BackgroundAotearoa-New Zealand (A/NZ) was the first country to pass a comprehensive commercial tobacco endgame strategy into law. Key components include the denicotinisation of smoked tobacco products and a major reduction in tobacco retail outlets. Understanding the potential long-term economic impacts of such measures is important for government planning.DesignA tobacco policy simulation model that evaluated the health impacts of the A/NZ Smokefree Action Plan was extended to evaluate the economic effects from both government and citizen perspectives. Estimates were presented in 2021 US$, discounted at 3% per annum.ResultsThe modelled endgame policy package generates considerable growth in income for the A/NZ population with a total cumulative gain of US$31 billion by 2050. From a government perspective, increased superannuation payments and reduced tobacco excise tax revenue result in a negative net financial position and a cumulative shortfall of US$11.5 billion by 2050. In a sensitivity analysis considering future labour force changes, the government’s cumulative net position remained negative by 2050, but only by US$1.9 billion.ConclusionsA policy such as the A/NZ Smokefree Action Plan is likely to produce substantial economic benefits for citizens, and modest impacts on government finances related to reduced tobacco tax and increases in aged pensions due to increased life expectancy. Such costs can be anticipated and planned for and might be largely offset by future increases in the size of the labour force and the proportion of people 65+ years old working in the formal economy.

Background The Aotearoa/New Zealand Government is aiming to end the tobacco epidemic and markedly reduce Māori:non-Māori health inequalities by legislating: (1) denicotinisation of retail tobacco, (2) 95% reduction in retail outlets and (c) a tobacco free-generation whereby people born after 2005 are unable to legally purchase tobacco. This paper estimates future smoking prevalence, mortality inequality and health-adjusted life year (HALY) impacts of these strategies. Methods We used a Markov model to estimate future yearly smoking and vaping prevalence, linked to a proportional multistate life table model to estimate future mortality and HALYs. Results The combined package of strategies (plus media promotion) reduced adult smoking prevalence from 31.8% in 2022 to 7.3% in 2025 for Māori, and 11.8% to 2.7% for non-Māori. The 5% smoking prevalence target was forecast to be achieved in 2026 and 2027 for Māori males and females, respectively. The HALY gains for the combined package over the population’s remaining lifespan were estimated to be 594 000 (95% uncertainty interval (UI): 443 000 to 738 000; 3% discount rate). Denicotinisation alone achieved 97% of these HALYs, the retail strategy 19% and tobacco-free generation 12%. By 2040, the combined package was forcat to reduce the gap in Māori:non-Māori all-cause mortality rates for people 45+ years old by 22.9% (95% UI: 19.9% to 26.2%) for females and 9.6% (8.4% to 11.0%) for males. Conclusion A tobacco endgame strategy, especially denicotinisation, could deliver large health benefits and dramatically reduce health inequities between Māori and non-Māori in Aotearoa/New Zealand.

Background We estimated the health gains and health inequality impacts for the Australian population alive in 2021 (n = 25.0 million) in the next 20 years and over their remaining lifespan, from shifting everyone above a BMI of 25 kg/m2 2 to 25 kg/m2 2 compared to the BMI distribution in 2021 persisting into the future. Methods National Health Survey 2017-2018 - 2018 was used to estimate BMI distributions by sex, age and, socio-economic status (Socio-Economic Indexes for Areas; SEIFA). A proportional multistate life table linking BMI to 19 associated diseases and allowing for time lags and competing morbidity and mortality, was used to estimate the future stream of health adjusted life years (HALYs) gained from eradicating high BMI. Findings Undiscounted health gains in the fi rst 20 years and lifetime of the population were, respectively, 2.00 million (95% uncertainty interval 1.70-2.32) - 2.32) and 20.4 million (17.0-24.2) - 24.2) (at a 3% annual discount rate, HALY gains were 1.37 and 5.77 million, respectively). Reductions in the incidence of cardio metabolic diseases contributed 61% (95% UI: 54%-68%) - 68%) of the undiscounted health gains in the fi rst 20 years, musculoskeletal diseases contributed 26% (20%-32%) - 32%) and cancer 5% (3%-8%). - 8%). HALY gains in the fi rst 20 years and lifetime, per person alive in 2021, were 2.5 (2.4-2.5) - 2.5) and 1.9 (1.9-2.0) - 2.0) times higher for the most compared to the least deprived SEIFA quintile. Interpretation The total theoretical envelope of health gains, and health inequality reductions, through eradication of BMI is substantial. Our modeling infrastructure can be used to estimate the health impacts and cost effectiveness of many actual interventions.

