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Assessing the impact of forced and voluntary behavioral changes on economic-epidemiological co-dynamics
\subtitle{A comparative case study between Belgium and Sweden during the 2020 COVID-19 pandemic}
\email{[email removed]}
\affil[1]{\orgdiv{BionamiX}, \orgname{Department of Data Analysis and Mathematical Modelling, Ghent University}, \orgaddress{\street{Coupure Links 653}, \city{Ghent}, \postcode{9000}, \country{Belgium}}}
{ \noindentAbstract During the COVID-19 pandemic, governments faced the challenge of managing population behavior to prevent their healthcare systems from collapsing. Sweden adopted a strategy centered on voluntary sanitary recommendations while Belgium resorted to mandatory measures. Their consequences on pandemic progression and associated economic impacts remain insufficiently understood. This study leverages the divergent policies of Belgium and Sweden during the COVID-19 pandemic to relax the unrealistic -- but persistently used -- assumption that social contacts are not influenced by an epidemic's dynamics. We develop an epidemiological-economic co-simulation model where pandemic-induced behavioral changes are a superposition of voluntary actions driven by fear, prosocial behavior or social pressure, and compulsory compliance with government directives. Our findings emphasize the importance of early responses, which reduce the stringency of measures necessary to safeguard healthcare systems and minimize ensuing economic damage. Voluntary behavioral changes lead to a pattern of recurring epidemics, which should be regarded as the natural long-term course of pandemics. Governments should carefully consider prolonging lockdown longer than necessary because this leads to higher economic damage and a potentially higher second surge when measures are released. Our model can aid policymakers in the selection of an appropriate long-term strategy that minimizes economic damage.\\
}
During the covid-19 pandemic, governments faced the challenge of managing population behavior to prevent their healthcare systems from collapsing. Sweden adopted a strategy centered on voluntary behavioral changes based on sanitary recommendations ludvigsson2020 while Belgium resorted to mandatory measures luyten2021. Their consequences on pandemic progression and associated economic impacts remain insufficiently understood nigmatulina2009,buonomo2020,yan2021. This study leverages the divergent policies of Belgium and Sweden during the COVID-19 pandemic to relax the unrealistic -- but persistently used -- assumption that social contacts are not influenced by the epidemic's dynamics. We develop an epidemiological-economic co-simulation model where pandemic-induced behavioral changes are a superposition of voluntary actions driven by fear, prosocial behavior or social pressure bavel2020, and compulsory compliance with government directives. Our findings emphasize the importance of early responses, which reduce the stringency of measures necessary to safeguard healthcare systems and minimize ensuing economic damage. Voluntary behavioral changes lead to a pattern of recurring epidemics, which should be regarded as the natural long-term course of pandemics. Governments should carefully consider prolonging lockdown longer than necessary because this leads to higher economic damage and a potentially higher second surge when measures are released. Our model can aid policymakers in the selection of an appropriate long-term strategy that minimizes economic damage.
Overview The epinomic models of Belgium and Sweden consist of three connected submodels: 1) A spatially explicit compartmental disease transmission model for sars-cov-2 with recurrent mobility and seasonal forcing of the transmission rate alleman2023a. 2) A dynamic production network model based on input-output tables with a relaxed Leontief production function and hiring and firing of workers, used to quantify the impact of supply and demand shocks on employment and gross output, inspired by Pichler et al. pichler2022 and validated for Belgium alleman2023c. 3) A collective memory feedback model to incorporate “voluntary" behavioral changes, making the present number of social contacts and consumption patterns dependent on the history of covid-19 hospitalizations. The collective memory feedback model is inspired by previous work on the application of control theory to pandemic response alleman2020, as well as the works of Ronan et al. ronan2021 and Nigmatulina and Larson nigmatulina2009. The model was implemented using our in-house simulation software for $n$-dimensional pySODM alleman2023b.\\
