Reducing the Smoking-Related Health Burden through Diversion to Electronic Cigarettes: A System Dynamics Simulation Study

Background: Electronic cigarettes (“e-cigarettes”) have altered nicotine use trends, and their impacts are controversial. Given their reduced risk prole relative to conventional cigarettes, e-cigarettes have potential for harm reduction. The current study presents a simulation-based analysis of an e-cigarette harm reduction policy. Methods: A system dynamics simulation model was constructed, with separate aging chains for cigarette smokers and e-cigarette users. These structures work together with a policy module to close the gap between actual (simulated) and a goal number of cigarette smokers, chosen to reduce the nicotine-attributable death rate to the accidental death rate. The policy is two-fold, rst removing existing regulations on e-cigarettes (e.g. avor bans) and second providing an informational campaign promoting e-cigarettes as a lower-risk alternative. Realistic practical implementation challenges are modeled in the policy sector, including time delays, political resistance, and budgetary limitations. Effects of e-cigarettes on conventional smoking occurs through three mechanisms: 1) diversion from ever initiating conventional smoking; 2) reducing smoking behavior and thus progression to established smoking; and 3) increasing smoking cessation. An important unintended effect was included, which increases the nicotine-related mortality accordingly with an increase in nicotine users due to e-cigarettes. Results: The base-case model replicated the historical exponential decline in conventional cigarette smoking and the exponential increase in e-cigarette use since their introduction circa 2010. The ideal-case policy was able to reduce conventional smoking to the goal level approximately 40 years after implementation. Policy scenarios that included realistic, practical obstacles to implementation delayed and weakened the effect of the policy by up to 95% in the worst case, relative to the same time point in the ideal-case scenario; however, these discrepancies substantially decreased over time in dampened oscillations. Conclusions: Current ndings demonstrate that the promotion of e-cigarettes as a harm-reduction policy is a viable strategy, given current knowledge of e-cigarettes’ effects on conventional smoking. Given the strong effects of implementation challenges on policy effectiveness in the short term, accurately modeling such obstacles is essential in policy design. Ongoing research is needed with forthcoming data on e-cigarette use prevalence and possible effects on cigarette smoking.


