Introduction

One of the most critical, and the most testing, tasks of modern society is the provision of personal and medical care for people who, due to their age or health conditions, are in a particular state of vulnerability and frailty. In particular, every society must provide child care for the care needs of their children, and social care for adults who need help with their activities of daily living (ADLs). In most developed countries, the state plays an important role in the provision of care for these vulnerable groups. However, formal and informal care provided within the household or broader kinship network is often critical to the health outcomes of vulnerable people. As populations of older people continue to increase while birth-rates drop in developed countries, some governments are confronted by a substantial increase in the demand for care.

In the UK the supply of carers is decreasing over time as birth-rates drop, even while the increasing elderly population requires ever more support [1]. A recent Age UK report states that almost 50% of over-75s are living with a long-term illness that limits their ADLs [2]. Given that this age group is among the fastest-growing in the country, expectations are that the demand for care will outpace the available carer population.

Consequently, unmet care need is of critical importance to health and social care policy-making in the UK. Ipsos MORI reports that a majority of the aged with care needs have at least some unmet care needs [3], while Age UK estimates that 1.2 million people received insufficient care in 2017 [2]. Carers UK estimates that in order to meet the skyrocketing levels of care demand, the population of carers would need to increase by 40% over the next 20 years [4]. According to Wittenberg and Hu (2015), demand for privately-funded social care is also expected to rise significantly over a similar period, with expenditure on private care to nearly triple by 2035 [5].

For the majority of households with social care needs, the problem of meeting these needs is compounded by the necessity of meeting their family’s child care requirements. According to FullFact, 79% of families in England with children aged 0 to 14 used some form of childcare, with 66% of them using formal childcare, 40% using informal childcare and 28% using both [6]. Further, according to the OECD report Society at a Glance 2016, UK families spend over 30% of their income on childcare [7].

The provision of social care in the UK is largely dependent on informal care, or care provided on a volunteer basis by family members. A 2018 report from the National Audit Office estimates the value of UK informal care at £100 billion per year [8]. Aldridge and Huges, using data from The Family Resources Survey 2013/14, report that there were 5.3 million informal carers in the UK [9] and the Health Survey for England 2017 states that 68% of participants aged 65 and over reported receiving help from unpaid helpers, while 21% said they had received help from both unpaid helpers and paid helpers [10]. In this regard, the importance of support and care-giving networks has long been recognized [11, 12]. Tennstedt et al. (1989) reported that informal care is provided mostly through networks of carers with an average of three to five members, predominantly composed of an individual’s close relatives [11].

Using data from the Family Resources Survey from 2011/12 to 2013/14, Aldridge and Huges find that 72% of carers provide informal social care to a member of their immediate family, i.e. a parent (40%), partner (18%), children (14%) [9]. Similarly, Petrie and Kirkup estimated that around 51% of carers provide care to a member of their own household [13]. Using data from the Health and Retirement Study 2011, Wettstein et al. show that 31% of informal care in the US was provided by partners; 47% by sons or daughters; and 18% by other close relatives (e.g. children-in-law or grandchildren), with non-relatives contributing for just 4% of the total informal care provided [14].

As for formal social care, the National Audit Office estimates that privately paid-for care amounts to approximately £11 billion in 2016-17, which increases to approximately £14 billions when we include private ‘top-ups’ to the cost of the care arranged by local authorities. Empirical research has also shown that the type and amount of social care provided is affected by socioeconomic status. Petrie and Kirkup (2018) report that people working in routine occupations and those with lower qualifications are more likely to provide informal care [13].

Given the demographic trends outlined above, an increasing number of households will need to manage their resources to provide for both child care and social care needs, meaning that in these cases these two types of care are deeply interrelated. In addition, both the social and child care provision processes taking place within these households, and their connected care-giving networks, are affected both directly and indirectly by the current government’s child and social care policies. With that in mind, we propose that understanding how child and social care need evolves over time, and the socioeconomic processes that underline the provision of care, are a vital component in any attempt to develop and implement effective and sustainable care policies.