Abstract Background Dynamic transmission models are often used to provide epidemiological guidance for pandemic policy decisions. However, how economic evaluation is typically incorporated into this technique to generate cost-effectiveness estimates of pandemic policy responses has not previously been reviewed. Methods We systematically searched the Embase, PubMed and Scopus databases for dynamic epidemiological modelling studies that incorporated economic evaluation of public health and social measures (PHSMs), with no date restrictions, on 7 July 2024. Results Of the 2,719 screened studies, 51 met the inclusion criteria. Most studies (n = 42, 82%) modelled SARS-CoV-2. A range of PHSMs were examined, including school closures, testing/screening, social distancing and mask use. Half of the studies utilised an extension of a Susceptible-Exposed-Infectious-Recovered (SEIR) compartmental model. The most common type of economic evaluation was cost-effectiveness analysis (n = 24, 47%), followed by cost-utility analysis (n = 17, 33%) and cost–benefit analysis (n = 17, 33%). Conclusions Economic evaluation is infrequently incorporated into dynamic epidemiological modelling studies of PHSMs. The scope of this research should be expanded, given the substantial cost implications of pandemic PHSM policy responses.

Background Aotearoa-New Zealand (A/NZ) is the first country to pass a comprehensive commercial tobacco endgame strategy into law. Key components include the denicotinisation of smoked tobacco products and a major reduction in tobacco retail outlets. Understanding the potential long-term economic impacts of these measures is important for government planning. Methods A tobacco policy simulation model that evaluated the health impacts of the A/NZ Smokefree Action Plan was extended to evaluate the economic effect of the new measures from both Government and citizen perspectives. Estimates were discounted at 3% per annum and presented in 2021 purchasing power parities US$. Findings The modelled endgame policy package generates considerable growth in income for the A/NZ population with a total cumulative gain by 2050 amounting to US$31 billion. From a government perspective, the policy results in foregone tobacco excise tax revenue with a negative net financial position estimated at US$11.5 billion by 2050. In a sensitivity analysis considering future changes to labour workforce, the government’s cumulative net position remained negative by 2050, but only by US$1.9 billion. Interpretation Our modelling suggests the Smokefree Aotearoa 2025 Action Plan is likely to produce substantial economic benefits for the A/NZ population, and modest impacts on government revenue and expenditure related to the reduction in tobacco tax and increases in aged pensions due to increased life expectancy. Such costs can be anticipated and planned for and might be largely offset by future increases in labour force and the proportion of 65+ year olds working in the formal economy. Funding This study was funded by a grant from the Australian National Health and Medical Research Council (GNT1198301) Evidence before this study Multiple countries have set targets to achieve a commercial tobacco endgame. Most simulation modelling studies have evaluated ‘traditional’ tobacco control interventions (e.g., tobacco excise tax increases, indoor smoking bans, smoking cessation health services). Very few have modelled the economic effects of endgame strategies. We searched PubMed with no language restrictions for articles published from 1 January 2000 to 8 February 2023 using the following search terms: (smoking[TW] OR tobacco[TW]) AND (endgame[TW] OR eliminat*[TW] OR “phasing out”[TW] OR “phase out”[TW] OR aboli*[TW] OR prohibit*[TW] OR ban[TW] OR “smoke free”[TW] OR “smoke-free”[TW]) AND (model*[TW] OR simulat*[TW]) AND (cost[TW] OR economic[TW]). We identified six economic evaluations of commercial tobacco endgame strategies, including different interventions and cost perspectives. Five studies modelled interventions in the Aotearoa/New Zealand (A/NZ) context and one in the UK. Four studies were conducted from a healthcare system perspective, estimating the costs to the health system associated with tobacco-related diseases. One of these studies additionally estimated ‘non-health social costs’, as the productivity loss resulting from smoking-associated morbidity and mortality. Another study estimated the cost to consumers resulting from a policy in which retail outlets selling tobacco were significantly reduced, considering both the actual cost of a pack of cigarettes and the cost of increased travel to retailers, and the last estimated excise tax revenue to the government resulting from increases to tobacco taxation (compared to no increases to current tobacco tax levels). Of the identified literature, none evaluated the effect of endgame strategies on citizen income nor the fiscal impacts to government revenue and expenditure. Added value of this study This study evaluates the economic impacts of a recently introduced commercial tobacco endgame legislation in A/NZ. We modelled the economic impacts by 2050 of a policy package that includes the four key measures in the new legislation (i.e., denicotinisation of smoked tobacco products, enhanced antismoking mass media campaigns, 90% reduction in the number of tobacco retail outlets, and a smoke-free generation law that bans sale of tobacco to anyone born after 2008). The analysis presents both a government and citizen perspective. The government fiscal impacts extend beyond health system expenditure to also include differences between business as usual (BAU) – i.e., no endgame strategy – and endgame scenarios in excise tax revenue, goods and services tax (GST) revenue, income tax revenue, and superannuation expenditure. A net government position is also calculated. The citizen perspective estimates the impact of the policy on population income and savings that may result from reduced tobacco consumption. Our model projects large economic gains for consumers from the tobacco endgame package resulting from a sharp reduction in smoking prevalence, morbidity and mortality. For the A/NZ Government, the policy is projected to result in reduced healthcare costs, and increased income tax and GST revenue. These gains are offset by increased superannuation payments resulting from a greater number of individuals living past the age at which superannuation is provided to all citizens (65 years in A/NZ and described in this article as “retirement age” for simplicity), as well as large reductions in excise tax revenue. Implication of all the available evidence Our findings support previous evidence indicating that ambitious tobacco control policies can produce large heath and economic benefits. Our model suggests that a commercial tobacco endgame strategy is likely to result in a large revenue transfer to the benefit of the A/NZ population. An endgame approach moves beyond the BAU model of incremental policy change to a deliberate strategy to permanently reduce tobacco smoking to minimal levels within a short timeframe. A logical result of such a strategy is a significant decrease in excise tax revenue for governments. Under the endgame scenario, the net position of the A/NZ Government is likely to be negative due mainly to the foregone excise tax revenue. In a sensitivity analysis of the endgame scenario that takes into account recent projections from Stats NZ of a future larger and older labour force in A/NZ, our model suggests that the net government position might become positive as early as 2036 – less than 15 years after the introduction of the endgame policy. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study was funded by a grant from the Australia National Health and Medical Research Council (GNT1198301) ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors

We recently reported the results of an integrated epidemiologic and economic agentbased model that assessed the costs and benefits of more than one hundred coronavirus disease 2019 (COVID19) control policies used in Victoria, in combination with nine scenarios of SARSCoV2 variant emergence, during the eighteen months from April 2022.2 We included mask interventions implemented only during large epidemic waves that increased both general mask wearing and the proportion of mask wearing that involved respirators (eg, N95 masks). These policies had minimal impact on health outcomes.2 For this study, we extended these analyses to determine the impact of agestratified consistent communitylevel mask wearing (ie, at all times when outside the home) on numbers of SARSCoV2 infections and COVID19related deaths.

Background: Cold indoor temperature (<18 C) is associated with hypertension-related and respiratory disease, depression, and anxiety. We estimate total health, health expenditure and income impacts of permanently lifting the temperature in living areas of the home to 18 C in cold homes in South-eastern Australia (N = 17 million). Methods: A proportional multistate lifetable model was used to estimate health adjusted life years (HALYs), health expenditure and income earnings, over the remainder of the lifespan of the population alive in 2021 (3% discount rate). Multiple data were integrated including the prevalence of cold housing (5.87%; mean temperature 15 C), the effect of temperature to hypertension-related, respiratory disease, depression and anxiety. Findings: Eradicating cold housing was predicted to lead to 89,600 (95% UI 47,700 to 177,000) lifetime HALYs gained over the population's remaining lifespan, nearly half of which occurred from 2021 to 2040. Respiratory disease (32.4%) and mental illness (60.6%) made large contributions to HALYs gained, but also had large uncertainty (95% UI 30.0%-42.9% and 45.1%-64.6%, respectively) due to uncertain estimates of their magnitude of causal association with cold housing. Health gains per capita were 6.1 times greater (95% UI 4.7 to 8.1) among the most compared to least deprived quintile. From 2021 to 2040, health expenditure decreased by AUD$0.87 billion (0.35-1.98) and income earnings increased by AUD$4.35 billion (1.89-9.81). Interpretation: Eliminating cold housing would lead to substantial health gains, reductions in health inequalities, savings in health expenditure, and productivity gains. Next steps require research to reduce uncertainty about the magnitude of causal associations of cold with mental and respiratory health.