Introduction
Cigarette smoking is a causal factor in a wide range of adverse health effects including cancers virtually anywhere in the body, cardiovascular disease, diabetes, macular degeneration, birth defects, rheumatoid arthritis, in ammation, and impaired immune function (1). Through a combination of public policy (e.g. cigarette taxes, age restrictions on purchasing, and bans on advertising to youth) and increased public awareness of the health dangers of smoking, the US has had success in drastically reducing the smoking prevalence over the past several decades, from 42% in 1965 to about 16% currently (1); however, recent years show this reduction hitting a plateau (2). As a result, reductions in smoking-related morbidity and mortality have stagnated, and cigarette smoking remains the primary cause of preventable death and disease in the US (1).
Adverse health outcomes attributable to smoking are primarily tied to combustible elements of conventional cigarettes (3,4) as well as tars and arsenic (5). For example, lung cancer is perhaps the most well-known health risk of cigarette smoking, and despite reductions in smoking prevalence, the incidence of lung cancer has remained high (incidence rates of 100 per 100,000 in 1980, with only a slight reduction to 70 cases per 100,000 in 2010) (1). Even more concerningly, cigarettes seem to be becoming deadlier over time: despite the declines in smoking prevalence, lung cancer incidence as well as mortality has increased, particularly adenocarcinoma. The increased cancer burden is thought to be due to changes in the composition and processing of cigarettes (1). Additionally, cigarettes cause a wide range of other health effects beyond lung cancer, including other cancers, respiratory diseases, cardiovascular diseases, diabetes, and immune disorders (1).
Although nicotine is the major, but not only addictive component in cigarettes (6), nicotine itself is not much more harmful than caffeine (5) as evidenced by low risk pro les of nicotine replacement therapy (NRT) products such as nicotine patches and gum (5). Given the vastly different risk pro le of nicotine alone vs. other components in cigarettes, a great deal of harm reduction can be achieved by encouraging smokers to transition away from conventional cigarettes to other nicotine products (5). Though some tobacco control advocates including the US Surgeon General argue for heavily regulating all nicotine products (7), studies supporting the "hardening hypothesis" (2,8,9) raise doubts that nicotine use can be eliminated entirely. That is, the population of smokers today have higher levels of nicotine dependence (2,8) and higher rates of mental health comorbidities (9), relative to in the past, suggesting that today's smokers are the remaining "hardened" group who face greater di culties in smoking. For example, over 60% of individuals suffering from schizophrenia smoke, which maybe be due to self-medication of their symptoms with nicotine (10). Taken together, diverting users to other sources of nicotine is a valid and likely effective harm reduction strategy.
Electronic cigarettes (e-cigarettes) are an alternate tobacco product that electronically heats nicotine liquid into vapor, and thus lacks the harmful combustible elements of conventional cigarettes (11). Ecigarettes rst appeared on the market around 2010, and have continually increased in popularity since then, resulting in more of today's youth using e-cigarettes than conventional cigarettes. Though long-term health data on e-cigarettes will not be available for some time, they are estimated to be only 5% as harmful as conventional cigarettes (11) and thus represent an important and appealing harm reduction alternative (5). Many established smokers use e-cigarettes to offset or quit conventional smoking (12)(13)(14)(15), and despite not being approved for this purpose by the Federal Drug Administration in the US, ecigarettes may be more effective than NRT for cessation (16).
A special consideration in smoking harm reduction is adolescents who are nicotine-naïve. Though recent research supports e-cigarette use as a harm reduction method among established, nicotine-dependent smokers who have di culty quitting (17), much literature has encouraged restricting youth access to and interest in e-cigarettes, for example via avor bans (18,19). The motivation for restricting adolescent ecigarette use stems from fears of e-cigarettes acting as a "gateway" to tobacco use, including conventional cigarettes (20,21). Evidence for the gateway mechanism includes e-cigarette users being at much higher risk for subsequent conventional smoking relative to nonusers (21,22); however, these adolescents have pre-existing risk factors that predisposed them to smoking, suggesting they would have gone on to use conventional cigarettes anyway (23,24). Population trend modeling studies have also raised doubts about a gateway effect, as declines in conventional smoking among youth have accelerated after the appearance of e-cigarettes (25,26). This suggests a possible "primary prevention" effect of e-cigarettes, which has been understudied (27) but is supported by recent studies showing that e-cigarettes may be diverting adolescents from ever using conventional cigarettes (28,29).
The current study tests a harm reduction policy of promoting e-cigarette use in order to divert current or would-be smokers away from conventional cigarettes, using system dynamics simulation modeling. The focus of this model is on adolescents, as smoking habits are almost always established during teen years; thus focusing tobacco control efforts on this age group is the most e cient way to reduce the population health burden of smoking (30). System dynamics modeling is used to rst replicate historical trends in youth use of cigarette and e-cigarette use, and then to project trends into the future under a base-case scenario and a policy scenario. The policy acts through two mechanisms: removing existing avor bans on e-cigarettes, and a public health marketing campaign promoting e-cigarettes as a lowerrisk alternative to cigarettes. Effects of this policy on the model are threefold: 1) diverting nicotine-naïve adolescents from ever using conventional cigarettes; 2) reducing conventional smoking behavior among existing smokers; and 3) increasing the cessation rate of conventional cigarettes. The model was calibrated using data from the US National Youth Tobacco Survey (NYTS). Long-term outcomes of cigarette smoking prevalence are examined as a function of different policy variants.

