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Objectives and importance of study: Colorectal cancer (CRC) is Australia's fourth most commonly diagnosed cancer. CRC screening is an effective intervention to reduce this burden. The National Bowel Cancer Screening Program (NBCSP) provides 2-yearly immunochemical faecal occult blood tests (iFOBTs) to Australians aged 50-74 years; a diagnostic colonoscopy is conducted after a positive iFOBT. Clinical guidelines inform colonoscopy usage, and appropriate use of these guidelines is vital to investigate gastrointestinal symptoms, detect bowel abnormalities and CRC, and remove precancerous polyps. Colonoscopy services are under strain, with limited formal strategies to prioritise patients. There are concerns among practitioners and patient advocates that the NBCSP generates additional colonoscopy requests and increases wait times, worsening patient outcomes and prolonging distress. In this research study, we estimate and project colonoscopy use in Australia from 2001 to 2030 and determine the impact of the NBCSP by examining model-estimated NBCSP colonoscopy demand.Colonoscopy use in Australia was compiled using Medicare Benefits Schedule (MBS) claims for colonoscopies from 2001 to 2019. From these data, projections were made from 2020 to 2030. Policy1-Bowel, a microsimulation model, was used to estimate NBCSP-related colonoscopy demand from screening follow-up and colonoscopic surveillance from 2006 to 2030.MBS-funded colonoscopy use increased from 284 676 in 2001 to 663 213 in 2019. Annual use is projected to be more than 780 000 by 2030. Of these, 10-14% are projected to be generated by the NBCSP. Per-capita MBS-funded colonoscopy utilisation increased 0.2% annually over 2015-2019, a slowing of growth compared to previous trends.The NBCSP accounts for a modest fraction of colonoscopy use in Australia, and a better understanding of colonoscopy use not associated with the NBCSP is needed. Promoting adherence to guideline-recommended iFOBT and colonoscopy use could ease pressure on services and improve outcomes.

BackgroundAustralia introduced COVID-19 infection prevention and control measures in early 2020. To help prepare health services the Australian Government Department of Health commissioned a modelled evaluation of the impact of disruptions to population breast, bowel and cervical cancer screening programs on cancer outcomes and cancer services.MethodsWe used the Policy1 modelling platforms to estimate outcomes for potential disruptions to cancer screening participation, covering periods of 3, 6, 9 and 12 months. We estimated missed screens, clinical outcomes (cancer incidence, tumour staging), and various diagnostic service impacts.ResultsWe estimated that a 12-month screening disruption would reduce breast cancer diagnoses (9.3% population-level reduction over 2020-2021) and colorectal cancer (up to 12·1% reduction over 2020-21), and increase cervical cancer diagnoses (up to 3·6% over 2020-2022), with upstaging expected for these cancer types.ConclusionsFindings illustrate that maintaining screening participation is critical to sustaining a reduced cancer burden. We provide program-specific insights into which outcomes are expected to change, when changes are likely to become apparent, and likely downstream impacts. This evaluation provided evidence to guide decision-making for screening programs, and emphasises the ongoing benefits of maintaining screening in the face of potential future disruptions.FundingAustralian Government Department of Health

