. 6 below represents, on a chart, the number of potential users (people aged 65 or above) per level of accessibility.
The accessibility levels' thresholds were chosen according to the quantile classification -a data classification method that distributes a set of values into groups containing an equal number of values (Shah & Adhvaryu, 2016; Bauer et al., 2018; Zhu et al., 2018) . The attribute values are added up, then divided into the predetermined number of classes. In this application, ten accessibility levels were considered, ordered from greater to poorer accessibility ). Fig. 6 shows that, due to restrictions to healthcare services and transport, the people who benefit from higher accessibility levels (1, 2 and 3) are far fewer during the Covid-19 emergency than in ordinary working conditions. On the contrary, an inverse relation is highlighted for the lower accessibility levels. Focusing on the main differences -also proven by the above chart -the medium levels of accessibility underwent no significant modification, at least in absolute terms, while there are considerable changes for both the high and low levels of accessibility. Bearing in mind that, between the two scenarios, the demand of potential users is unvarying, levels 1 and 2 demonstrate considerable decreases (from 9% and 13% to 3% and 8%). This means that all of these users were re-distributed in lower accessibility levels: under the same quality-of-life standards, fewer people have had access to primary healthcare services during the Covid-19 disease outbreak in Milan. The matrix shown in Tab. 6 focuses on how the framework of healthcare provision accessibility was rebuilt for the elderly. In the rows and the columns are the respective levels for the ordinary scenario and the Covid-19 scenario. Each element of the matrix represents the number of territorial units that changed their classification between the two conditions. On the diagonal are the percentages of cells that maintained the same level of accessibility. The matrix is an upper triangular matrix, meaning that the whole territory of Milan underwent a significant decrease in accessibility to primary healthcare services during the very first days of the pandemic outbreak. No improvements in accessibility have been recorded, as there are no values in the lower triangle of the matrix.
The matrix representation was introduced to better evaluate how accessibility changed within the city of Milan due to the restrictions that deeply changed healthcare provision as well as the public transport system. The matrix focuses on how potential users were reallocated in terms of accessibility levels. The Tab. 6 and Fig. 7 represent these changes between accessibility classes.
The results data are interesting in understanding how the accessibility paradigm could be implemented both in base conditions and during emergencies: local authorities could introduce smart decision-support tools in ordinary planning practices to better allocate and distribute resources from the supply side. At the same time, this data could be actually useful only if associated with the territory and, hence, the base locations of potential users of primary healthcare services. Images below represent the levels of accessibility for the whole city of Milan, and how they were modified during Covid-19 restrictions. In particular, Fig. 8 shows the spatial accessibility of the elderly to primary healthcare services in the base scenario. Fig.   9 refers to the Covid-19 pandemic scenario and to the changes made to healthcare provision at the beginning of the J o u r n a l P r e -p r o o f
Covid-19 outbreak in Milan -and consequently in Italy, according to DGR Lombardy n°XI/2906 of 08/03/2020 -that designated some of the main healthcare centres -Covid hospitals‖ for detecting and hospitalising people affected by the coronavirus.
The third map highlights where the Covid-19 restrictions particularly changed the accessibility conditions for the elderly.
It shows that due to the reduction of healthcare provision overall, the whole city suffered a reduction of accessibility.
Moreover, neighbourhoods where hospitals were turned into Covid-19 hospital hubs severely decreased their usual standards for the elderly, who are the most vulnerable users and, at the same time, those who most probably have several healthcare needs.
Although the results present some limitations due to the lack of reliable input data reliable input data, their representations show that accessibility-oriented tools for decision-makers could also be very helpful in emergency conditions for guaranteeing high quality-of-life standards, especially for those who are more vulnerable and in need than others. In fact, since the methodology considers both the supply and the demand of primary healthcare services, as well as the transport component, it is possible to identify a range of compatible solutions to manage both the emergency (a health emergency, in this case) and satisfy the essential needs of the more vulnerable users, limiting changes to the accessibility and, hence, the quality-of-life standards.