As schematically shown in Figure (ref), the epinomic model has four inputs: 1) The shocks to investments and exports, which evolve exogenously in accordance with trade data for Belgium and Sweden (Appendix (ref)). 2) The prohibition of an economic activity (Table (ref)), from hereon referred to as “sector closure", 3) The obligation to work from home in a given economic activity. 4) The prohibition of leisure contacts in the private sphere. The collective memory feedback model, incorporating the “voluntary" behavioral changes requires no external inputs, but its parameters have to be calibrated (Appendix (ref)). At every timestep, the production network submodel and dynamic transmission submodel exchange information. We model the impact of laid-off employees on sars-cov-2 spread by using the (sectoral) labor compensation obtained from the production network model to compute the reduction of workplace contacts. We also model the impact of symptomatic covid-19 on labor supply and household demand, as symptomatic individuals are less likely to go to work or attend leisure activities if they are sick vankerckhove2013. Our model keeps track of three output variables: 1) The gross economic output, 2) labor compensation, and 3) the regional hospital load. Because simulated trends in gross economic output and labor compensation are similar, we restrict our attention to labor compensation. The model is presented in full detail in Appendix (ref).\\
The definition of voluntary and forced behavioral changes In this work, “voluntary" behavioral changes are a black box encompassing all behavioral changes that result from awareness to sars-cov-2, including sanitary recommendations, fear, prosocial behavior, and social pressure bavel2020. Awareness can be spread by individuals, scientific institutes, and governments. Opposed, “forced" behavioral changes are the result of enforcement by law and are thus always induced by governments. Behavioral changes in Sweden were predominantly “voluntary" according to our definition ludvigsson2020, although we do not imply the Swedish population's mentality during the 2020 covid-19 pandemic was as a “business-as-usual" one. We do not expect an uninformed or misinformed population to alter its behavior timely in response to an epidemic. Pressure to alter behavior increases as sars-\textsc{c}o\textsc{v}-2 incidence surges, blurring the line as “voluntary" behavioral changes may eventually be perceived as “forced". Opposed to Sweden, Belgian policies were predominantly “forced", hence our choice to compare these countries in a case study.\\
Collective memory feedback model A collective memory feedback model is used to incorporate “voluntary" behavioral changes by making the present number of social contacts and consumption patterns dependent on the history of covid-19 hospitalizations. As its input, the collective memory feedback model uses the hospital load obtained from the disease transmission model. To mimic the exponentially decaying nature of an individual's memory white2001, on every timestep, we add the hospital load in every spatial patch (Swedish county or Belgian province) to a six-month-long “memory" which we then weigh degressively using a negative exponential function with a mean lifetime of $\nu$ days ronan2021. To account for the fact that awareness of local surges in sars-cov-2 spreads spatially, we model the Exponential Moving Average (EMA) hospital load in every spatial patch $g$ as a connectivity-weighted average (Fig. (ref)) between the EMA hospital load on spatial patch $g$ and the EMA hospital load on the spatial patch with the maximum hospital load nigmatulina2009. In this way, we allow awareness to \textsc{sars}-\textsc{c}o\textsc{v}-2 induced by a local epidemic to spread nationally, arguably due to coverage in national media and government communication. To take into account the detrimental impact of a healthcare system (HCS) collapse, which we assume happens when the maximum number of available IC beds has been surpassed, we normalize the EMA hospital load with the number of IC beds available in both countries. We then translate the “perceived" hospital load in every spatial patch to a behavioral change, bound between zero and one, by means of a two-parameter Gompertz function. We model three behavioral changes: 1) A decrease in the per-contact effectivity to spread \textsc{sars}-\textsc{c}o\textsc{v}-2 as awareness rises with increasing hospital loads alleman2021, 2) a voluntary reduction in leisure activities, both privately and publicly, as the hospital load increases google_mobility,alleman2021, 3) a voluntary reduction in workplace contacts as the hospital load increases, first through workers voluntarily working from home and eventually due to absenteeism google_mobility,alleman2021.\\