Causal Loop Diagram
A causal loop diagram showing the minimal essential set of relationships describing cigarette use, ecigarette use, their hypothesized relationship between them, and the policy under examination is shown in Fig. 1. This conceptual diagram guides the development of the subsequent simulation model (see below). The causal loop diagram shows primarily feedback loops, either positive/reinforcing (whereby a change in one variable accelerates its own future change through the chain of causal relationships) or negative/balancing (whereby a change in one variable limits its own future change).
Loop B1 and B2 describe the central dynamic in this model: that established cigarette use leads to an unacceptable number of preventable deaths (relative to some goal); this motivates a harm reduction policy, which in this case is twofold: 1) implementing an informational campaign which promotes ecigarettes as a less risky alternative to cigarettes; and 2) removing existing restrictions on e-cigarette purchasing (here, avor bans that are in place in many places). This in turn increases e-cigarette initiation. Increasing e-cigarette initiation has 3 intended effects: 1) decreasing the cigarette progression rate by offsetting of cigarettes with e-cigarettes (B1), 2) reducing the initiation rate by diversion away from conventional cigarettes (B3), and increasing the smoking cessation rate (B4). An important unintended consequence is also included: progression to established e-cigarette use will increase the preventable deaths (though not as much as conventional cigarettes), which can counteract the policy to some degree (R1).

Stock-and-Flow Diagram
Based on the CLD above, a stock-and-ow diagram (Fig. 2) was constructed in Stella Architect, version 1.9.5 (31), which consists of "aging chains" for both cigarette and e-cigarette use (a structure consisting of stocks in series, here representing different stages of use, with appropriate in ows and out ows, representing transition rates). The cigarette aging chain has three stocks: experimenters, established users, and former users; while the e-cigarette aging chain only has the rst two. Ex-e-cigarette users were intentionally excluded from the model because there is lack of available data on this group to calibrate parameters. Instead, a simplifying assumption was made (e.g. due to the hardening hypothesis) that once a person becomes an established e-cigarette user, they remain there for life. This is a conservative assumption (see Limitations). The ows from one stock to another are assumed to encompass two mechanisms: 1) a "social-recruitment" mechanism, in which the new initiation rate is positively affected by the proportion of established users; and 2) a "self-recruitment" mechanism in which there is a stable base of nicotine users regardless of usage in the population, consistent with the hardening hypothesis (2).
The two aging chains feed into the Goal-Gap of Nicotine Mortality Module), which calculates the discrepancy between the actual nicotine deaths (from cigarettes and e-cigarettes, based on the respective stocks of established users, as this is the relevant measure from a health perspective (32)) and a goal value. Since it is unrealistic to entirely eliminate nicotine-related related deaths, a goal value approximating the accidental death rate was chosen. The discrepancy in the actual vs. desired deaths in turn affects the policy implementation, as a much higher-than-desired nicotine-related death rate motivates regulatory policy.
The policy itself, captured in the Policy Implementation Module, consists of removing existing regulations (i.e. removing existing avor bans) as well as an educational campaign promoting e-cigarettes as a less harmful alternative. The effect of the policy is to increase the e-cigarette initiation rate, which has a 3pronged effect on the cigarette aging chain: increasing diversion away from conventional cigarette initiation, reducing smoking and thus progression rates to established use, and increasing smoking cessation. The Policy Implementation Module includes pragmatic considerations, such as political resistance to overturning a avor ban, and resources for implementing an informational campaign (both budgetary and workforce-related). The structure of this model allows for ideal, best-case scenarios (no resistance and su cient resources) as well as more realistic, limited scenarios through changing corresponding parameters (i.e. the likelihood of removing a avor ban; the proportion of required funding that is approved, and time delays). The overall policy is linked to a binary "switch" that can be turned on or off.
The model was run over the period 2000-2100, with e-cigarettes rst appearing around 2010, and the policy also being implemented in 2010. The detailed model structure and equations, including the modules, can be downloaded for free (33); the model can be opened and run using the free software isee Player (34).