Background. This study aimed to assess the validity of 2 microsimulation models of colorectal cancer (CRC), Policy1-Bowel and ASCCA. Methods. The model-estimated CRC risk in population subgroups with different health statuses, “dwell time” (time from incident precancerous polyp to symptomatically detected CRC), and reduction in symptomatically detected CRC incidence after a one-time complete removal of polyps and/or undetected CRC were compared with published findings from 3 well-established models ( MISCAN, CRC-SPIN, and SimCRC). Furthermore, 6 randomized controlled trials (RCTs) that provided screening using a guaiac fecal occult blood test (Funen trial, Burgundy trial, and Minnesota Colon Cancer Control Study [MCCCS]) or flexible sigmoidoscopy (NORCCAP, SCORE, and UKFSST) with long-term follow-up were simulated. Model-estimated long-term relative reductions of CRC incidence (RR inc) and mortality (RR mort) were compared with the RCTs’ findings. Results. The Policy1-Bowel and ASCCA estimates showed more similarities to CRC-SPIN and SimCRC. For example, overall dwell times estimated by Policy1-Bowel (24.0 years) and ASCCA (25.3) were comparable to CRC-SPIN (25.8) and SimCRC (25.2) but higher than MISCAN (10.6). In addition, ∼86% of Policy1-Bowel’s and ∼74% of ASCCA’s estimated RR inc and RR mort were consistent with the RCTs’ long-term follow-up findings. For example, at 17 to 18 years of follow-up, the MCCCS reported RR mort of 0.67 (95% confidence interval [CI], 0.51–0.83) and 0.79 (95% CI, 0.62–0.97) for the annual and biennial screening arm, respectively, and the UKFSST reported RR mort of 0.70 (95% CI, 0.62–0.79) for CRC at all sites and 0.54 (95% CI, 0.46–0.65) for distal CRC. The corresponding model estimates were 0.65, 0.74, 0.81, and 0.61, respectively, for Policy1-Bowel and 0.65, 0.70, 0.75, and 0.58, respectively, for ASCCA. Conclusion. Policy1-Bowel and ASCCA’s estimates are largely consistent with the data included for comparisons, which indicates good model validity.

Objectives The Australian National Bowel Cancer Screening Program (NBCSP) offers free 2-yearly immunochemical faecal occult blood testing to individuals aged 50–74 years; national participation in 2015–2016 was 41%. In 2017, a 7-week television-led mass-media campaign to increase participation in the Australian state of Victoria was associated with a 1.31-fold increase in participation for 11 weeks. We aimed to evaluate the cost-effectiveness and health benefits of the 2017 campaign and scaled-up equivalent campaigns run over 4 years in Victoria and nationally. Study design This study used microsimulation modelling. Methods A comprehensive microsimulation model of colorectal cancer (CRC), Policy1-Bowel, was used to simulate three scenarios. Scenario 1 simulated the 2017 campaign in Victoria; Scenarios 2 and 3 assumed that campaigns were run three times annually from 2019 to 2022 in Victoria and Australia-wide, respectively. Total campaign costs of AUD$1million, AUD$10million, and AUD$40million were assumed for Scenarios 1, 2, and 3, respectively. The incremental effects and costs of the campaign on the NBCSP were assessed. A governmental perspective was used. Results All campaign scenarios were predicted to be highly cost-effective, with cost-effectiveness ratios under AUD$4,800/life-year saved. The actual 2017 campaign in Victoria is estimated to prevent 319 CRC cases and 183 deaths over the following 40 years. A 4-year campaign would prevent 1,750 CRC cases and 987 deaths if conducted in Victoria, and 8,100 cases and 4,330 deaths if conducted Australia-wide. Conclusion Mass-media participation campaigns could be highly cost-effective and maximise the potential life-saving impact of bowel screening. These results support ongoing investment in major bowel screening campaigns.

Refereed/Peer-reviewed Background: Australian Aboriginal and Torres Strait Islander peoples experience health and socioeconomic disparities, including lower life-expectancy, have a younger mean age of colorectal cancer (CRC) diagnosis, and lower CRC survival than non-Indigenous Australians. The National Bowel Cancer Screening Program (NBCSP) provides biennial CRC screening for Australians aged 50–74 years to reduce the burden of CRC. The 2019 participation rate was 42% nationwide and 23% in Aboriginal and Torres Strait Islander peoples. For Aboriginal and Torres Strait Islander peoples, this study aims to estimate the health outcomes and cost-effectiveness of the current NBCSP and extensions to include people < 50 years. Methods: An existing microsimulation model, Policy1-Bowel, was adapted to the Aboriginal and Torres Strait Islander population and was used to evaluate three strategies assuming biennial iFOBT screening from 50-74, 45–74, or 40–74 years under two participation scenarios: 23% and 42% per screening round (psr.). Results: At 23–42% participation psr., the current NBCSP was predicted to reduce lifetime CRC incidence and mortality by 14–24% and 23–39%, respectively, be cost-effective (incremental cost-effectiveness ratio 95 (> 60). Conclusion: For Aboriginal and Torres Strait Islander peoples, the current NBCSP is cost-effective but participation is limited. Lowering the screening start age will further reduce CRC incidence and mortality. Policy summary: These findings highlight a need to increase NBCSP participation whilst exploring the feasibility and acceptability of lowering the NBCSP start age for Aboriginal and Torres Strait Islander peoples. These findings could inform new co-designed, community-led strategies to improve CRC outcomes for Aboriginal and Torres Strait Islander peoples.