By using an EMA of the hospital load as the input to our Gompertz behavioral response model, a delay is introduced compared to the actual hospital load (Fig. (ref)a). In the upward phase of an epidemic, individuals underestimate their likelihood of contracting the disease because of “optimism bias", and hence, the initial voluntary response will likely be too slow bavel2020. In the downward phase of an epidemic, there is a tendency to prolong measures longer than needed alleman2023a. The introduced delay thus results in the incorporation of favorable dynamics in the model. The time lag makes the voluntary behavior changes irreversible, introducing “hysteresis" in the trajectory of the epidemic liu2016,lacitignola2021. The Gompertz behavioral model and phase trajectory of the voluntary behavioral change are shown in Figure (ref) (b), while the time course of the voluntary behavioral change is shown in Figure (ref) (c). A mathematical description of the collective memory feedback model can be found in Appendix (ref).\\
Disease transmission model The compartmental structure and parameters of the disease transmission model for sars-cov-2 used in this work are similar to our previously developed model alleman2023a. A flowchart depicting the various compartments of the sars-co\textsc{v}-2 model used in this work is shown in Fig. (ref). The model incorporates pre-symptomatic transmission and asymptomatic transmission of \textsc{sars}-\textsc{c}o\textsc{v}-2, and accounts for different \textsc{covid}-19 severities, ranging from asymptomatic disease to death. Waning of antibodies (seroreversion) is included, and we have previously demonstrated the model and its parametrization adequately captures the seroprevalence in the Belgian population during the 2020-2021 \textsc{covid}-19 pandemic alleman2021,alleman2023a. Every disease compartment is stratified into 17 five-year age categories to account for the fact that social contact and disease severity differ substantially with age. Inspired by Haw et al. haw2022, we analyzed the 2012 social contact survey by B\'eraud et al. beraud2015 in metropolitan France to construct contact matrices because it is the only (large-scale) study that includes sector-specific information of respondents (Appendix (ref)). The model is further stratified into 21 counties for Sweden (Fig. (ref)) and 11 provinces for Belgium (Fig. (ref)) to account for spatial heterogeneity across the territories. Publicly available data on the daily number of commuters residing in spatial patch $g$ and working in spatial patch $h$ were used to quantify the inter-patch connectivity. The Belgian provinces are more strongly connected than the Swedish counties implying diseases will spread more readily and homogeneously across the Belgian territory (Fig. (ref)). We use the composition of the labor market to inform the number of social contacts in every spatial patch (Figs. (ref), (ref), (ref), (ref), (ref)). We use seasonal forcing on the transmission rate to fit the model to the epidemiological data of (more than) one year gavenciak2022,alleman2023a. We present a detailed overview of the disease transmission model in Appendix (ref).\\
Production network model The dynamic production network model is used to track the labor compensation and gross output for the 63 economic activities listed in the Nomenclature des Activit\'es \'Economiques dans la Communaut\'e Europ\'eenne (NACE) NACE. A detailed index of the 63 economic activities (sectors) is given in Table (ref) and an aggregation of 21 economic activities is given in Table (ref). The model uses the $63 \times 63$ input-output matrix of Belgium and Sweden to inform the intermediate flows of services and products in the country's domestic production networks. The economy uses intermediates and labor to satisfy the demand of two end users: households and other sources (government and non-profit consumption, investments, and exports). We model the changes in other demand exogenously using trade data for Belgium and Sweden obtained from various sources (Appendix (ref)). Household demand and labor supply evolve in function of government restrictions and voluntary behavioral changes. The gross output of sector $k$ is the sum of the intermediate consumption of its goods and services by all other sectors, household consumption, and exogenous consumption. Prices are assumed time-invariant and capital is not explicitly modeled. One representative firm is modeled for each sector and there is one representative household pichler2022.\\