In this paper, we present an agent-based model (ABM) of the UK informal and privately-funded formal care system, with the goal of capturing the complex relationships between social and child care, and the impact of social policies on these processes. This model provides a theoretical framework that enables us to improve our understanding of the complex care allocation system, where demographic, social and economic factors interact to determine the dynamics of care demand and supply. Further, using ABMs enables us to model scenarios of economic and social policy change, providing a means to test social policies which are meant to affect child and social care provision, and reveal any possible unintended side-effects (spillover effects) of those policies prior to implementing them in the real world.

Our previous work has explored social care provision and policy solutions using ABMs [15–17]. Social care is not a frequent topic for modelling, and to our knowledge only one other agent-based simulation explicitly including informal and formal social care has been published besides our own work: an examination of the impact of demographic change on formal and informal care in Spain [21]. While the topics are related, the model produced by Spijker et al. is significantly different in its construction and intended purpose. The Spijker et al. model is microsimulation-based with ABM elements, uses different mechanisms than those presented in the present model and its ancestors, does not simulate interactions within families across their kinship networks, and does not investigate the impact of policy interventions.

The model presented here extends our previous efforts significantly, and models the provision of care not just as a simple transaction from one agent to another, but as a negotiation conducted across kinship networks with reference to numerous social, economic and geographical factors. As a result, we propose that this model can support and inform child and social care policy-making more comprehensively than other methods.

Basics of the model

In this section we provide a summary of the model’s core economic and social processes. This model is a comprehensive re-implementation and extension of previous work in Noble et al. [15] and Silverman et al. [16], adding numerous processes and sub-processes to that basic framework. Complete Python 2.7 source code for the simulation is available in our GitHub repository at https://github.com/UmbertoGostoli/Social-and-Child-Care-Model-PLoS.

The modelling framework is under continuous development, and as such we recommend that any interested colleagues follow our updates on GitHub. Releases will be produced periodically when new major features are added to the simulation. Agents in the virtual UK depicted in this model occupy households, clusters of which form towns. The sizes of these towns are set with rough correspondence to real UK population densities, scaled down by a factor of 1:10,000. The simulation runs in one-year time steps; within each year processes taking place on a weekly scale are modelled. The simulation begins in the year 1860, which allows sufficient time for the population dynamics to stabilise before 1951, at which point UK Census data is incorporated into the simulation. The simulation finishes in the year 2050.

Given the complexity of this simulation, we provide only brief summaries of some aspects which are explained in detail elsewhere, and refer readers to those papers for further information. Changed and additional aspects of the current model are explained here in full. Please see Table 1 for a comparison of the various iterations of this model and the features that have been developed and added over time.

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Table 1. Comparison of social care modelling efforts.

https://doi.org/10.1371/journal.pone.0242779.t001

Health status and care need

Agents start their lives in a state of good health, and later may enter a state of care need according to gender- and age-specific probabilities. Care needs may develop at any age, though entering such a state becomes increasingly likely as agents grow older, and male agents have slightly higher probabilities of developing care needs compared to female agents of the same age. The five categories of care need (which will be referred to as care need levels in this paper) and the amount of hours per week of care required at each level are shown in Table 2. We assume that, once agents develop a health condition associated with a certain level of care need, they do not recover but progress to more severe conditions (and so, to higher levels of need) over time. The chance of agents progressing to higher care need levels increases with age and with the sum of the agent’s past unmet care needs (and decreases with higher socioeconomic status, see the Socioeconomic Status Groups subsection below). We thus assume that long periods of unmet care need will increase frailty, and that higher income and wealth allows for high-quality care to be purchased to increase quality-of-life.

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Table 2. Care need categories/levels and number of hours of care required.

https://doi.org/10.1371/journal.pone.0242779.t002

Model enhancements

The model we present in this paper is an offshoot of the Linked Lives model presented in Silverman et al. [16], further extended in Gostoli and Silverman [17] where the following features were introduced: socio-economic status (SES) groups; kinship networks; relocation’s decision-making; formal (i.e. privately paid-for) care; public social care; a salary function; and hospitalization probabilities (which depend positively on levels of unmet care need). We provide very brief summaries of the 2019 additions of SES, kinship networks, the salary function, formal and public care provision aspects here, and refer the reader to Gostoli and Silverman [17] for more details. Subsequently we will describe the enhancements made to the current version in full.