A bstract Background Identifying optimal COVID-19 policies is challenging. For Victoria, Australia (6.6 million people), we evaluated 104 policy packages (two levels of stringency of public health and social measures [PHSMs], by two levels each of mask-wearing and respirator provision during large outbreaks, by 13 vaccination schedules) for nine future SARS-CoV-2 variant scenarios. Methods We used an agent-based model to estimate morbidity, mortality, and costs over 12 months from October 2022 for each scenario. The 104 policies (each averaged over the nine future variant scenarios) were ranked based on four evenly weighted criteria: cost-effectiveness from (a) health system only and (b) health system plus GDP perspectives, (c) deaths and (d) days exceeding hospital occupancy thresholds. Findings More compared to less stringent PHSMs reduced cumulative infections, hospitalisations and deaths but also increased time in stage ≥3 PHSMs. Any further vaccination from October 2022 decreased hospitalisations and deaths by 12% and 27% respectively compared to no further vaccination and was usually a cost-saving intervention from a health expenditure plus GDP perspective. High versus low vaccine coverage decreased deaths by 15% and reduced time in stage ≥3 PHSMs by 20%. The modelled mask policies had modest impacts on morbidity, mortality, and health system pressure. The highest-ranking policy combination was more stringent PHSMs, two further vaccine doses (an Omicron-targeted vaccine followed by a multivalent vaccine) for ≥30-year-olds with high uptake, and promotion of increased mask wearing (but not Government provision of respirators). Interpretation Ongoing vaccination and PHSMs continue to be key components of the COVID-19 pandemic response. Integrated epidemiologic and economic modelling, as exemplified in this paper, can be rapidly updated and used in pandemic decision making. Funding Anonymous donation, University of Melbourne funding. A bstract Background Identifying optimal COVID-19 policies is challenging. For Victoria, Australia (6.6 million people), we evaluated 104 policy packages: (a) two levels of stringency of public health and social measures (PHSMs; lower, higher), by (b) two levels each of mask wearing (low, high) and Government respirator provision (nil, yes) during large outbreaks (defined as when the projected number of people in hospital reached >270 or >130 per million population for lower and higher stringency PHSM settings respectively), by (c) 13 vaccination schedules (nil, and four combinations of low/high coverage for ≥30/60-year-olds, each with an Omicron-targeted (OT) booster in the last quarter of 2022 followed by one of: nil, another OT booster in the second quarter of 2023, or a multivalent booster in the second quarter of 2023). These policies were modelled in the setting of nine future SARS-CoV-2 variant scenarios (no major new variant of concern and one of eight variants arriving in November 2022 with different virulence, antigenic, and immune escape profiles). Methods We used an agent-based model to estimate morbidity, mortality, and costs over 12 months from October 2022 for each scenario. The 104 policies (each averaged over the nine future variant scenarios) were ranked based on four evenly weighted criteria: cost-effectiveness from (a) health system only and (b) health system plus GDP perspectives (HALYs valued at AUD 70,000; discount rate 3%), (c) deaths and (d) days exceeding hospital occupancy thresholds. Findings More compared to less stringent PHSMs reduced cumulative infections, hospitalisations and deaths by an average of 25%, 24% and 24% respectively across 468 policy comparisons (other policy and variant scenarios held constant), but also increased time in stage ≥3 (out of 5) PHSMs by an average of 42 days (23 days for low virulence and 70 days for high virulence variants). Any further vaccination from October 2022 decreased hospitalisations and deaths by 12% and 27% respectively compared to no further vaccination, however the cumulative number of infections increased by 10% due to vaccination preferentially decreasing hospitalisation rates that were used to dynamically set PHSM stages. Any further vaccination was of marginal cost-effectiveness from a health system perspective (an average of AUD 77,500 per HALY gained for vaccinating ≥60-year-olds, and AUD 41,600 for 30- to 59-year-olds incremental to ≥60-year-olds), but vaccination also resulted in 36% fewer days in Stage ≥3 PHSMs usually making it a cost-saving intervention from a health expenditure plus GDP perspective. High versus low vaccine coverage reduced deaths by 15% and reduced time in Stage ≥3 PHSMs by 20%. Promotion to increase mask wearing or government provision of respirators during large outbreaks reduced cumulative infections, hospitalisations and deaths over the 12 months by 1% to 2%, and reduced days with hospital occupancy exceeding 750 COVID-19 patients by 2% (4% to 5% in the context of highly virulent variants). The highest-ranking policy combination was more stringent PHSMs, two further vaccine doses (an Omicron-targeted vaccine followed by a multivalent vaccine) for ≥30-year-olds with high uptake, and promotion of increased mask wearing (but not Government provision of respirators). Interpretation Ongoing vaccination and PHSMs continue to be key components of the COVID-19 