Model Calibration
The model was calibrated to match the "behavior modes" (i.e. the fundamental shape of the trend, such as exponential growth or exponential decline) observed in youth cigarette and e-cigarette use in the US over the period 2000-2019 (most recently available data). Since this model is not intended to nely replicate historical behavior or provide precise future projections, calibration to a broad behavior mode was su cient. Some parameters were selected based on external data (e.g. lifetime probability of quitting cigarettes), while others were calibrated by running "live" simulations over a range of parameters to determine the optimal value with respect to stocks of established users (cigarettes and e-cigarettes), as these are the stocks relevant for public health. Stocks of established cigarette and e-cigarette users according to NYTS and other historical data show approximately goal-seeking behavior towards a plateau (based on the proportion who are self-recruiters), and exponential growth for established ecigarette use. Remaining parameters of ows (e.g. social contagion effect) were calibrated to achieve a reasonable match between simulated and historical data, based on the observed behavior mode and approximate magnitude (e.g. estimates of 46.5 million smokers in the US in 2000).

Model Validation
A range of validation tests were performed on the model, which identi ed errors that were corrected in the nal model. Boundary conditions were examined conceptually to determine which variables and causal relationships were included in the model. Parameter assessment was based on external data sources and calibration to observed data. Extreme conditions testing was conducted by setting in ows and initial values of stocks to 0 and very high values, and ensuring the model behaved reasonably (e.g. stocks do not fall negative).

Model Analysis
A base-case model was constructed to replicate approximate trends in cigarette and e-cigarette use among the general US population over 2000-2019, and projected into the future (year 2100). Several policy scenarios were run, including an ideal-world, best-case scenario (no practical obstacles to implementation), and scenarios where policy implementation is delayed, faces resistance (i.e. low likelihood of removing avor bans, due to controversy), and faces limited funding for an informational campaign. Speci cally, time delays for the best-case scenario were set to 0.1 years (for time to approve both policies, time to approve funding, and time to hire and train workforce) and 10 years (for workforce turnover rate); and in the time-delayed model, were set to larger values (time to approve removal of avor bans = 2, time to approve informational campaign = 1 year, time to adjust workforce = 1 year, time to train workforce = 0.25 years, and time to approve funding = 1 year). With respect to uncertainty in approving the removal of avor bans, probability of approval was set to 1 and 0.5 for the ideal-case and uncertainapproval scenarios, respectively. With respect to budgetary constraints, the fraction of required budget that is approved is set to 1 (full budget) and 0.7 in the ideal-case and budget-restricted scenarios, respectively. Additionally, the model is publicly available and can be run through a web interface, allowing users to vary policy implementation parameters and other assumptions of the model (e.g. the strength of diversion, smoking reduction, and cessation effects).