Kinship networks

Agents with social care needs are associated to their next-of-kin’s households through kinship networks, i.e. networks of households whose inhabitants have a consanguineous or affinal relationship with the agent with social care need. We define ‘degrees’ of kinship based on the network distance D between households in the network; this kinship distance value ranges from 0 (same household) to III (uncles/aunts and nieces/nephews).

When an agent in a particular household is in a state of care need, the size of the kinship network associated with that agent, the kinship distances characterizing the kinship relations, and the individual states of the members of the households which are part of the agent’s network determine the supply of care available to that agent. Table 3 shows the hours of care supply associated with each agents’ status and network distance:

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Table 3. Amount of care agents can provide depending on their status and kinship distance from the care receiver.

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Physical distance also affects care provision, as we assume that only households in the same town as the care receiver can provide informal care. In addition we assume that formal care is restricted by kinship distance, with provision of privately paid-for care occurring only among members of the same household or, if living in different households, only between parents and children.

Child care

In this updated version of the social care model from Gostoli and Silverman [17], we included another critical aspect of understanding care: child care provision (in this model, children are agents of age 0 to 11). In our model, we assume that all children, except newborns (agents of age 0), have the same care need, whic is set to 56 hours per week. However, the net care need of each child depends on his age, due to the presence of age-specific child care and education policies, which determine the quantity of child care provided by the state through nurseries and schools. Newborns are treated as a special case, as they have a much higher need which is entirely supplied by their mother, who allocates all of her available supply of care to the newborn.

Although child care and social care seem similar on a surface level, there are deep differences between these two kinds of care which require us to treat them as two separate but interrelated processes. First, in the UK and most other developed countries there is a parental duty of care defined by law, while social care mostly rests on a social/moral obligation to care for one’s relatives. Second, while child care is defined purely by the age of the recipient, social care implies a pathological condition which limits the recipients’ activities of daily living. Consequently, child care need is usually more predictable than social care need and can be supplied on a ‘one-to-many’ basis, whereas social care usually is delivered on a ‘one-to-one basis’. Finally, due to this ‘one-to-one’ characteristic of social care, formal social care prices are between three and four times higher than formal child care.

These differences have important implications for the modelling of care provision. First, because of the legal frameworks related to the the provision of child care, we assume that it will have priority over the provision of social care, which therefore will be allocated the residual care supply remaining after the child care allocation process. Second, while social care need is linked to the single individuals needing care, we consider the child care need to be associated with the household rather than the individual children, and therefore characterise it by a certain amount of ‘aggregate’ child care need whose structure depends on the number and age of the household’s children. In other words, we assume that while social care is always personal, as it is provided directly to individuals, child care is provided to households.

Finally, because of the different prices, we assume that, all else being equal, households will preferentially allocate their income to provide for formal child care (i.e. the cheapest kind of care) and their time to provide for informal care for the most expensive kind of care need. Although most of the time, the most expensive kind of care need will be social care need, because of the ‘one-to-many’ nature of child care (that is, the possibility to satisfy multiple sources of child care need with each ‘time unit’ of informal care), households with many children may find it more convenient to allocate their available time to provide for informal child care. This in turn saves them the cost of multiple nursery fees, which may exceed the cost of formal social care depending on the number of children present. These differing characteristics mean that care provision is a complex social process, the computational implementation of which is discussed in the next section.

Care allocation

The care allocation we propose in this paper represents a complex negotiation conducted across kinship networks through which the two separated, but deeply interrelated processes of child and care provision take place. Care allocation takes place in two stages: first the available care supply (composed of available time and income for care) is allocated to child care, and second the remaining resources are used to satisfy social care needs.

In each stage the allocation process starts by randomly sampling a care-receiving unit (either a household with children, in the case of child care, or a person with care need, in case of social care) with a probability proportional to the unit’s unmet care need. The care receiver is then associated with a care-giving household within the care receiver’s kinship network (including the care-receiving household itself), sampled among all the potential care giving households with a probability proportional to the household’s available care supply. This stochastic mechanism is based on the assumption that the higher the care need (care supply), the higher the probability of receiving (providing) care.