We study stability of unidirectional flows for the linearized 2D \begin{document}$ \alpha $\end{document} -Euler equations on the torus. The unidirectional flows are steady states whose vorticity is given by Fourier modes corresponding to a vector \begin{document}$ \mathbf p \in \mathbb Z^{2} $\end{document} . We linearize the \begin{document}$ \alpha $\end{document} -Euler equation and write the linearized operator \begin{document}$ L_{B} $\end{document} in \begin{document}$ \ell^{2}(\mathbb Z^{2}) $\end{document} as a direct sum of one-dimensional difference operators \begin{document}$ L_{B,\mathbf q} $\end{document} in \begin{document}$ \ell^{2}(\mathbb Z) $\end{document} parametrized by some vectors \begin{document}$ \mathbf q\in\mathbb Z^2 $\end{document} such that the set \begin{document}$ \{\mathbf q +n \mathbf p:n \in \mathbb Z\} $\end{document} covers the entire grid \begin{document}$ \mathbb Z^{2} $\end{document} . The set \begin{document}$ \{\mathbf q +n \mathbf p:n \in \mathbb Z\} $\end{document} can have zero, one, or two points inside the disk of radius \begin{document}$ \|\mathbf p\| $\end{document} . We consider the case where the set \begin{document}$ \{\mathbf q +n \mathbf p:n \in \mathbb Z\} $\end{document} has exactly one point in the open disc of radius \begin{document}$ \mathbf p $\end{document} . We show that unidirectional flows that satisfy this condition are linearly unstable. Our main result is an instability theorem that provides a necessary and sufficient condition for the existence of a positive eigenvalue to the operator \begin{document}$ L_{B, {\mathbf q}} $\end{document} in terms of equations involving certain continued fractions. Moreover, we are also able to provide a complete characterization of the corresponding eigenvector. The proof is based on the use of continued fractions techniques expanding upon the ideas of Friedlander and Howard.

Summary Background Colorectal cancer screening programmes worldwide have been disrupted during the COVID-19 pandemic. We aimed to estimate the impact of hypothetical disruptions to organised faecal immunochemical test-based colorectal cancer screening programmes on short-term and long-term colorectal cancer incidence and mortality in three countries using microsimulation modelling. Methods In this modelling study, we used four country-specific colorectal cancer microsimulation models–Policy1-Bowel (Australia), OncoSim (Canada), and ASCCA and MISCAN-Colon (the Netherlands)—to estimate the potential impact of COVID-19-related disruptions to screening on colorectal cancer incidence and mortality in Australia, Canada, and the Netherlands annually for the period 2020–24 and cumulatively for the period 2020–50. Modelled scenarios varied by duration of disruption (3, 6, and 12 months), decreases in screening participation after the period of disruption (0%, 25%, or 50% reduction), and catch-up screening strategies (within 6 months after the disruption period or all screening delayed by 6 months). Findings Without catch-up screening, our analysis predicted that colorectal cancer deaths among individuals aged 50 years and older, a 3-month disruption would result in 414–902 additional new colorectal cancer diagnoses (relative increase 0·1–0·2%) and 324–440 additional deaths (relative increase 0·2–0·3%) in the Netherlands, 1672 additional diagnoses (relative increase 0·3%) and 979 additional deaths (relative increase 0·5%) in Australia, and 1671 additional diagnoses (relative increase 0·2%) and 799 additional deaths (relative increase 0·3%) in Canada between 2020 and 2050, compared with undisrupted screening. A 6-month disruption would result in 803–1803 additional diagnoses (relative increase 0·2–0·4%) and 678–881 additional deaths (relative increase 0·4–0·6%) in the Netherlands, 3552 additional diagnoses (relative increase 0·6%) and 1961 additional deaths (relative increase 1·0%) in Australia, and 2844 additional diagnoses (relative increase 0·3%) and 1319 additional deaths (relative increase 0·4%) in Canada between 2020 and 2050, compared with undisrupted screening. A 12-month disruption would result in 1619–3615 additional diagnoses (relative increase 0·4–0·9%) and 1360–1762 additional deaths (relative increase 0·8–1·2%) in the Netherlands, 7140 additional diagnoses (relative increase 1·2%) and 3968 additional deaths (relative increase 2·0%) in Australia, and 5212 additional diagnoses (relative increase 0·6%) and 2366 additional deaths (relative increase 0·8%) in Canada between 2020 and 2050, compared with undisrupted screening. Providing immediate catch-up screening could minimise the impact of the disruption, restricting the relative increase in colorectal cancer incidence and deaths between 2020 and 2050 to less than 0·1% in all countries. A post-disruption decrease in participation could increase colorectal cancer incidence by 0·2–0·9% and deaths by 0·6–1·6% between 2020 and 2050, compared with undisrupted screening. Interpretation Although the projected effect of short-term disruption to colorectal cancer screening is modest, such disruption will have a marked impact on colorectal cancer incidence and deaths between 2020 and 2050 attributable to missed screening. Thus, it is crucial that, if disrupted, screening programmes ensure participation rates return to previously observed rates and provide catch-up screening wherever possible, since this could mitigate the impact on colorectal cancer deaths. Funding Cancer Council New South Wales, Health Canada, and Dutch National Institute for Public Health and Environment.