Results
The base model was able to successfully replicate the approximate behavior modes observed in historical data (Fig. 3), namely the slow, approximately exponential decline in established cigarette use over 2000-2019, and approximately exponential increase in established e-cigarette use from 2010-2019. Figure 4 shows the base-case simulation run through the year 2100, under the scenario of the status quo (no policy) and the ideal-case policy scenario relative to the goal number of established cigarette smokers (which increases over time with population growth). Under the status quo, the (simulated) number of established cigarette users declines, continuing the preexisting trend of exponential decline from 2000-2019; however, it remains higher than the target number. This persistent discrepancy leads to an unacceptably high number of preventable nicotine-related deaths throughout this time horizon. The idealpolicy scenario shows the policy (implemented in 2010) accomplishing its goal shortly after 2050, and subsequently showing some minor oscillations around that goal which is caused by delays in the implementation (e.g. workforce adjustment for the informational campaign). Figure 5 shows the e-cigarette initiation rates, since this is the ow being regulated by the policy. The desired initiation rate (i.e. the e-cigarette initiation rate required to achieve the policy goal) is shown against what is achievable within the practical constraints of the policy (e.g. time needed for potential ecigarette users to adjust their expectations) even if the policy were implemented with minimal delay, no political resistance, and full budgetary resources. The desired initiation rate is zero before 2010, as the policy is not yet implemented before then. The initial spike in desired e-cigarette initiation is due to the larger discrepancy between actual and desired cigarette users in 2010, and the sudden enactment of the policy. This then closes as the actual cigarette users approaches its goal. However, the achievable ecigarette initiation rate is slower and lacks the initial overshoot, as it takes time for potential users to adjust their expectations about e-cigarettes and convert to use. Around 2060, the sudden drop in the desired e-cigarette initiation rate corresponds a decline in e-cigarette users below the goal (see Fig. 4), with a lag due to the delay between e-cigarette initiation and the stock of conventional cigarette smokers, resulting in the harm reduction policy no longer being necessary to achieve this goal (e.g. it becomes unnecessary to continue the informational campaign). Figure 6 shows the ideal-case e-cigarette initiation rate (i.e. the achievable rate shown in Fig. 5) against more realistic scenarios that include time delays to policy implementation and/or uncertainty in removing avor bans and reduced budgetary resources for an informational campaign. For greater clarity, the time range displayed in the gure is 2010 (policy start date) through 2023. Compared to the ideal-case scenario, time delays in policy implementation produce a lagged response in e-cigarette initiation rates accomplished by the policy, which is most severe at rst, due to delay in policy approval. E-cigarette initiation rates then overshoots the ideal-case scenario while maintaining a discrepancy with the idealcase scenario, due to continuing delays in workforce adjustment related to the informational campaign. A scenario with time delays in addition to uncertain approval of removing avor bans shows similar behavior, with less overshoot in e-cigarette initiation rates relative to the ideal case. A scenario with time delays in addition to budgetary constraints shows a delay and consistent undershoot in e-cigarette initiation rates relative to the ideal-case scenario. Finally, a scenario with all constraints (time delays, uncertain approval, and budgetary constraints) shows a delayed and consistently undershooting ecigarette initiation rate relative to the ideal case.
In order to quantify these differences between the ideal-case and scenarios that include realistic practical limitations, values from 2012 are examined (2 years after policy implementation, and the year of approximately greatest spread in e-cigarette initiation rates across scenarios). In the ideal case, 2.22 million people/year initiate e-cigarette use; versus approximately 171,000 in both the time-delayed and time-delayed with reduced budget scenarios (a 92% difference relative to the ideal-case scenario at the same time point); 108,000 in the time-delayed plus uncertain approval scenario (a 95% difference); and 107,000 in the scenario with all three types of limitation (a 95% difference). This discrepancy closes as time passes: all policies start to converge in 2050. However, oscillations persist into the future whenever the effective policy status changes (i.e. when established cigarette users oscillates past the goal value, and the need to actively encourage e-cigarette initiation is present or absent). These oscillations are dampened: for example, in the second oscillation, the ideal-case scenario shows approximately 613,000 people/year initiating e-cigarettes, versus 943,000 in the time-delayed scenario (a 54% difference relative to the ideal-case scenario at the same time point), 960,000 in the time-delayed plus uncertain approval scenario (a 57% difference), 949,000 in the time-delayed plus reduced budget scenario (a 55% difference), and 964,000 in the scenario with all three types of limitations (a 57% difference). Thus, the more time passes, the closer all scenarios become to each other, indicating that the system has recovered from the initial implementation obstacles.
With respect to the distal goal of reducing nicotine-attributed preventable deaths to the accidental death rate in the population, this policy achieves its goal around 2039 (29 years after policy implementation) (data available on downloadable model (33)), after which the preventable deaths remains far below the goal (3.28 million simulated deaths/year vs. a goal of 6.9 million deaths/year in 2021). Notably, this gure includes the potential unintended consequence of preventable deaths attributable to e-cigarettes.
A user-friendly and interactive interface is publicly available on the web (35). This interface version allows the user to modify the above parameters related to implementation obstacles along their full possible ranges, as well as other parameters (namely, the hypothesized strength of the diversion, smoking reduction, and smoking cessation effects of e-cigarettes, from 0 to 100% of the e-cigarette initiation rates). In addition, the full model is also available for download (33), and can be viewed and run using the free software isee Player (34). This can allow continued utility of this model as forthcoming data provide more precise estimates of relevant parameter values in the model.