Accessibility is a complex and multidisciplinary topic and historically, nobody has been responsible for ensuring that people can access key services, employment sites, places of interest, etc.; as a result, services have been developed with inadequate attention to accessibility (Farrington J. & Farrington C., 2005) . At the same time, accessibility has often been seen as a problem for transport planners to solve, rather than one that concerns and can be influenced by other organisations, for example, in locating, designing and delivering services that are easily and conveniently available (Social Exclusion Unit, 2003) . Thus, scientific research and planning practices demonstrate that the evaluation of urban accessibility can be a useful instrument in supporting transport and land-use planners in the localisation and integration of different urban services to improve the quality of life in the different inhabitants' various categories. Common practices in urban planning lack some insight on the accessibility issue because of some noticeable critical aspectsnamely, from the large amount of data needed, to the use of spatial analysis instruments and their interpretability.
Accessibility measures and their potentialities may be difficult to understand and to be managed by both decision-makers and technicians. Furthermore, structures, offices or technicians that work to define common strategies for transport and land-use planning are missing for territorial planning authorities. This gap in planning practices is one of the main causes of accessibility issues for urban services, especially for the most vulnerable groups of citizens.
During the following years, the continuous growth of the proportion of elderly people in developed countries will increase the demand for services, suitable for satisfying the needs of this group of interest. Hence, urban services need to be properly designed: structures' locations, the types of services, the transport system supply and the urban morphology are some of the main features influencing users' accessibility to urban services.
The Covid-19 emergency has increased the need to manage the movements of people and organise access to essential public services to reduce congestion, especially in urban areas and during peak hours. The authorities need to reorganise essential urban services, including public transports, to ensure safe access to all users. In particular, access within safe conditions to primary health buildings is very important to avoid the possibility of people renouncing normal routine examinations, and thus worsening the health situation.
This is most important for elderly people, who were already hit hard by the virus and obligated to change their habits through the limitation of movements and contacts. In many cases, these people could give up normal health checks for the fear of contracting the virus.
separation between users and primary health buildings and understanding the secondary impacts related to the health emergency of the Covid-19 pandemic and the reduction of accessibility. The results highlight that for the base scenario, some districts need to improve for their own elderly inhabitants the accessibility to primary health services, most of which are located in peripheral areas. The results for the Covid-19 scenario show that a high reduction of accessibility is localised near the primary health centres closed in the peripheral areas, and in the central areas the reduction of accessibility is even more widespread. As shown, the application also allows technicians to provide policymakers with some meaningful and interesting suggestions related to the characteristics and locations of health services, the mobility supply system and the urban morphology (Tira et al., 2018) . It must be said that such an approach needs a holistic and integrated attitude to the city context, in order to take into account both the components of land use and transport systems defining urban accessibility.
For local planning practices, the urban structure and organisation of the Health Local Agency limit the range of actions to improve accessibility to healthcare services from the elderly perspective. Furthermore, the spread of the new coronavirus has reshaped the design of healthcare provision with specialised structures, limiting the number of available services dedicated to the elderly. The following measures represent feasible ways of enhancing the supply of essential services in dense-populated urban areas: as for the urban component, policymakers can design public transport routes and/or schedules according to the demands of healthcare services; from the perspective of local health agencies, the outputs of the model could be used to better allocate resources (such as number of physicians, number of beds or work schedules) within the existing structures.
In terms of international practices, the planning of healthcare services in urban areas -in particular for the elderly who are the most vulnerable users -should follow two basic guidelines. The first is equity-oriented, since the allocation of resources within cities should take into account the varied socio-economic backgrounds of different groups. As noted in previous paragraphs, studies have shown that due to the lack of mobility capital, elderly people suffer from poor accessibility to essential services. The trip mode has significant influence when assessing accessibility as the availability of multiple choices is crucial to satisfying personal and social needs. The Covid-19 virus raised new unforeseen questions related to perceived safety; public transport companies are working on this issue, limiting the capacity of each vehicle while increasing the number of bus or railway routes, assuring intense and capillary cleaning, etc. The second guideline is related to the equilibrium of supply and demand. Bearing in mind that, in big cities, the high density of structures cannot allow the reallocation of healthcare or transport structures, the balance of supply and demand can be achieved by improving the level of services designed for the elderly and their peculiar needs. For example, local health agencies can develop and implement strategic plans to promote healthy ageing in urban areas, with the partnership of local authorities and stakeholders, to provide specialized services to the elderly. On the other hand, policymakers can improve road and public transport networks in such a way that the urban fabric could be accessible not only for an average adult but also for the weakest users, promoting special equity and social justice. These are just a few examples of how healthy ageing policies could be implemented in ordinary urban planning tools, especially in light of the new and unprecedented challenges posed by the novel coronavirus.