pandemic response. Integrated epidemiologic and economic modelling, as exemplified in this paper, can be rapidly updated and used in pandemic decision making. Funding Anonymous donation, University of Melbourne funding. R esearch in context Evidence before this study We searched Ovid MEDLINE to 28 July 2022 for studies using the terms (economic evaluation.mp. OR cost effectiveness.mp. OR health economic*.mp.) AND (simulation.mp. OR model*.mp.) AND pandemic*.mp. to identify existing simulation modelling analyses of pandemic preparedness and response that incorporated cost effectiveness considerations. All identified literature examined pandemic influenza and COVID-19 and was highly heterogeneous in terms of modelled interventions (which included school closures, masks, hand hygiene, vaccination, testing strategies, antiviral medication, physical distancing measures, indoor ventilation, and personal protective equipment), quality, context, model structure, and economic evaluation approach. Systematic reviews of COVID-19 modelling studies that include a health economic component generally indicate that SARS-CoV-2 testing, personal protective equipment, masks, and physical distancing measures are cost-effective. However, few prior studies consider optimal packages of interventions (as opposed to standalone interventions), and none explicitly account for ongoing viral evolution or accurately capture the complexities of vaccine- or natural infection-derived immunity to SARS-CoV-2. For example, a previous study integrating a dynamic SARS-CoV-2 transmission model with an economic analysis using a net monetary benefit approach published in early 2021 emphasized the combined public health and economic advantages of COVID-19 vaccination combined with physical distancing measures in the UK. However, considering current knowledge regarding the substantial waning of vaccine effectiveness and relatively low protection against infection conferred by vaccination (compared to more severe clinical outcomes), this model likely over-estimated the impact of COVID-19 vaccination on viral transmission. Scenarios that considered the emergence of SARS-CoV-2 variants of concern and thus associated changes in viral transmissibility, immune escape capacity (which has, in the case of the Omicron variant, greatly reduced protection following vaccination and prior infection) or virulence were also not modelled. Added value of this study To our knowledge, our study is the first that utilises a dynamic disease transmission model combined with an integrated economic evaluation framework to systematically compare COVID-19 policy intervention packages while accounting for ongoing SARS-CoV-2 evolution and waning population immunity. At a high-level, we found that a considerable degree of COVID-19 disease burden should be expected in the future, with modelled interventions only able to partly mitigate pandemic-associated morbidity and mortality in the medium-term. Across nine plausible future SARS-CoV-2 variant scenarios, higher stringency PHSMs notably reduced cumulative infections, hospitalisations and deaths in the 12-month period modelled but had the tradeoff of higher expected societal economic losses. Increasing community mask-wearing and substituting cloth and surgical masks for government supplied respirators during periods of high SARS-CoV-2 morbidity both reduced the number of days with hospital occupancy exceeding 750 COVID-19 patients by 2% on average across scenarios, and minimally reduced the cumulative infection, hospitalization and death burden. Compared to no further vaccines, the modelled vaccination schedules (with next-generation vaccines; one or two further doses) reduced hospitalisations by an average of 12%, and deaths by 27%. Vaccinating ≥30-year-olds was modestly superior to just vaccinating ≥60-year-olds (reducing cumulative deaths, for example, by 3.1%). Considering all policy options together, and ranking by optimality on cost-effectiveness, health system pressure and deaths, the highest ranking policy combinations tended to be a mix of higher stringency PHSMs, promotion to increase mask wearing but no Government-funded respirator provision during large outbreaks, and the administration of two booster vaccine doses within the 12-month period to ≥30-year-olds with associated high coverage (noting gains from vaccinating ≥30-year-olds compared to ≥60-year-olds were modest). Implications of all the available evidence The policy implications of this study are three-fold. Firstly, it reinforces the cost-effectiveness of ongoing vaccination of the public to mitigate morbidity and mortality associated with COVID-19. Secondly, the characteristics of emerging SARS-CoV-2 variants, outside the control of policy makers, will likely substantially influence public health outcomes associated with the pandemic in the future. Finally, at a phase of the pandemic characterised by growing intervention options urgently requiring prioritisation by decision makers alongside a large degree of ongoing uncertainty about future variants, this study provides a framework within which to systematically compare the health and economic benefits and burdens of packages of interventions that can be rapidly updated with new information (such as estimated effectiveness and waning kinetics of newly-developed vaccines) to support policy making.