Discussion
This study presents a novel system dynamics model examining the promotion of e-cigarettes as a harm reduction policy towards the goal of reducing nicotine-related death and disease, which is primarily due to conventional cigarettes. This simulated policy, which acts through removing existing restrictions (e.g. avor bans) and implementing an informational campaign promoting e-cigarettes as a less harmful alternative, has a 3-pronged effect: 1) diverting adolescents from ever using conventional cigarettes; 2) reducing smoking among recent initiators, thereby lowering the progression rate to established cigarette use; and 3) increasing smoking cessation. Policy simulations show that promoting e-cigarettes can achieve a successful reduction of cigarette smokers to the goal number, given the assumptions in this model. Realistic obstacles to policy implementation such as delays in decision-making, uncertain approval, and budgetary limitations have the effect of delaying and weakening the policy's effects (by up to 95% in the rst years after policy implementation, though these effects diminish over time. This system dynamics model is publicly available both as a full model (33) and useable via a user-friendly web format (35), allowing decision makers to test out the effects of different parameters and assumptions within a simulation setting. E-cigarette policy remains a controversial topic. Some argue for strict regulation comparable to that of conventional cigarettes, based on health concerns and the addictive potential of nicotine, particularly on young and/or novice users (7). Due to the more favorable risk pro le of e-cigarettes (11), many agree that highly addicted, established smokers who have di culty quitting are better off switching to e-cigarettes (5). On the other hand, e-cigarette use among adolescents and/or novice users remains controversial, due to fears of a "gateway" effect whereby e-cigarettes cause youth to become nicotine-dependent and increase their risk of later conventional cigarette smoking (21). However, given recent research supporting a common-liability hypothesis which postulates that the apparent relationship between e-cigarette use and smoking is attributable to a pre-existing liability for nicotine use (23,24), the question of primary prevention becomes relevant (27). That is, for youth who have a propensity to use a nicotine product, it is important to direct them to a less harmful product. Furthermore, tightening restrictions on e-cigarettes too strictly may have the unintended consequence of directing would-be nicotine users back to conventional cigarettes (36)(37)(38), which are more harmful due to the nature of combustible smoking (3,5).
Through simulation modeling, the current study shows that a harm reduction policy promoting ecigarettes could successfully reduce conventional smoking prevalence through a combination of diversion, smoking reduction, and cessation. In turn, this drastically reduces the preventable, nicotineattributed deaths to below the goal value of the accidental death rate in the population. This reduction in nicotine-attributable deaths remains substantial even after accounting for the important unintended consequence of deaths from e-cigarettes: this model allows for e-cigarettes to increase the population of users of any nicotine product (cigarettes or e-cigarettes) and consequently the total deaths from ecigarettes. This is consistent with previous research on the trade-off between the prevalence of use and the risk pro le of a product: that is, a greater number of users are allowable from a public health perspective when using a less-risky product (39).

Limitations
This study should be interpreted in the context of important limitations. The central limitation of system dynamics modeling is that the results may not re ect what occurs in reality; however, the series of validation tests performed increase con dence that this model captures the relevant causal relationships in the real-world system. Though additional elements can be added to the model, parsimony is desirable once the minimally essential features have been captured. A speci c simplifying assumption was excluding ex-e-cigarette users from the model. Since the stocks relevant to nicotine-related death and disease are established users, excluding a stock for ex-users has the effect of assuming established users remain at the same risk for life. Thus, this is a conservative assumption that likely overestimates the mortality from established e-cigarette use.
Other model assumptions are based on imperfect data, and impact the magnitude and trends of ecigarette initiation rates and stocks of established cigarette and e-cigarette users. In particular, the strength of the diversion, smoking reduction, and cessation effects are based on estimates from current literature, which may be limited. The diversion effect is particularly controversial, as much existing literature has argued for a gateway effect of e-cigarettes, which is an opposing effect. However, recent studies show that population-level trends are inconsistent with a gateway account, as the cigarette smoking prevalence continues to decline and may even have accelerated after the introduction of ecigarettes (25,26). This suggests a net diversion effect (29), the magnitude of which is estimated based on the diversion effect necessary to account for the accelerating decline in conventional smoking after ecigarettes appeared (28). The current system dynamics model will be updated as new data emerge. Additionally, these assumptions and their implications on simulation results can be further tested using the publicly available web interface for this model.
Additional limitations of the model include the focus on only two nicotine products (cigarettes and ecigarettes). Other products may alter the dynamics presented here, especially with cigar use surpassing cigarette use among youth (40). Similarly, the current policy was limited to overturning existing regulations (e.g. avor bans) and delivering an informational campaign; however, additional policies could alter the ndings, such as age restrictions on purchasing e-cigarettes. Additional implementation challenges that were not included in the model may also be relevant, and would have the effect of delaying and weakening the policy effects. Future research is necessary to explore other policies and implementation challenges in more detail, as the goal of the current study was to show general feasibility of a harm reduction policy promoting e-cigarettes, rather than to compare and contrast speci c policies for doing so.