There are two main differences between social care and child care provision. First, while formal child care is provided only within the child’s household, formal social care can be provided also through the income of households within distance 1 from the care recipient, in the care recipient’s kinship network (i.e. the parents’ and the children’s households, if different from the care recipient’s household). Second, besides the households’ income, formal social care can be bought through another financial resource, which is the care recipient’s own financial wealth. Therefore, the choice of care supply depends on the relative amounts of: a) time availability for all the households in the care receiver’s kinship network living in the same town of the care receiver; b) the income of the households up to distance one from the care receiver; c) the care receiver’s own financial wealth.

Once the care supplier has been selected, a 4-hour ‘quantum’ of care is transferred from one member of the supplying household with available supply to the individual with care need (note that receiving and supplying agent may live in the same household). However, if a household within distance 1 from the care receiver is selected, a further decision needs to be taken about whether the time (i.e. informal care) or income (i.e. formal care) of the house is to be used.

While the selection of time will result in 4 hours of informal care being provided (and, correspondingly, 4 hours of time being subtracted from the care-giving household’s time resources), if the resource selected is income, the care-giving household must decide whether to use income to buy formal care or to use the working time of a household’s worker to provide for informal care (i.e. taking time off work). The choice depends on the hourly wage of the household’s worker with the lowest wage: if it is lower than the price of formal care, the worker will prefer to take time off to provide care, whereas in the opposite case purchasing formal care is preferred.

Note that the way the prices of care are computed will differ between child and social care, due to the aforementioned ‘one-to-many’ aspect of child care. While the price of social care is fixed, the child care price to which the workers’ wages are compared, in order to make the informal/formal care choice, is the price of formal child care multiplied by the number of children, because of the ability of the informal carer to satisfy multiple child care needs concurrently. We call these values informal child care values (ICVs), representing the cost that the household avoids by providing informal child care. The underlying assumption is that while multiple children will increase the total cost of formal child care, informal care can satisfy multiple children’s care needs per time unit provided, therefore allowing the household to avoid this cost. A household’s ICVs depend on the household’s number and ages of children and determine whether that household will elect to pay for formal care or take time off for informal care.

When a household has both child and social care need, it will preferentially allocate informal care to the most expensive variety and formal care to the least (again, given the possibility of satisfying child care needs concurrently for multiple children, the relevant cost of child care in this regard are the household’s ICVs). After all the household’s child care needs are satisfied, the remaining availability of time and income for care within the household’s kinship network will be used to satisfy the household’s social care need.

Social policy experiments

Given the importance of child and social care provision to many families, most developed nations design and implement social policies intended to reduce the care burden on families and, in general, facilitate care provision. Furthermore, child care provision is affected by the education policies in place, to the extent that they affect the hours children spend in school. In this model, we included the current child care, education and social care policies in force in England (neglecting, at this stage, differences between the UK regions). The inclusion of these policies and the related policy levers allows us to simulate care outcomes and costs under alternative social care policies, represented by different combinations of policy parameters, making this model a unique tool for developing and evaluating care policy interventions.

In these early-stage results, we investigated the effects of four policy interventions related to some key policy ‘levers’ where policy-makers attempt to influence social care outcomes. We developed four potential policy interventions designed to reduce the overall social care burden to UK society. These four scenarios were chosen in order to investigate key policy levers that have previously been targeted by policy-makers: cost contribution schemes; free care provision; and changes to eligibility requirements. We chose two scenarios that target only child care, and two that target only social care, in order to examine the interdependence of these two types of care.

The four policy levers targeted by out policy intervention experiments (and their current values) are listed below:

• Percentage of public child care cost contribution (α): the government adds an extra £2 for every £8 that working families spend on child care, up to £2,000 per child per year (i.e. there is a 20% government contribution to child care costs).
• Hours of free child care per week (β): working families can get up to 20 hours per week, or 1,040 hours per year of free child care for every child aged 3 and 4.
• Minimum care need level for government-funded care (γ): local authorities pay the full social care cost of people with a critical level of social care need (care need level 4) with savings of less than £14,250. If their savings are between this lower bound and £23,250, the person receiving the social care will contribute a pound for every £250 of savings to the weekly cost.
• Public social care cost contribution (θ): the fraction of the cost of social care contributed by the government. Currently there is no such scheme in the UK.