IntroductionWith almost 50% of cases preventable and the Australian National Bowel Cancer Screening Program in place, colorectal cancer (CRC) is a prime candidate for investment to reduce the cancer burden. The challenge is determining effective ways to reduce morbidity and mortality and their implementation through policy and practice. Pathways-Bowel is a multistage programme that aims to identify best-value investment in CRC control by integrating expert and end-user engagement; relevant evidence; modelled interventions to guide future investment; and policy-driven implementation of interventions using evidence-based methods.Methods and analysisPathways-Bowel is an iterative work programme incorporating a calibrated and validated CRC natural history model for Australia (Policy1-Bowel) and assessing the health and cost outcomes and resource use of targeted interventions. Experts help identify and prioritise modelled evaluations of changing trends and interventions and critically assess results to advise on their real-world applicability. Where appropriate the results are used to support public policy change and make the case for optimal investment in specific CRC control interventions. Fourteen high-priority evaluations have been modelled or planned, including evaluations of CRC outcomes from the changing prevalence of modifiable exposures, including smoking and body fatness; potential benefits of daily aspirin intake as chemoprevention; increasing CRC incidence in people aged Pathways-Bowel is a unique, comprehensive approach to evaluating CRC control; no prior body of work has assessed the relative benefits of a variety of interventions across CRC development and progression to produce a list of best-value investments.Ethics and disseminationEthics approval was not required as human participants were not involved. Findings are reported in a series of papers in peer-reviewed journals and presented at fora to engage the community and policymakers.

Introduction Colorectal cancer (CRC) care costs the Australian healthcare system more than any other cancer. We estimated costs and days in hospital for CRC cases, stratified by site (colon/rectal cancer) and disease stage, to inform detailed analyses of CRC-related healthcare. Methods Incident CRC patients were identified using the Australian 45 and Up Study cohort linked with cancer registry records. We analysed linked hospital admission records, emergency department records, and reimbursement records for government-subsidised medical services and prescription medicines. Cases’ health system costs (2020 Australian dollars) and hospital days were compared with those for cancer-free controls (matched by age, sex, geography, smoking) to estimate excess resources by phase of care, analysed by sociodemographic, health, and disease characteristics. Results 1200 colon and 546 rectal cancer cases were diagnosed 2006–2013, and followed up to June 2016. Eighty-nine percent of cases had surgery, chemotherapy or radiotherapy, and excess costs were predominantly for hospitalisations. Initial phase (12 months post-diagnosis) mean excess health system costs were $50,434 for colon and $60,877 for rectal cancer cases, with means of 16 and 18.5 excess hospital days, respectively. The annual continuing mean excess costs were $6,779 (colon) and $8,336 (rectal), with a mean of 2 excess hospital days each. Resources utilised (costs and days) in these phases increased with more advanced disease, comorbidities, and younger age. Mean excess costs in the year before death were $74,952 (colon) and $67,733 (rectal), with means of 34 and 30 excess hospital days, respectively–resources utilised were similar across all characteristics, apart from lower costs for cases aged ≥75 at diagnosis. Conclusions Health system costs and hospital utilisation for CRC care are greater for people with more advanced disease. These findings provide a benchmark, and will help inform future cost-effectiveness analyses of potential approaches to CRC screening and treatment.