Every firm keeps an inventory of inputs from all other firms and draws from these inventories to produce outputs. Intermediates in production are modeled explicitly as deliveries replenishing the firm's inventory. Due to shocks in household demand, exogenous demand, and labor supply caused by the epidemic, firms may run out of intermediate inputs and may need to stop production. Depending on their ability to meet demand, firms may also hire or fire workers. By using a survey on the criticality of inputs to production, it is possible to relax the Leontief production function, which assumes every intermediate input is critical to production pichler2022. For instance, the closure of restaurants during the covid-19 pandemic would restrain the output of construction companies, which is not realistic and leads to large exaggerations of economic damages. To the best of our knowledge, DAEDALUS by Haw et al. haw2022 does not include such a relaxed Leontief production function. Further, Haw et al. haw2022 make the limiting assumption that consumer demand does not evolve in response to the pandemic. We present a detailed overview of the production network model in Appendix (ref), a flowchart is available in Fig. (ref). We have previously implemented the model of Pichler et al. pichler2022 and found its projections are in excellent agreement with data on B2B transactions, surveys on revenue and employment, as well as GDP data, made available by the Belgian National Bank alleman2023c. We further found the model economy to be more sensitive to shocks in the supply of labor than to shocks in household demand. We present a detailed overview of the production network model in Appendix (ref).\\
Empirical data and policies For both countries, time series on the evolution of the (regional) hospitalization incidence, gross domestic product, and employment are publicly available socialstyrelsen2023,sciensano2023,scb2023b,nbb2023a,ermg2021,scb2023a. During 2020, Belgium and Sweden faced a similar pattern of two sequential sars-cov-2 epidemics with a period of less circulation in between them during summer (Fig. (ref)). Belgium faced both greater surges in covid-19 hospital incidence and greater economic damage than Sweden. During 2020, Belgium faced a 13.4 % decline in GDP while Sweden only faced a 3.1 % decline. Especially during the first covid-19 epidemic in the second quarter of 2020, Belgium was much more severely struck, with a 29.2 % decline in GDP while Sweden only faced an 8.5 % decline. Labor compensation, which was partly furloughed by both governments, faced a similar decline during 2020 of 4.3 % in Sweden and 12.2 % in Belgium (Table (ref)). The economic impact of the second \textsc{covid}-19 surge and lockdown in Belgium is more pronounced than in Sweden. \\
The governments of Belgium and Sweden imposed very different measures to counter the spread of sars-cov-2. The Belgian government forced behavioral changes by imposing two lockdowns (Fig. (ref)) which involved the mandatory closures of many economic activities, distance learning, and restrictions on private leisure contacts luyten2021. In contrast, Sweden responded earlier, at a hospital incidence of 0.2 instead of 0.6 patients per \num{100000} inhabitants, relied mostly on voluntary sanitary recommendations, and was able to keep most of its schools open for children up to the age of 16 ludvigsson2020. Only on January 7, 2021, did the Swedish government impose restrictions in restaurants and commercial areas, household quarantine, and the obligation to wear facemasks on public transport ludvigsson2023. From the start, the Swedish strategy was aimed at mitigation, while the Belgian policy was aimed at suppression.\\
Calibration procedure The values of 12 model parameters are a priori unknown and are calibrated using epidemiological and economic data from Belgium and Sweden (Table (ref)). We fit the parameters to data from both countries simultaneously as fitting our model parameters to both countries separately would not yield a valid basis for comparisons. We implemented the government-mandated policies imposed during the 2020 covid-19 pandemic in Belgium and Sweden as realistically as possible (Tables (ref) and (ref), Fig. (ref)). In addition to the 12 model parameters, the initial condition that resulted in the observed initial spatial spread of sars-cov-2 in Belgium and Sweden was unknown. We used an iterative optimization procedure in which the initial condition and parameters were calibrated sequentially. For Sweden, the strongest seed was located in the Stockholm metropolitan area, and to a much lesser extent J\"onk\"oping. Keeping the initial condition fixed, we used the obtained estimates of the 12 parameters to start the affine-invariant ensemble sampler for Markov Chain Monte Carlo (MCMC) goodman2010,emcee2013. The calibration procedure and its results are described in detail in Appendix (ref). In Figure (ref), we present a comparison between the model realizations and the empirical data. In Table (ref), we compare the observed and modeled reductions of gross aggregated output and labor compensation at the quarterly temporal level. Our model is able to capture the long-term epidemiological and economic trends in two countries using one calibrated set of parameters justifying its use in modeling counterfactual scenarios.