In Table 4 we show the benchmark (default) and intervention levels of these four key parameters. In the Results section below, we compare the benchmark scenario with four policy scenarios, one for each intervention (leaving, in each scenario, the other policy levers at their benchmark level). In the first scenario, we increase the public child care cost contribution from 20% to 80% of the cost (i.e. the state refunds £8 for every £10 spent on child care); in the second scenario, the hours of free child care for children aged 3 and 4 are increased from 20 to 32 per week; in the third scenario, the minimum care need level for eligibility for publicly-funded social care is lowered from 4 to 3 (see Table 2); in the fourth scenario, a public social care cost contribution scheme is introduced in which the state pays 50% of the cost of social care.

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Table 4. Benchmark and intervention levels for the four policy levers.

https://doi.org/10.1371/journal.pone.0242779.t004

We assume that the four policies are implemented from simulation year 2020 and compare the outputs of these four policy scenarios with the benchmark no-change scenario over the period 2020–2050.

Results

Benchmark simulation results

Here we present the outcomes of ‘benchmark’ simulations (Figs 1 to 10), then compare some of these these to the effects of possible social policy interventions (Figs 11 to 20). Figs 1 to 10 summarize the outcome of 15 repetitions, with the central line representing the average across the repetitions and the shaded area around it the 95% confidence interval. As mentioned in the section ‘A note on validation’, given the lack of empirical time series data on social care demand and supply variables, we are unable to compare these results to the empirical data but they can still give important insights regarding the direction and scale of change.

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Fig 1. Population and tax payers.

https://doi.org/10.1371/journal.pone.0242779.g001

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Fig 2. Employment rate.

https://doi.org/10.1371/journal.pone.0242779.g002

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Fig 3. Informal, formal, public care and unmet care need.

https://doi.org/10.1371/journal.pone.0242779.g003

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Fig 4. Total social care need.

https://doi.org/10.1371/journal.pone.0242779.g004

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Fig 5. Total unmet social care need.

https://doi.org/10.1371/journal.pone.0242779.g005

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Fig 6. Average social care burden.

https://doi.org/10.1371/journal.pone.0242779.g006

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Fig 7. Cost of public social care.

https://doi.org/10.1371/journal.pone.0242779.g007

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Fig 8. Hospitalization costs.

https://doi.org/10.1371/journal.pone.0242779.g008

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Fig 9. Share of informal social care.

https://doi.org/10.1371/journal.pone.0242779.g009

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Fig 10. Gender pay gap.

https://doi.org/10.1371/journal.pone.0242779.g010

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Fig 11. Unmet care need: Total period 2020-2050.

https://doi.org/10.1371/journal.pone.0242779.g011

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Fig 12. Policies’ direct cost: Total period 2020-2050.

https://doi.org/10.1371/journal.pone.0242779.g012

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Fig 13. Hospitalization cost: Total period 2020-2050.

https://doi.org/10.1371/journal.pone.0242779.g013

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Fig 14. Social care need: Total period 2020-2050.

https://doi.org/10.1371/journal.pone.0242779.g014

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Fig 15. Formal child care.

https://doi.org/10.1371/journal.pone.0242779.g015

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Fig 16. Share informal child care.

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Fig 17. Informal social care: Total period 2020-2050.

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Fig 18. Formal social care: Total period 2020-2050.

https://doi.org/10.1371/journal.pone.0242779.g018

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Fig 19. Public social care provided: Total period 2020-2050.

https://doi.org/10.1371/journal.pone.0242779.g019

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Fig 20. Off-work hours for care: Total period 2020-2050.

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Fig 1 shows the population and the proportion of tax-paying agents. Although the population keeps growing from 1960 to 2050, it grows at a decreasing rate. One of the main effects of population ageing can be seen from the dynamics of the working-age population (i.e. the taxpayers), which is essentially flat after 1990, and this produces a growing gap between the total population and the working population.

Fig 2 shows the share of the adult population (i.e. people from age 16 to age 65) who are employed (the others being students or having health conditions preventing them from working). We can see that it fluctuates mostly between 70 and 75%, a level which is consistent with the empirical data.

Fig 3 shows the dynamics of the three kinds of social care supply we considered (i.e. informal, privately paid-for and public) and unmet social care need; we omitted the confidence intervals in this case for greater visual clarity. Although all three kinds of care supply increase until the second half of the 2030s, supply cannot keep pace with the social care demand, as shown by the dynamics of the unmet care need. Our simulations show that from around the second half of the 2030s the informal care supply reaches a plateau (with the current social policies in place).