Strengths
The current study is novel in its examination of a harm reduction policy promoting e-cigarettes, particularly with respect to 3 possible mechanisms by which e-cigarette use can decrease the conventional smoking prevalence. The question of diversion, or primary prevention of cigarette use, is particularly novel, as this is a di cult effect to estimate empirically and has thus been understudied to date (27). Additionally, the use of system dynamics modeling allows for a systematic examination of different scenarios, ranging from the status quo (no policy) to an ideal-world policy, as well as a range of realistic scenarios in between that present obstacles and delays to policy implementation. The current model has its focus on practical considerations with respect to policy implementation, ranging from time delays to political resistance to budgetary limitations. Finally, the model is publicly available via a userfriendly web interface (35) as well as a downloadable full model (33), allowing further testing of policy scenarios and assumptions of the model.

Conclusions
The system dynamics simulation model presented here demonstrates that promoting e-cigarettes as a less harmful alternative can be a successful harm-reduction policy for reducing the conventional smoking prevalence and consequently the nicotine-attributable deaths in the population. Practical challenges such as delays and limited resources can substantially weaken and delay the effect of the policy, at least initially; therefore, it is important to account for such obstacles when designing policy and projecting its effects. Ongoing evaluation of these ndings is warranted with forthcoming data on the likely effects of e-cigarettes on conventional smoking, particularly with respect to a diversion effect. Causal loop diagram of the major feedback loops in cigarette smoking, e-cigarette use, and the current policy. Arrows denote causal links, and the polarity (+/-) at the arrow head denotes a positive relationship and an inverse relationship, respectively. Loops are denoted with an R (reinforcing/positive reinforcing loop) or B (balancing/negative reinforcing loop) and are numbered accordingly. The policy is twofold (public health campaigns that promote e-cigarettes as a less harmful alternative to cigarettes; removing restrictions on e-cigarette purchasing (here, removing avor bans)). E-cigarettes have 3 possible intended effects on cigarette smoking (diversion from initiation, offsetting consumption, and increasing cessation) and one possible unintended effect (deaths from e-cigarette use, since they are not completely safe).

Figure 2
Simpli ed structure of the stock-and-ow model. Separate aging chains represent cigarette use (top sector) and e-cigarette use (bottom sector) with stocks (represented as squares) for different stages of use, and corresponding ows (represented as valves). The stock of established cigarette and e-cigarette users drives mortality, and this motivates policy implementation which targets e-cigarette initiation rate. This policy acts in 3 ways: diversion from cigarette initiation, reduction of the smoking progression rate, and increasing the cigarette cessation rate. No policy is implemented in this simulation. Note the different y-axis scales for each line.   Optimal vs. Achievable E-Cigarette Initiation Rates. The ow of e-cigarette initiation rates is the direct target of the policy. The e-cigarette initiation rate required to achieve the goal instantly (solid blue line) is shown against the e-cigarette initiation rate achievable within the limitations of the system (dot-dashed red line).