Scenario 1: How does the timing of restrictions influence the strictness needed to safeguard the Belgian healthcare system? \\
We define four possible policy interventions for the Belgian government to impose on three dates: March 12, 2020, March 15, 2020, and March 18, 2020 (Table (ref)). We then gradually release the measures over a two-month period starting on May 4, 2020, as happened in reality. We set our model up to replicate the 2020 covid-19 pandemic in Belgium. We use the calibrated initial condition for Belgium, we include seasonal forcing on the transmission rate, we distinguish between regular weeks and holiday weeks, and we impose shocks to investments and exports to replicate the 2020 covid-19 pandemic in Belgium. These scenarios will allow us to assess the epidemiological and economic impact of four policy alternatives ranging from very strict to completely voluntary. Additionally, we can gauge if voluntary recommendations, as used in Sweden, would have worked in Belgium.\\
Scenario 2: How does the timing of releasing lockdown affect the subsequent resurgence of hospitalizations? \\
We now set up our model without seasonal forcing on the transmission rate, we do not distinguish holidays and we impose no shocks to investments and exports, thus no references to events from the 2020 covid-19 pandemic are made. We assume the first infected individuals are located in Stockholm County and Brussels in Sweden and Belgium respectively. We start the simulation with an $R_0=3$ and trigger awareness to sars-cov-2 and a government intervention. The date of the intervention is chosen so that the peak hospital incidence of the first sars-co\textsc{v}-2 epidemic is (quasi) equal to the nominal number of IC beds available in both countries. The government intervention is assumed to be equal to the lockdown measures taken by the Belgian government during the first 2020 \textsc{sars}-\textsc{c}o\textsc{v}-2 epidemic (Table (ref), policy P1). We then release the imposed measures after 2, 3, 4, and 5 months and observe the impact on the IC load during the next year.\\
Scenario 3: How does adjusting social contacts based on the history of the hospital load influence an epidemic's dynamics? \\
We set up our epinomic model without seasonal forcing on the transmission rate, without distinguishing holidays, and without imposing shocks to investments and exports so no references to events from the 2020 covid-19 pandemic can be made. Additionally, we do not incorporate any government measures and assume the simulation starts with an $R_0=3$ and general awareness to sars-cov-2 already triggered. We assume the first infected individuals are located in Stockholm County and Brussels in Sweden and Belgium respectively. We simulate the model while varying the mean lifetime of the population's collective memory ($\nu$; Eq. (ref)), which is a key parameter governing how much weight people give to past hospital loads when making decisions in the present (Fig (ref)a). We simulate the model for two years using three values of $\nu$: 7, 28, and 62 days. During the model's calibration, a mean lifetime of $\nu=20.8\ \text{d.}$ (Table (ref)) was obtained.\\
Scenario 4: What would have been the impact of multiple points-of-entry of sars-cov-2 in Sweden and Belgium during the March 2020 covid-19 surge? \\
In Sweden, sars-cov-2 seems to have spread mostly from the Stockholm metropolitan area, and to a much lesser extent from J\"onk\"oping, where the first case was detected on January 31, 2020 krisinformation2020 (Appendix (ref)). Our aim is to exploit the spatially explicit nature of our epinomic model to study how multiple points-of-origin of sars-cov-2 would have impacted the course of the first \textsc{covid}-19 epidemic in 2020. We once again set up our epinomic model without seasonal forcing on the transmission rate, without distinguishing holidays, and without imposing shocks to investments and exports. We assume the epidemic is seeded by two individuals infected with \textsc{sars}-\textsc{c}o\textsc{v}-2. We assume the first infected individual is always located in Stockholm and Brussels for Sweden and Belgium respectively. The second infected individual is placed in every other Swedish county or Belgian province, so we simulate 20 and 10 trajectories for Sweden and Belgium respectively. We start the simulation with $R_0=3$, we trigger general awareness to \textsc{sars}-\textsc{c}o\textsc{v}-2 at a hospital incidence of 0.2 patients per \num{100 000} inhabitants. The threshold was computed by interpolating the weekly hospital incidence data by Socialstyrelsen socialstyrelsen2023 to March 11th, 2020, corresponding to day the first sanitary recommendations were issued ludvigsson2020. We simulate the model for 150 days, resulting in an epidemic trajectory similar to the actual first \textsc{covid}-19 epidemic in Sweden and Belgium ludvigsson2020,stralin2021,sciensano2023.\\
Scenario 1: Responding late necessitates restrictions with higher economic damages \\
An early response reduces the stringency of measures necessary to safeguard the Belgian HCS and minimizes ensuing economic damage (Figs. (ref) and (ref), Table (ref)). Regardless of the date measures are imposed, economic damages are the smallest for policy P4a (mandated telework). If policy P4a had been imposed on March 3, 2020, the cumulative number of IC patients in the second quarter of 2020 would have been identical to policy P1 implemented on March 15, 2020, but the gross aggregated output would have fallen by only 12.2 % instead of 24.0 % (Table (ref)). Stricter measures are more effective at countering the epidemic trend than voluntary measures. Indeed, implementing policy P1 over P2 or P3 has diminishing epidemiological gains but results in much more economic damage (Table (ref)). However, the scope of the epinomic model presented in this work is too limited to adequately balance public health and the economy, as reductions in labor income and the occupied number of IC beds are only two of several societal costs of the covid-19 pandemic. To address this important limitation, we should transform the model into a whole-of-society modeling framework to quantify the foremost damages to the population’s health and the economy.\\