Immunity to SARS-CoV-2 following vaccination wanes over time in a non-linear fashion, making modelling of likely population impacts of COVID-19 policy options challenging. We observed that it was possible to mathematize non-linear waning of vaccine effectiveness (VE) on the percentage scale as linear waning on the log-odds scale, and developed a random effects logistic regression equation based on UK Health Security Agency data to model VE against Omicron following two and three doses of a COVID-19 vaccine. VE on the odds scale reduced by 47% per month for symptomatic infection after two vaccine doses, lessening to 35% per month for hospitalisation. Waning on the odds scale after triple dose vaccines was 35% per month for symptomatic disease and 19% for hospitalisation. This log-odds system for estimating waning and boosting of COVID-19 VE provides a simple solution that may be used to parametrize SARS-CoV-2 immunity over time parsimoniously in epidemiological models.

Objective To estimate the health gains and Māori:non-Māori health inequality reductions of the Aotearoa/New Zealand Government’s proposed endgame strategy.Design Simulation modelling: a Markov model to estimate future yearly smoking and vaping prevalence (for business-as-usual [BAU] and intervention scenarios) linked to a proportional multistate lifetable model with 16 tobacco-related diseases to estimate future morbidity and mortality rates, and health adjusted life years (HALYs).Setting Aotearoa.Participants Population alive in 2020 (5.08 million) simulated over the rest of their lifespan.Interventions 1. Denicotinisation of all retail tobacco in 2023, 2. 1 plus media promotion, 3. 95% reduction in tobacco retail outlets in 2023, 4. a tobacco free-generation whereby people born in 2006 and later are never legally able to purchase tobacco, 5. combined package of 2, 3 and 4.Main Outcome Measures Future smoking prevalence, deaths averted and HALYs by sex and ethnic group. Percent reduction in Māori:non-Māori all-cause mortality rate difference in 2040 under interventions compared to business as usual (BAU).Results The combined package of strategies was estimated to reduce adult smoking prevalence from 31.8% in 2022 to 7.3% in 2025 for Māori, and 11.8% to 2.7% for non-Māori. The 5% smoking prevalence target was forecast to be achieved in 2026 and 2027 for Māori males and females, respectively.The HALY gains for the combined package (compared to BAU) over the population’s remaining lifespan was estimated to be 594,000 (95%UI: 443,000 to 738,000; 3% discount rate). The denicotinisation strategy alone achieved 97% of these HALYs, the retail strategy 19%, and tobacco-free generation 12%.The future per capita HALY gains for the combined package for Māori were estimated to be 4.75 and 2.14 times higher than for non-Māori females and males, respectively. The absolute difference between Māori and non-Māori all-cause mortality for 45+ year olds in 2040 was estimated to be 23.4% (19.1% to 27.6%) less for females under the combined package compared to BAU, and 9.5% (7.5% to 11.3%) less for males.Conclusion A tobacco endgame strategy, especially denicotinisation, could dramatically reduce health inequities.Funding New Zealand Ministry of Health.What is already known on this topic What this study adds ### Competing Interest StatementThe authors have declared no competing interest.### Funding StatementThis study was funded by the New Zealand Ministry of Health### Author DeclarationsI confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.YesThe details of the IRB/oversight body that provided approval or exemption for the research described are given below:N/AI confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesAll data produced in the present study are available upon reasonable request to the authors

Population-level immunity to SARS-CoV-2 directly impacts the incidence of COVID-19 morbidity and mortality. Understanding how this immunity is likely to change over time in the context of future vaccination schedules and emerging SARS-CoV-2 variants is critical to inform pandemic policy. This study simulates population-level COVID-19 immunity (including relative contributions of vaccination and previous infection) in Victoria, Australia over 18 months using an agent-based model and logistic regression equations that predict immunity and waning following vaccination and/or infection. Previous infection was found to drive most immunity against infection even with ongoing regular vaccination, however a greater proportion of overall immunity against mortality was accounted for by vaccination. Although previous infection appears to be driving a substantial component of population-level COVID-19 immunity currently, improved vaccines providing longer lasting (and better sterilizing) immunity are likely to be a critical component of the future pandemic response given the risks associated with SARS-CoV-2 infection.