Aims Colorectal cancer (CRC) screening programs worldwide have been disrupted during the COVID-19 pandemic. Thisstudy aimed to estimate the impact of hypothetical disruptions to organized FIT-based CRC screening programs on short-and long-term CRC incidence and mortality in three countries using microsimulation modelling. Methods Using CRC microsimulation models for Australia (Policy1-Bowel), Canada (OncoSim) and the Netherlands (ASCCAand MISCAN-Colon) participating in the COVID-19 and Cancer Global Modelling Consortium (CCGMC), we simulated a rangeof scenarios to assess the potential impact of disruptions to screening on CRC incidence and mortality. Modelled scenariosvaried by disruption duration (3-, 6-and 12-months), post-disruption participation reduction, and catch-up screeningstrategy (no catch-up, immediate and 6-month delayed catch-up). Results Without catch-up screening, CRC incidence increased by 0.1-0.3 %, 0.2-0.6 %, and 0.4-1.2 % over 2020-2050among individuals aged 50 years and older in the three modelled countries after 3-, 6-, and 12-month disruptions,respectively, compared to undisrupted screening and CRC mortality increased by 0.2-0.5 %, 0.4-1.0 %, and 0.8-2.0 % over2020-2050 among individuals aged 50 years and older compared to undisrupted screening. A 6-month disruption withoutcatch-up resulted in an estimated 3,552, 2,844 and 803-1,803 additional CRC diagnoses and 1,961, 1,319, and 678-881 additional CRC-related deaths in Australia, Canada and the Netherlands, respectively. A post-disruption reduction inparticipation increased CRC diagnoses by 0.2-0.9 % and CRC-related deaths by 0.5-1.6 % compared to undisruptedscreening. Providing catch-up screening minimized this impact to 0.0-0.2 %. Conclusions Although the relative impact of the modelled CRC screening disruptions due to the COVID-19 pandemicappears modest, given a high burden of CRC, there is a substantial impact on CRC diagnoses and deaths across allcountries considered. It is crucial that, if disrupted, screening programs ensure participation rates return to previouslyobserved rates and provide catch-up screening wherever possible, as the impact of any disruption could be considerablylarger otherwise.

Background The Australian National Bowel Cancer Screening Program (NBCSP) provides biennial immunochemical faecal occult blood test (iFOBT) screening for people aged 50–74 years. Previous work has quantified the number of colorectal cancer (CRC) deaths prevented by the NBCSP and has shown that it is cost-effective. With a 40% screening participation rate, the NBCSP is currently underutilised and could be improved by increasing program participation, but the maximum appropriate level of spending on effective interventions to increase adherence has not yet been quantified. Objectives To estimate (i) reductions in CRC cases and deaths for 2020–2040 attributable to, and (ii) the threshold for cost-effective investment (TCEI) in, effective future interventions to improve participation in the NBCSP. Methods A comprehensive microsimulation model, Policy1-Bowel, was used to simulate CRC natural history and screening in Australia, considering currently reported NBCSP adherence rates, i.e. iFOBT participation (∼40%) and diagnostic colonoscopy assessment rates (∼70%). Australian residents aged 40–74 were modelled. We evaluated three scenarios: (1) diagnostic colonoscopy assessment increasing to 90%; (2) iFOBT screening participation increasing to 60% by 2020, 70% by 2030 with diagnostic assessment rates of 90%; and (3) iFOBT screening increasing to 90% by 2020 with diagnostic assessment rates of 90%. In each scenario, we estimated CRC incidence and mortality, colonoscopies, costs, and TCEI given indicative willingness-to-pay thresholds of AUD$10,000-$30,000/LYS. Results By 2040, age-standardised CRC incidence and mortality rates could be reduced from 46.2 and 13.5 per 100,000 persons, respectively, if current participation rates continued, to (1) 44.0 and 12.7, (2) 36.8 and 8.8, and (3) 31.9 and 6.5. In Scenario 2, 23,000 lives would be saved from 2020–2040 vs current participation rates. The estimated scenario-specific TCEI (Australian dollars or AUD$/year) to invest in interventions to increase participation, given a conservative willingness-to-pay threshold of AUD$10,000/LYS, was (1) AUD$14.9M, (2) AUD$72.0M, and (3) AUD$76.5M. Conclusion Significant investment in evidence-based interventions could be used to improve NBCSP adherence and help realise the program’s potential. Such interventions might include mass media campaigns to increase program participation, educational or awareness interventions for practitioners, and/or interventions resulting in improvements in referral pathways. Any set of interventions which achieves at least 70% iFOBT screening participation and a 90% diagnostic assessment rate while costing under AUD$72 million annually would be highly cost-effective (