The cost of policies P1, P2, and P3, which involve economic closures, is almost identical, regardless of the date the measures are imposed, whereas the cost of mostly voluntary policies P4a and P4b increases when measures are taken late. Opposed to policies P1, P2, and P3, policies P4a and P4b in themselves incur no direct economic shocks, but as the hospital load increases, individuals will voluntarily start avoiding activities outside the house, as was observed in Sweden yarmolMatusiak2021. On March 18, 2020, the implementation of voluntary policies P4a and P4b can incur more damage to gross output and employment than policy P3, in which only accommodation, recreation, and activities of membership organizations (e.g. religious gatherings) are closed (Fig. (ref)).\\
Voluntary recommendations, as given by the Swedish government, and implemented on March 15, 2020, had likely not succeeded in safeguarding the Belgian HCS. However, the Belgian government reacted later than the Swedish government, triggering measures at a hospital incidence of 0.6 and 0.2 patients per \num{100000} inhabitants respectively. Imposing the obligation to work from home (P4a), or a milder lockdown (P3) just three days earlier on March 12, 2020, could have sufficed to safeguard the Belgian HCS. As compared to scenario P1 imposed on March 15, 2020, the cost of furloughing for policies P3 and P4a implemented on March 12, 2020, would have been 14.0 billion euros and 16.3 billion euros, or 2.7 % and 3.1 % of Belgian GDP lower (2019 prices). The best way to minimize damages is thus by acting timely, a finding consistent with our previous review vandepitte2021. Consequently, we recommend policymakers to implement measures earlier rather than later.\\
Scenario 2: Prolonging lockdown increases economic damage and can lead to increased strain on the HCS when measures are released\\
In Fig. (ref) we demonstrate the impact of prolonging lockdown under low sars-cov-2 incidences after an initial covid-19 surge in Belgium and Sweden. When releasing lockdown after 2 months, we observe no divergence in the number of occupied IC beds in the first month post-relaxation compared to maintaining the lockdown. Prolonged restrictions lead to a higher peak incidence in the second covid-19 surge, potentially straining the HCS. Maintaining lockdown results in only a small decline in IC patients but significantly higher economic damages (Fig. (ref), Table (ref)). Overall, sustaining restrictions appears to carry more risks and costs than benefits. However, our epinomic model's scope is currently too limited to comprehensively balance public health and the economy.
By prolonging restrictions “forcefully" after the initial surge, sars-cov-2 incidence gradually decreases. However, this approach risks erasing the urgency associated with the past covid-19 wave from collective memory, leading society to desire a return to 'normal' life, even if not permitted by the government. Easing restrictions suddenly results in a sharp rise in social contacts, potentially causing a worse second covid-19 surge, as happened in Belgium luyten2021. Based on our simulations, releasing lockdown measures early and gradually is preferred over releasing measures late and suddenly. Prolonging restrictions in pursuit of a “crush-the-curve" (suppression) strategy will inevitably result in increasing friction between the government and the population, with increasing pressure to relax measures. Given that both Belgium and Sweden never managed to eliminate sars-\textsc{c}o\textsc{v}-2 completely from their territories during the entire pandemic, and the efficacy of testing, tracing, and quarantine was insufficient to control \textsc{sars}-\textsc{c}o\textsc{v}-2 kucharski2020, we have herein implicitly presented an argument against a suppression strategy. Before pursuing such a strategy, epidemiologists and policymakers should carefully consider whether the virus can be realistically controlled at low prevalence using testing, tracing, and quarantine or fully eliminated without the chance of re-importation.\\
Scenario 3: Making social contacts dependent on the hospital load's history introduces oscillations in the epidemic dynamics \\
Making the number of social contacts dependent on the history of the hospital load introduces oscillations in the system's dynamics (Fig. (ref)). Every time the hospital load surges, individuals adjust their behavior and make fewer contacts, which in turn lowers the effective reproduction number, as such curbing the epidemic. Because we feed back an exponentially weighted average hospital load to compute the behavioral change, we introduce a time lag in an individual's response (Fig. (ref)a). Hence, after the epidemic is curbed, individuals will not immediately make more contacts, gradually lowering sars-cov-2 incidence further. Eventually, the first surge will fade from the collective memory, restarting the cycle. A pattern of re-emergent hospitalization waves should be regarded as the natural long-term course of a pandemic and should be accounted for by epidemiologists and policymakers looking to manage a pandemic.