Background: Māori (Indigenous peoples of Aotearoa New Zealand [A/NZ]) have high tobacco smoking rates, a legacy of colonisation. We estimated the health gains and inequality reductions of the A/NZ Government's proposed endgame strategy implemented in 2023 of denicotinising tobacco, reducing retail outlets by 95%, and a making it illegal for people born after 2006 to purchase tobacco (tobacco-free generation).Methods: A Markov smoking-vaping cohort model was parameterised for business-as-usual (BAU) using Health Survey data projections, and for endgame strategies using research and expert knowledge inputs. The difference in smoking and vaping prevalence between BAU and each endgame policies was merged with incidence rate ratios for 16 tobacco-related diseases and fed into a proportional multistate lifetable model to estimate future health-adjusted life years (HALYs) and mortality rates.Findings: The combined package of strategies reduced adult smoking prevalence from 31.8% in 2022 to 7.6% in 2025 for Māori, and 11.8% to 2.8% for non-Māori. The 5% smoking prevalence target was achieved in 2026 and 2027 for Māori males and females, respectively. The HALY gains for the combined package (compared to BAU) over the remaining lifespan of the A/NZ population alive in 2020 (5.08 million) was 598,000 (95%UI: 517,000 to 698,000; 3% discount rate). The denicotinisation strategy alone achieved 97% of these HALYs, the retail strategy 19%, and tobacco-free generation 12%. The per capita HALY gains for the combined package for Māori were 4.75 and 2.14 times higher than for non-Māori females and males, respectively. The absolute difference between Māori and non-Māori all-cause mortality for 45+ year olds in 2040 was 22.9% (19.9% to 26.2%) less for females under the combined packaged compared to BAU, and 9.6% (8.4% to 11.0%) less for males.Interpretation: A tobacco endgame strategy – especially denicotinisation – could dramatically reduce health inequities.Funding Information: This study was supported by the New Zealand Ministry of Health. Declaration of Interests: None.

The COVID-19 pandemic has brought the combined disciplines of public health, infectious disease and policy modelling squarely into the spotlight. Never before have decisions regarding public health measures and their impacts been such a topic of international deliberation, from the level of individuals and communities through to global leaders. Nor have models—developed at rapid pace and often in the absence of complete information—ever been so central to the decision-making process. However, after nearly 3 years of experience with modelling, policy-makers need to be more confident about which models will be most helpful to support them when taking public health decisions, and modellers need to better understand the factors that will lead to successful model adoption and utilization. We present a three-stage framework for achieving these ends.

ABSTRACTBackgroundSocioeconomic inequalities in mortality are evident in all high-income countries and ongoing monitoring is recommended using linked census-mortality data. Using such data, we provide first estimates of education-related inequalities in cause-specific mortality in Australia, suitable for international comparisons.MethodsUsing Australian Census (2016) linked to 13-months of Death Registrations data (2016-17), we estimated relative rates (RR) and rate differences (RD, per100 000 person-years), comparing rates in low (no qualifications) and intermediate (secondary school) with high education (tertiary), for individual causes of death (among those 25-84y) and grouped according to preventability (25-74y), separately by sex and age group, adjusting for age, using negative binomial regression.ResultsAmong 13.9M people contributing 14 452 732 person-years, 84 743 deaths occurred. We observed inequalities in most causes of death for each age-sex group. Among men aged 25-44y, absolute and relative inequalities (low versus high education) were largest for injuries, e.g. transport accidents (RR=10.1 [95%CI: 5.4-18.7], RD=21.1 [15.9-26.3]). Among those aged 45-64y, inequalities were greatest for chronic diseases, e.g. lung cancer (men RR=6.6 [4.9-8.9], RD=55.6 [51.1-60.1]) and ischaemic heart disease (women RR=5.8 [3.7-9.1], RD=19.2 [17.0-21.5]), with similar patterns for people aged 65-84y. When grouped according to preventability, inequalities were large for causes amenable to behaviour change and medical intervention for all ages and causes amenable to injury prevention among young men.ConclusionsAustralian education-related inequalities in mortality are substantial, generally higher than international estimates, and related to preventability. Findings highlight opportunities to reduce them and the potential to improve the health of the population.Key messagesUsing linked Australian Census (2016) and Death Registrations data (2016-17), we provide the first estimates of education-related inequalities in cause-specific mortality for Australia, broadly suitable for international comparisons.Among men aged 25-44 years, inequalities were largest for injuries, with mortality rates among those with low education six-to-ten times that of those with high education. Among the mid- and older-age groups, inequalities were largest for chronic diseases, where mortality rates among those with the lowest education were between two- and seven-times those with the highest education.In 2016-17, around half of all deaths for men and one-third of deaths for women aged 25-84 were associated with less than tertiary education. The majority of these excess deaths were attributable to leading causes.The substantial inequalities seen in preventable deaths highlight ongoing opportunities to reduce inequalities in mortality and to improve the overall health of the Australian population.Australian estimates are generally consistent with, but higher than, those for comparable countries and earlier time periods, but further standardisation of methods and reporting would enhance the validity of such comparisons