We can see more clearly the social care effects of these demographic trends in Fig 4, which shows the relentless and steady growth of social care need, with a slight increase of the growth rate in the late 1990s. Our simulations show that social care need increased by a factor of 5 between 1960 and 2050, while the population increased just by a factor of 1.6 in the same period.

The increase of social care need results in an equally remarkable increase of unmet care need, shown in Fig 5, where we can see a steady growing trend starting from around 1990.

In Fig 6 we can see that increasing social care need causes the per capita hours of care delivered to increase, from just above 8.5 hours in 1960 to more than 11.5 hours in 2040. After 2040, the average hours of care delivered appears to flatten out, a trend which reflects the dynamics of the informal care supply shown in Fig 3. This is due to the fact that, at the end of the 2030s, the demographic structure of UK society will be such that the number of people available to provide informal social care will decrease drastically.

Fig 7 shows the dynamics of the cost of public social care, which follows quite closely the dynamics of social care need shown in Fig 4.

Hospitalization costs follow a similar dynamic to public social care costs, as shown in Fig 8. From 1960 to 2050 the hospitalization costs increase by a factor of 6.

Fig 9 shows that, due to changes to the demographic structure of the population, the share of informal care supply over the total care supply is expected to decrease from around 90% in the 1960 to around 65% in 2050. This means that the other forms of care supply grow at a faster rate than the growth rate of informal care, although not enough to satisfy the growing social care need (as shown by the increase of the unmet care need in Fig 5).

Finally, in Fig 10 we show the dynamics of the gender pay gap, expressed as the ratio between female and male incomes. Overall the simulation’s outcome is quite consistent with the empirical data, showing a gender pay gap that fluctuates around 10% after the year 1980 (meaning that pay for women is 90% that of men).

Discussion

This paper expands upon our previous efforts to model informal social care using agent-based modelling techniques [16, 17]. Following those previous projects, we consulted with social care experts, and were advised that child care commitments can create challenges for families faced with significant adult social care demand. Therefore, this model for the first time incorporates child care processes alongside informal social care supply and demand, allowing us to begin to investigate more nuanced policies directed at informal care.

We conducted a series of policy experiments to illustrate how the model can be used to compare the effects of different policies, allowing the policy-maker to investigate possible spillover effects and unintended consequences of polices before implementation in the real world. We propose that this ABM can be a valuable tool for policy development and evaluation, as it explicitly models the complex interactions between child care and social care provision, and the negotiations that happen within families as they decide whether and how to allocate their time and money to care provision. As a consequence of this detailed modelling of care decision-making and the effects of macro-level social policies, we can provide more sophisticated evaluations of policies that illuminate both their impact on government finances and their social and economic ramifications.

As mentioned in the Introduction, little agent-based modelling work has been done on informal social care; one study from Spain was directed more at demographic modelling rather than simulating policy outcomes [21]. We hope that by constructing this detailed simulation framework and providing it to the research community, other colleagues may make use of these resources to examine other aspects of the complex world of social care policy.

One of the benefits of ABM in the case of social care is that it allows us to discover possible spillover effects that may arise due to a policy change, given its ability to explicitly model complex interactions between policies. Rolling out new policies is a slow, expensive and challenging process, as are revamping or retracting those policies in the event of unintended consequences; further, social care policy is of significant concern to millions of households, so policy-makers need to be confident that the policies being considered will not produce negative outcomes. Being able to test policies in simulation and uncover any spillover effects in advance could help policy-makers to avoid significant and costly problems after implementation. By experimenting with novel policies in the model, policy makers are able to assess which policies are best suited to tackle the problem of increasing unmet care need.

In future work, we will continue to refine this modelling framework to allow users to more easily construct policy scenarios for evaluation. We will enable the model to be adapted to other countries’ social care systems by replacing the map and the mortality/fertility rates, and by implementing new social care policies. We will also collaborate with social care policy experts and researchers to more accurately parameterise model processes, to the extent allowed by the data that is available. Once the simulation framework is fully mature, we will generate analyses of proposed real-world policy interventions directed at child and social care, both within the UK and elsewhere.