In Fig. (ref) we demonstrate the impact of varying the length of this collective memory, defined by the memory's mean lifetime $\nu$. Larger values of $\nu$ imply individuals assign more weight to the history of the hospital load in their present decision-making, which results in slower behavioral adjustments. Increasing the memory's mean lifetime results in low-frequency, high-amplitude oscillations while lowering the memory's mean lifetime results in high-frequency, low-amplitude oscillations. For $\nu=7~\text{days}$, we observe an endemic equilibrium at $\approx50\%$ of the nominal IC bed capacity available in both countries. The emergence of such an endemic equilibrium with oscillatory dynamics is consistent with the model of Ronan et al. ronan2021. Changing the memory's mean lifetime does not seem to alter the dynamic equilibrium of the system, only the frequency and amplitude of the oscillations. We intend to study the properties of the dynamic equilibrium in future research. Keeping the mean lifetime short minimizes the system's oscillations, rendering it more easy to control. However, translating this shorter mean lifetime into practical advice is challenging. An important limitation of the collective memory feedback model is the absence of a temporal delay caused by the process of collecting, interpreting and communicating the daily hospital incidence, whose influence will likely destabilize the system, which will be addressed in future work.\\
Scenario 4: Sweden may be more resilient to the spread of sars-cov-2 than Belgium but its economy is not - Why Sweden may have been fortunate \\
In Fig. (ref), we exploit the spatially explicit nature of our epinomic model to demonstrate the difference between having a sars-cov-2 epidemic that spreads from a single point-of-origin (black) versus two points-of-origin (gray). In Belgium, having two points-of-origin, and thus a more spatially uniform initial spread of sars-cov-2, results in more occupied IC beds as compared to having a single point-of-origin for seven out of ten provinces. In contrast, in Sweden, this results in a considerably lower number of occupied IC beds in 17 out of 20 counties. From an epidemiological point-of-view, the Swedish territory thus seems more robust to the spread of \textsc{sars}-\textsc{c}o\textsc{v}-2 than Belgium's. \\
Most notable for Sweden is the effect of seeding one infected individual in Stockholm and the other in the counties of Skåne or Västra Götaland, which are Sweden's number two and three counties in terms of population density, as well as containing Sweden's number two and three largest cities, Malmö and Göteborg. If the epidemic had simultaneously been seeded in either county, the resulting epidemic could have surpassed the nominal IC bed capacity by 22 %. On the other hand, if the epidemic had been seeded in the much more sparsely populated V\"armland, the epidemic would likely have been much smaller. In Belgium, no relationship exists between the population density of the second individual's seed province and the maximum impact of the resulting sars-cov-2 epidemic on the occupied number of IC beds and the reduction in labor income (Fig. (ref)). In Sweden, seeding the epidemic in more sparsely populated areas results in fewer occupied IC beds but more economic damage (Fig. (ref)). This is caused by the way we model the spatial spread of awareness to sars-cov-2. Indeed, if the epidemic is seeded in a more rural area, the ensuing surge will overwhelm local HCS capacity, even though its absolute magnitude is small. Similar to the early March 2020 \textsc{covid}-19 surge in Bergamo, Italy, images of overcrowded hospitals will make it into (inter)national media, raising awareness to \textsc{sars}-\textsc{c}o\textsc{v}-2 as such resulting in voluntary behavioral changes cereda2021. The result is a smaller overall epidemic but larger economic damage due to reductions in consumption outside the impacted county. The Swedish territory, which is much larger, more sparsely populated, and less connected than Belgium's, therefore lends itself more to a strategy of voluntary recommendations. However, Swedish policymakers should be wary of pursuing such a strategy during future epidemics. If \textsc{sars}-\textsc{c}o\textsc{v}-2 had simultaneously reached Sweden from Denmark at Malmö in March 2020, a counterfactual scenario that is not unimaginable at all, there could have been an acute IC bed shortage during the first \textsc{covid}-19 surge. Instead, based on the counterfactual scenarios for Belgium (Fig. (ref)), mandating work-at-home (policy P4a) would result in less \textsc{sars}-\textsc{c}o\textsc{v}-2 circulation without inducing economic shocks, thus being the least disruptive alternative policy.