Abstract Background and Aims The New South Wales (NSW) COVID-19 outbreak is at 478 daily cases on August 16, 2021. Our aims were to: 1) estimate the time required to reach ≤5 cases per day under three lockdown strengths (weak, moderate, strong), and four vaccination rollouts: (a) per the original plan, (b) prioritizing essential workers, (c) b plus rapid vaccination of 25% of <60-year-olds with AstraZeneca (AZ25), and (d) b plus rapid vaccination of 50% of <60-year-olds with AstraZeneca (AZ50). 2) estimate the number of cases, hospitalizations, and deaths in the 100 days after 1/August for the 12 scenarios. Methods An agent-based model was adapted to NSW and the Delta variant. Hospitalization and mortality rates for unvaccinated COVID-19 infections were doubled given the virulence of Delta. Results The business-as-usual rollout fully vaccinates 50%, 70% and 80% of >16-year-olds by 10/Oct, 21/Nov, and 28/Dec, respectively. This reduced to 1/Oct, 30/Oct, and 22/Nov for the fastest (AZ50) rollout. A strong lockdown with a rapid vaccine rollout was the fastest to reach ≤5 cases (14-day average), with a median of 78 days (90% Uncertainty interval 61 - 103) or 18/Oct, compared to 207 days (166 - 254) or 24/Feb for a weak lockdown with no rollout acceleration. Increased lockdown strength had more impact than rollout acceleration. Under the AZ25 vaccination scenario, there were 1,440 (90% UI 262 - 10,600 deaths in the first 100 days of cases under a weak lockdown, compared to 71 (90% UI 26 - 178) under a strong lockdown scenario. Conclusion NSW will likely achieve 70% vaccination of >16-year-olds before reaching ≤5 daily cases. Accelerating the vaccine rollout is important for the medium-term, but in the short-term increased restriction strength was more effective at reducing caseload (and subsequently mortality and hospitalisation) than accelerating the vaccine rollout.

Background A major goal of evolutionary developmental biology is to discover general models and mechanisms that create the phenotypes of organisms. However, universal models of such fundamental growth and form are rare, presumably due to the limited number of physical laws and biological processes that influence growth. One such model is the logarithmic spiral, which has been purported to explain the growth of biological structures such as teeth, claws, horns, and beaks. However, the logarithmic spiral only describes the path of the structure through space, and cannot generate these shapes. Results Here we show a new universal model based on a power law between the radius of the structure and its length, which generates a shape called a ‘power cone’. We describe the underlying ‘power cascade’ model that explains the extreme diversity of tooth shapes in vertebrates, including humans, mammoths, sabre-toothed cats, tyrannosaurs and giant megalodon sharks. This model can be used to predict the age of mammals with ever-growing teeth, including elephants and rodents. We view this as the third general model of tooth development, along with the patterning cascade model for cusp number and spacing, and the inhibitory cascade model that predicts relative tooth size. Beyond the dentition, this new model also describes the growth of claws, horns, antlers and beaks of vertebrates, as well as the fangs and shells of invertebrates, and thorns and prickles of plants. Conclusions The power cone is generated when the radial power growth rate is unequal to the length power growth rate. The power cascade model operates independently of the logarithmic spiral and is present throughout diverse biological systems. The power cascade provides a mechanistic basis for the generation of these pointed structures across the tree of life.

An array is row-Latin if no symbol is repeated within any row. An array is Latin if it and its transpose are both row-Latin. A transversal in an n x n array is a selection of n different symbols from different rows and different columns. We prove that every n x n Latin array containing at least (2 - root 2)n(2) distinct symbols has a transversal. Also, every n x n row-Latin array containing at least 1/4 (5 - root 5)n(2) distinct symbols has a transversal. Finally, we show by computation that every Latin array of order 7 has a transversal, and we describe all smaller Latin arrays that have no transversal. (c) 2017 Wiley Periodicals, Inc.

An anagram is a word of the form WP where W is a non-empty word and P is a permutation of W . A vertex coloring of a graph is anagram-free if no subpath of the graph is an anagram. Anagram-free graph coloring was independently introduced by Kam\v cev, \ Luczak, and Sudakov [Combin. Probab. Comput., 27 (2018), pp. 623--642] and ourselves [Electron. J. Combin., 25 (2018), pp. 2--20]. In this paper we introduce the study of anagram-free colorings of graph subdivisions. We show that every graph has an anagram-free 8-colorable subdivision. The number of division vertices per edge is exponential in the number of edges. For trees, we construct anagram-free 10-colorable subdivisions with fewer division vertices per edge. Conversely, we prove lower bounds, in terms of division vertices per edge, on the anagram-free chromatic number for subdivisions of the complete graph and subdivisions of complete trees of bounded degree.

An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. We answer this question in the negative by constructing graphs with maximum degree 3 and unbounded anagram-free chromatic number. We also prove upper and lower bounds on the anagram-free chromatic number of trees in terms of their radius and pathwidth. Finally, we explore extensions to edge colouring and $k$-anagram-free colouring.