We derive a simple Poisson structure in the space of Fourier modes for the vorticity formulation of the Euler equations on a three-dimensional periodic domain. This allows us to analyse the structure of the Euler equations using a Hamiltonian framework. The Poisson structure is valid on the divergence free subspace only, and we show that using a projection operator it can be extended to be valid in the full space. We then restrict the simple Poisson structure to the divergence-free subspace on which the dynamics of the Euler equations take place, reducing the size of the system of ODEs by a third. The projected and the restricted Poisson structures are shown to have the helicity as a Casimir invariant. We conclude by showing that periodic shear flows in three dimensions are equilibria that correspond to singular points of the projected Poisson structure, and hence that the usual approach to study their nonlinear stability through the Energy-Casimir method fails.

We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain $$[0,2\pi )\times [0,2\pi / \kappa )$$ for $$\kappa \in \mathbb {R}^+$$ , the Euler equations admit a family of stationary solutions given by the vorticity profiles $$\Omega ^*(\mathbf {x})= \Gamma \cos (p_1x_1+ \kappa p_2x_2)$$ . We show linear stability for such flows when $$p_2=0$$ and $$\kappa \ge |p_1|$$ (equivalently $$p_1=0$$ and $$\kappa {|p_2|}\le {1}$$ ). The classical result due to Arnold is that for $$p_1 = 1, p_2 = 0$$ and $$\kappa \ge 1$$ the stationary flow is nonlinearly stable via the energy-Casimir method. We show that for $$\kappa \ge |p_1| \ge 2, p_2 = 0$$ the flow is linearly stable, but one cannot expect a similar nonlinear stability result. Finally we prove nonlinear instability for all steady states satisfying $$p_1^2+\kappa ^2{p_2^2}>\frac{{3(\kappa ^2+1)}}{4(7-4\sqrt{3})}$$ . The modification and application of a structure-preserving Hamiltonian truncation is discussed for the anisotropic case $$\kappa \ne 1$$ . This leads to an explicit Lie-Poisson integrator for the approximate system, which is used to illustrate our analytical results.

This paper demonstrates the existence of twistless tori and the associated reconnection bifurcations and meandering curves in the planar circular restricted three-body problem. Near the Lagrangian equilibrium L 4 a twistless torus is created near the tripling bifurcation of the short period family. Decreasing the mass ratio leads to twistless bifurcations which are particularly prominent for rotation numbers 3 / 10 and 2 / 7 . This scenario is studied by numerically integrating the regularised Hamiltonian flow, and finding rotation numbers of invariant curves in a two-dimensional Poincare map. To corroborate the numerical results the Birkhoff normal form at L 4 is calculated to eighth order. Truncating at this order gives an integrable system, and the rotation numbers obtained from the Birkhoff normal form agree well with the numerical results. A global overview for the mass ratio μ ∈ ( μ 4 , μ 3 ) is presented by showing lines of constant energy and constant rotation number in action space.