We developed an economic-epidemiological co-simulation model to explore the impact of voluntary and forced behavioral changes on pandemic progression and its associated economic impacts. Leveraging the divergent policies in Sweden and Belgium, alongside their respective epidemiological and economic outcomes, we calibrated our model and set up several scenarios to showcase the impact of behavioral changes in pandemic management. Our findings emphasize the importance of early responses, which reduce the stringency of measures necessary to safeguard healthcare systems thereby minimizing ensuing economic damage. Early and voluntary reactions seem better than late and forced ones. However, we demonstrated that Sweden's sparsely populated and poorly connected territory may be better suited to a strategy based on voluntary recommendations than Belgium's small, urban, and highly connected territory. Making present voluntary behavioral changes dependent on past hospitalizations introduces fluctuations in the system's dynamics. Re-emergent surges due to behavioral changes should be regarded as the natural long-term course of a pandemic. We also demonstrated that prolonging lockdown after an initial surge leads to higher economic damage and a potentially higher second surge when measures are released. Before pursuing such a strategy, consideration should be given to the possibility of controlling the virus at low incidences using testing, tracing, and quarantine, or fully eliminating the virus without the chance of re-importation. Our adaptable model offers valuable insights for policymakers aiming to minimize economic damage while managing long-term pandemics effectively.
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\bmhead{Availability of Data and Code}
The source code of the model is freely available on GitHub: \url{https://github.com/twallema/pyIEEM}. The model is implemented using our in-house code for simulating $n$-dimensional dynamical systems in Python 3 named pySODM alleman2023b. All data used are publicly available.
\bmhead{Supplementary information}
This work contains supplementary information on the (geospatial) differences in demography, recurrent mobility, and employment between Belgium and Sweden (Appendix (ref)). An index of economic activities in the Nomenclature des Activit\'es Economiques dans la Communaut\'e Europ\'eenne (NACE) Rev. 2 (Appendix (ref)). The analysis of the contact survey by B\'eraud et al. beraud2015 (Appendix (ref)). A detailed mathematical description of the epinomic model presented in this study (Appendix (ref)). An overview of the model's limitations and assumptions (Appendix (ref)). A detailed description of the epinomic model's calibration to empirical data (Appendix (ref)). A sensitivity analysis of the collective memory feedback model's parameters, in support of the detailed mathematical description of the model (Appendix (ref)). Supplementary results not included in the main text (Appendix (ref)).
\bmhead{Author contributions}
Tijs W. Alleman: Conceptualization. Methodology. Formal Analysis. Software. Writing – original draft. Writing – review & editing. Funding acquisition. Jan M. Baetens: Conceptualization. Writing – review & editing. Supervision. Project administration. Funding acquisition.
\bmhead{Acknowledgements}
The authors would like to thank Ruben Savels (Ghent University), Tim Van Wesemael (Ghent University), Michiel Rollier (Ghent University), Veerle Vanlerberghe (Institute of Tropical Medicine Antwerp), and Prof. Koen Schoors (Ghent University) for proofreading the manuscript. We would like to extend our gratitude to Prof. Philip Gerlee (Chalmers University of Technology) for proofreading the manuscript and providing us with more insights on the Swedish 2020 covid-19 pandemic. This work was financially supported by Crelan, the Ghent University Special Research Fund, by the Research Foundation Flanders (FWO), Belgium, project numbers G0G2920N/3G0G9820, and, by VZW 100 km Dodentocht Kadee, through the organization of the 2020 100 km COVID-Challenge.
\bmhead{Conflict of interest} The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The funding sources played no role in study design; in the collection, analysis, and interpretation of data; in the writing of the report; and in the decision to submit the article for publication.